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triggers MBBC.Deliver (s,m), that implies the (∆ b, ∆c)-Validity property. The MBBC-delivery of a message m from a process ps may occur either because ps was correct in round rb and executed MBBC.Broadcast (m)or since ps was faulty at some round rd 5f , given that n − 2f
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> (n + f )/2, and line 32 is executed preparing 〈READY , s, r b, m〉 message to P2P -send in round rb+3 . Finally, in round rb+3 , the same reasoning given for round rb+2 applies and n − f processes execute lines 39-41, given n − 2f > 2f and Remark 13, and thus they trigger Deliver with parameters s and m. At every round rj > r b+3 the 〈READY , s, r b, m〉 message is P2P -sent by all the correct processes not faulty in round rj−1 (that are at least n − f ). The if statement at line 40 guarantees that every process that was faulty in round rb+3 delivers message m from ps at the first round rk > r b+3 it is correct. Finally, in case (i) process ps was faulty and P2P -sent the SEND message with payload m in round rk r k and executes MBBC.Broadcast (m), then the claim still follows: the message m has been already MBBC-delivered (further details can be found in the Agreement property’s proof). No duplication : The second sub-condition of the if statement at line 40 guarantees that the entire if statement is verified only for the minimum rj among all the tuples 〈s, ∗, m 〉 (i.e. the MBBC-delivery is independent from the rb parameter). The first sub-condition inside the if statement at line 40 is verified only once among all the rounds a mobile agent does not control the process. More in detail, if the cured variable is False , the condition is verified only in round rb+3 for the tuple 〈s, r b, m 〉.
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Otherwise, the if statement in line 40 is verified in round rk > r b+3 when a mobile agent, arrived on the process in round rj ≤ rb+3 , leaves the process, that occurs only once on a process during the entire lifetime of the system given Remark 13. The condition rc > r b+3 in line 40 is not required but simplifies this proof. (∆ b = 2) -Integrity : For the sake of contradiction, let us assume that a pro-cess pi is correct in round rk and executes MBBC.Deliver (s,m), that process ps is correct in rounds rb and rb+1 (that is, ∆ b = 2), and that it does not execute MBBC.Broadcast (m) in round rb.Process pi MBBC-delivers m from ps either in round rk = rb+3 if pi is cor-rect, or at the first round rk > r b+3 when pi is correct. In the former case, more than 2 f processes sent message 〈READY , s, r b, m〉 in round rb+3 , therefore more than ( n + f )/2 processes sent message 〈ECHO , s, r b, m〉 in round rb+2 , that implies that at least ( n + f )/2 − f processes were correct in round rb+1 and received 〈SEND , s, r b, m〉 in round rb+1 from ps (lines 28-29). No procedure in PM BBC −RB allows a correct process ps to P2P-send 〈SEND , s, r b, m〉 messages except Broadcast (m). It follows that the latter scenario occurred and process pi was faulty in round rb+3 . As a matter of fact, correct process pi P2P-received more than 2 f 〈READY , s, r b, m〉 messages from distinct processes in round rk.For the same reasoning as in the former case, this implies that a correct
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pro-cess ps sent 〈SEND , s, r b, m〉 messages but no procedure except Broadcast (m)allows it. This leads to a contradiction and the claim follows. (∆ c = 1) -Agreement : We proved, in the Validity proof, that this property is satisfied in the case of a correct source. Faulty processes cannot collude to make one of the if statements at lines 31, 33, 36 and 39 verified for a message m never sent over the P2P links of a process ps. More in detail, the attacker cannot at-tempt to make any correct process MBBC-deliver a message m from ps without compromising ps. We prove that if ps is faulty and P2P -sends 〈SEND , s, r b, m〉 messages in round rb, then either all ∆ c-infinitely correct processes delivers m from ps or no ∆ c-infinitely correct processes delivers m from ps. For the sake of contradiction, let us assume that all ∆ c-infinitely often correct processes but some, p1, p 2, . . . , p i, MBBC-delivered a message m from ps. It follows that there is no round rj where more than 2 f correct processes concurrently P2P -send 〈READY , s, r b, m〉. This implies that the correct processes that delivered m are at most 2 f . According to the protocol, such processes receive a quorum of ECHO messages and at most f ABORT messages about m, to generate the re-19 quired READY messages. More in detail, they received ECHO messages from at least 2 f + 1 correct processes. At that point, the faulty processes decided which correct processes reached the quorum of ECHO messages. Nevertheless, each correct process that did not reach the quorum generated an ABORT message. It follows that at most f correct processes did not reach
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the quorum, whereas n − f − f processes were correct and generated the READY message, which was disseminated by at least n − 3f of them in the subsequent round. Given that n > 5f , at least 2 f + 1 correct processes concurrently disseminate a READY message and thus all correct processes in round rb+3 must MBBC-deliver it. This lead to a contradiction and the claim follows. Lemma 15. The Mobile Byzantine Broadcast Channel problem (MBBC) is solvable in 〈SYNC, S-MOB +, OFFA 〉 only if n > 5f .Proof. The claim follows by extending the results proven by Backes and Cachin and by Raynal . The former states that the BRB problem can be solved in a static distributed system where at most t processes may fail-stop, and at most f processes are Byzantine, if and only if n > 3f + 2 t. Similarly, Raynal proved that the BRB problem can be solved in a static distributed sys-tem, where tl processes may not send messages, and ts processes may send spurious messages (processes may exhibit both behaviors during the lifetime of the system), if and only if n > 2tl + ts.Both scenarios can be simulated by an attacker in our system: the mobile agents can continuously alternate between two disjoint sets P1 and P2 of f processes, namely it can turn faulty all processes in P1 in all rounds rj , j ∈ N,and all processes in P2 in all rounds rj+1 , sending spurious messages from process in P1 and no message from peers in P2. Therefore, all processes in P1 send spurious messages (behaving like f Byzantine faulty processes), and all the processes in P2 send no message (like f fail-stop faulty processes), and the claim follows. Theorem 16. The Mobile
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Byzantine Broadcast Channel problem (MBBC) is solvable in 〈SYNC, S-MOB +, OFFA 〉 with OFFA if and only if n > 5f .Proof. It follows from Lemmas 14 and 15. The following Corollary extends the optimality of PM BBC −RB to the case of slower agents. In other words, even if the mobile agents are slower we are not able to tolerate more agents solving MBBC. Corollary 17. The Mobile Byzantine Broadcast Channel problem (MBBC) is solvable in 〈SYNC, S-MOB +, OFFA 〉 if and only if n > 5f , for each ∆s ≥ 1 round. Furthermore, the actual value of ∆s can be unknown to the processes. Proof. In the S-MOB + model, ∆ s is expressed as a (strictly positive) number of rounds. The claim follow from the fact that whatever number of rounds is spec-ified by ∆ s, all the mobile agents can move in one of the three protocol phases when the SEND, ECHO, or READY messages are exchanged for a broadcast instance. 20 Furthermore, the actual value of ∆ s is irrelevant solving the MBBC problem in ( SYNC, S-MOB +, OFFA ): mobile agent are constrained to move only between two consecutive rounds and the PM BBC −RB protocol is correct assuming the minimum value for ∆ s in S-MOB + (that is, one round). Note that MBBC and MBBR specifications do not allow processes to be terminate , namely to eventually stop propagating messages through the P2P primitive. Intuitively, processes need to continuously relay the messages in order to enforce ∆ c-Totality/Agreement and thus allow every temporarily faulty process to eventually deliver a broadcast message. Furthermore, as argued in Section 5, processes are not able to infer if a specific process has delivered a message, and thus conclude if all processes delivered
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a message when correct. Additional assumptions enabling termination can be considered, such as an upper-bound on the time a process becomes correct when faulty. # 7 MBBC with multiple deliveries The impossibilities identified in Section 5 arise for the general specification we defined. In fact, alternative or weaker specifications could be implementable under weaker assumptions. More in detail, we proved that no protocol can solve the MBBC in 〈SYNC, S-MOB +, OBFA 〉. We therefore investigate the pos-sibility of a weaker primitive that can be realized when the stringent conditions identified in Theorem 16 are not satisfied. We start by considering the case where no local failure detector is available, that is, the case of ONFA . The following Theorem show that a weaker MBBC primitive, where the No duplication property is not satisfied, is realizable in 〈SYNC, S-MOB +, ONFA 〉. Theorem 18. A weaker Mobile Byzantine Broadcast Channel primitive, not guaranteeing the No duplication property, is realizable in 〈SYNC, S-MOB +, ONFA 〉 if ∆b = 2 rounds, ∆c = 1 round, and n > 6f .Proof. Let us consider the PM BBC −RB protocol defined in Algorithm 1. Let us ignore the lines that interacts with the local failure detector, namely 7, 8 and 40. Let us substitute all the occurrences of parameter f with ¯f = 2 f in Algorithm 1. The difference with respect the setting considered in Lemma 14 is that pro-cesses are not aware of being compromised. In particular, they may diffuse messages with P2P-links previously generated by mobile agents. As a matter of fact, the protocol is restored right after the mobile agent left the process. The proof follows from the same reasoning stated in Lemma 14 except for No duplication considering ¯f instead of f in Algorithm 1. The following theorem
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show that having a slightly better oracle about fail-ures, namely OBFA , permits to withstand more Byzantine agents, for the same weaker problem that does not guarantees no duplication. 21 Theorem 19. A weaker Mobile Byzantine Broadcast Channel primitive, not guaranteeing the No duplication property, is realizable in 〈SYNC, S-MOB +, OBFA 〉 if ∆b = 2 rounds, ∆c = 1 round, and n > 5f .Proof. The OBFA failure oracle enables a correct process just freed from a mobile agent to take corrective actions, specifically to discard all messages queued to be sent in the current round. As a matter of fact, the OBFA oracle does not allow a process to know whether it was correct in a defined period in the past, therefore the same technicality employed in PM BBC −RB and detailed in Lemma 14 in the No duplication part cannot be adopted. The claim follows combining the argumentation provided in Theorem 12 and Lemma 14. Abandoning the No duplication guarantee, the number of message delivered becomes unbounded: the following theorem shows that it is not possible to bound the number of duplicate messages that are delivered, even assuming an intermediate oracle, namely OBFA . Theorem 20. Given a constant ¯k ∈ N+, it is not possible to define a weaker Mobile Byzantine Broadcast Channel primitive, not guaranteeing the No du-plication property, in 〈SYNC, S-MOB +, OBFA 〉 where a message m MBBC-Broadcast by a process ps is MBBC-Delivered by a process pi at most ¯k time when correct. Proof. The proof follows by extending the argument provided in Theorem 12. In the defined local execution histories H′ > 1 and H′′ > 1 , it is not possible to define an MBBC primitive where both No duplication and Validity properties are satisfied for a message m
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MBBC-Broadcast by a process ps. As a matter of fact, if the No duplication has not to be satisfied, process pi can always deliver message m after the cured () event generated by OBFA .Let us extend the execution history H′′ > 1 . At round r∆1+∆ 2+1 process pi executes MBBC.Deliver( m). Subsequently, the pattern of H′′ > 1 repeats: pro-cess pi get faulty and subsequently correct. Process pi, again, is not able to know whether message m from ps has been previously MBBC-Delivered, thus it executes MBBC.Deliver( m) to satisfy the Validity property. It follows that process pi MBBC-Deliver message m from ps every time that a mobile agent moves away from pi with the described procedure. Therefore, if the a mobile agent arrives and frees process pi ¯k + 1 times after the MBBC-Broadcast, process pi MBBC-Deliver ¯k + 1 times message m from ps. Alterna-tively, if process pi does not MBBC-Deliver m from ps when it get correct, it may not satisfy the Validity property, and the claim follows. Corollary 21. Suppose a solution to a weaker Mobile Byzantine Broadcast Channel primitive, not guaranteeing the No duplication property, in 〈SYNC, S-MOB +, OBFA 〉. If a process pi gets faulty and correct k times after the MBBC-Broadcast of a message m from ps, then pi MBBC-Delivers m from ps at least k times. 22 Proof. It follows from the same argument provided for Theorem 20. Every time a process pi is freed by a mobile agent after a MBBC-Broadcast, the process has to decide whether to MBBC-Deliver or not a message m MBBC-Brodcast by a process ps. As a matter of fact, process pi does not known how many times it has been correct in the past, it is only aware that it has been freed
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by a mobile agent. It follows that if pi decide to not MBBC-Deliver once a message m from ps it may invalidates the Validity property and the claim follows. Theorem 22. Suppose a solution to a weaker Mobile Byzantine Broadcast Channel primitive, not guaranteeing the No duplication property, in 〈SYNC, S-MOB +, ONFA 〉. If a process ps MBBC-Broadcast a message m, then every process pi must MBBC-Deliver m from ps infinitely often. Proof. A correct process pi at round rk is not aware of its failure state at all round rj , j ∈ N, j k and the claim follows. # 8 Conclusion We provided a specification for the Byzantine Reliable Broadcast and Byzantine Broadcast Channel problems in distributed systems affected by mobile Byzan-tine faults. We identified some impossibilities; in particular, we showed that both speed constraints on the mobile agents and timing assumptions on the system evolution are required to solve the problems under investigation, and we proved that the Byzantine Reliable Broadcast cannot be solved even in one of the most constrained mobile Byzantine failure models presented so far. The Byzan-tine Broadcast Channel problem proved to be solvable, assuming a stronger local failure detector than the ones previously considered in the literature. Lastly, we investigated a weaker Byzantine Broadcast Channel primitive, not guaranteeing the No duplication property, in settings equivalent to the ones assumed in re-lated works. Our results characterise the solvability of a fundamental problem in a general dynamic process failure model, and open the path for research on addi-tional important tasks. In particular, to understand the gap that exists between
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the theoretical model (assumed in this and in related work [4, 6, 17, 24, 31, 27]) and the practical world, investigating the feasibility of the oracles and defining solutions that are as practical as possible. Furthermore, it may be interesting to relax the assumptions of instantaneous fault detection and recovery (of the protocol), to investigate whether the assumption of digitally signed messages has an impact on the solvability of the considered problems, and to analyse the Mobile Byzantine Channel problem assuming the S-MOB agent mobility model (which we have left open for analysis and we conjecture its solvability). 23 Appendix A The Byzantine Reliable Broadcast and Channel Problems Specifica-tion [12, 14] The Byzantine Reliable Broadcast and the Byzantine Broadcast Channel prob-lems aim at specifying a communication primitive, respectively BRB and BBC , exposing two operations, BRB/BBC-broadcast( m) and BRB/BBC-deliver( s, m ), where m is a message and s is a process identifier. The BRB primitive enables all correct processes of a distributed system to agree on a single message diffused by a (potentially faulty) particular process, the source. The BBC primitive extends BRB allowing all processes to diffuse an arbitrary number of messages so that all correct processes eventually deliver the same set of messages. We say that a process pi “BRB/BBC-broadcasts a message m” when it invokes BRB/BBC-broadcast( m), and pi “BRB/BBC-delivers a message m from ps” when it manage the BRB/BBC-deliver( s, m ) event. We remark that both BRB and BBC primitives assume a static process failure model where every process is permanently correct or faulty. ## A.1 Byzantine Reliable Broadcast (BRB) The BRB communication primitive guarantees the following properties: • Validity : If a correct process ps BRB-broadcasts a message m, then every correct process eventually BRB-delivers m from ps. • No duplication : Every
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correct process BRB-delivers at most one message from ps. • Integrity : If some correct process BRB-delivers a message m from ps and process ps is correct, then m was previously BRB-broadcast by ps. • Consistency : If some correct process BRB-delivers a message m from ps and another correct process BRB-delivers a message m′ from ps, then m = m′. • Totality : If some message is BRB-delivered by any correct process, every correct process eventually BRB-delivers a message. ## A.2 Byzantine Broadcast Channel (BBC) The BBC communication primitive guarantees the following properties: • Validity : If a correct process ps BBC-broadcasts a message m, then every correct process eventually BBB-delivers m from ps. • No duplication : No correct process BBC-delivers a message m from ps more than once. 24 • Integrity : If some correct process BBC-delivers a message m from ps and process ps is correct, then m was previously BBC-broadcast by ps. • Agreement : If some correct process BBC-delivers a message m from ps then every correct process eventually delivers message m from ps. # Appendix B PM BBC −RB execution examples We detail in this Section several execution examples for the PM BBC −RB protocol defined in Section 6. Given what claimed in Theorem 16, we assume that the correctness conditions for our protocol, i.e. a 〈SYNC, S-MOB +, OFFA 〉 system and n > 5f , are satisfied in all of the provided examples. We detail one example where the source is correct and two in which the source is faulty. SEND(1,1,m) > r2 > p1 > p2 > p3 > p4 > p5 > p6 > ECHO(1,1,m) > ECHO(1,1,m) > ECHO(1,1,m) > ECHO(1,1,m) > ECHO(1,1,m) > READY(1,1,m) > READY(1,1,m) > READY(1,1,m) > READY(1,1,m) > READY(1,1,m) > READY(1,1,m) > READY(1,1,m) > READY(1,1,m)
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> READY(1,1,m) > READY(1,1,m) ✓m ✓m ✓m ✓m ✓m > READY(1,1,m) ✓m > READY(1,1,m) > READY(1,1,m) > READY(1,1,m) > READY(1,1,m) > r3r4r5r6 > r1 Figure 2: An execution of PM BBC −RB with a correct source and f = 1. In the execution example in Figure 2, the correct source p1 starts the MBBC-Broadcast preparing the related SEND message in round r1, that is P2P -sent to all processes in round r2 (∆ b = 2). Process p2 is faulty in round r1, then the mobile agent moves to process p6 in round r2. All processes but f are correct in round r2, thus they receive the SEND message from p1 and generate the related ECHO message. Such message is then P2P -sent to all peers by at least n − 2f processes during the send phase in round r3 (at most f processes could have been faulty in round r2, p6 in our example, and at most f processes could become faulty in round r3, p1 in our example where the mobile agent moves in 25 SEND(1,1,m) r2 p1 p2 p3 p4 p5 p6 ECHO(1,1,m) ECHO(1,1,m) ECHO(1,1,m) ECHO(1,1,m) READY(1,1,m) READY(1,1,m) READY(1,1,m) ABORT(1,1,m) r3 r4 r5 r6 r1 ABORT(1,1,m) READY(1,1,m) ✓m READY(1,1,m) ✓m READY(1,1,m) ✓m READY(1,1,m) ✓m READY(1,1,m) ✓m READY(1,1,m) ✓m READY(1,1,m) ✓m READY(1,1,m) ✓m READY(1,1,m) ✓m READY(1,1,m) ✓mFigure 3: An execution of PM BBC −RB with a faulty source, f = 1 and all infinitely often correct processes delivering. SEND(1,1,m) r2 p1 p2 p3 p4 p5 p6 ECHO(1,1,m) ECHO(1,1,m) ECHO(1,1,m) ECHO(1,1,m) READY(1,1,m) READY(1,1,m) ABORT(1,1,m) ABORT(1,1,m) r3 r4 r5 r6 r1 ABORT(1,1,m) Figure 4: An execution of PM BBC −RB with a faulty source, f = 1 and no infinitely often correct process delivering. 26 round r3). It follows that n − f processes reach the quorum of ECHO messages
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generating the related READY message. Again, at least n − 2f processes are correct in round r4, P2P -send the READY message and deliver the associated payload from p1, m, during the compute phase of the same round. The processes that were faulty in round r4, p2 in our example, deliver the message at the first round rk > r 4 they get correct, because all processes that are correct in a round rj > r 4 diffuse the associated READY message. The only MBBC property that mobile agents may attempt to invalidate in a execution of PM BBC −RB is the Agreement property: the No duplication is guaranteed by the if statement at line 40 in Algorithm 1 and both Validity and Integrity consider a correct source. Any source must P2P-send a well-formed SEND message (i.e., with valid source id and round label) to make a correct process proceed in the protocol to deliver a payload m. If the SEND message is P2P-sent to all correct processes, then all ∆ c-infinitely often correct processes will eventually deliver m, as shown in the previous execution, satisfying the MBBC specification. It follows that a Byzantine source must not P2P-send the SEND message to some processes. This behavior has two possible outcomes in our protocol: either all correct processes MBBC-deliver the diffused message or no correct process does it. Let us assume that the mobile agent commands p1 to P2P-send the SEND message to b(n − f )/2c − f processes, in order to control which ones will proceed in the PM BBC −RB protocol generating the READY message in round r4.In the execution depicted in Figure 3, process p1 is a faulty source that attempts to prevent the Agreement property of MBBC from being satisfied. Specifically, it P2P-sends the ECHO message
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only to part of the processes, process p2, p3,and p4, that reach the quorum required to generate the READY message. In this case, processes p5 and p6 generate the ABORT message but only f of them, namely p5, P2P-send it, thus blocking no correct process from proceeding in the MBBC-delivery of m from p1. Nonetheless, in this case more than 2 f processes are correct and P2P-send the READY message in round r4. It follows that all ∆c-infinitely often correct processes eventually deliver the associated payload m.Differently from the previous example, in the execution in Figure 4 process p1 sends the ECHO message to processes p2 and p3. It follows that all other correct processes, p4, p5, and p6, generate the ABORT message. At most f of them, process p6 in the example, can be blocked from P2P-sending the ABORT message. It follows that more than f processes diffuse to all correct ones the ABORT message and thus no process delivers the associated payload m. It follows that the specification is not violated in such execution. 27 Appendix C Additional details on PM BBC −RB # (Algorithm 1) We provide in this Appendix an additional detailed description of the PM BBC −RB protocol and its variables defined in Algorithm 1 for the sake of completeness. • The Init procedure initializes all the data structures and variables em-ployed by the protocol. More in detail, it defines: 1. The To send set variable to collect the messages (of any type) to P2P-send during the send phase of a round; 2. The Sends set to store the SEND messages received in a round; 3. The cured boolean variable to keep track of the occurrence of the OFFA .cured event; 4. The rc integer variable to store the current round index; 5. The Echos
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, Readys , and Aborts maps to collect, for every tuple 〈s, m, r 〉 associated with single MBBC-instance, the identifier of the processes that P2P-send the ECHO , READY , and ABORT for such tuple respectively in the current round; 6. The RC map that associates, for every process, the value of the round index that it P2P-sends in the current round. • The Broadcast procedure implements the Broadcast operation of MBBC by enqueueing the SEND message to P2P-send in set Sends . • PM BBC −RB is partitioned in three parts accordingly with the three phases assumed in the system model. • During the send phase of a round, all the messages that have been en-queued to P2P-send in the previous round, stored in To send , are dis-carded if the failure detector generated the Cured event in the current round, they are P2P-send to all processes otherwise. • The receive phase of a round starts by wiping all maps data structures. The aim is to limit the capability of mobile agents to P2P-send spurious information only from f processes in every round. Subsequently, all pro-tocol’s messages that have been P2P-received in the current round, SEND , ECHO , READY , and ABORT , are partitioned in the dedicated data struc-tures. The same occurs also for the messages exchanged to implement the fault-tolerant round counter: the P2P-received values are collected in the dedicated data structure. • The compute phase analyzes all information received during the receive phase and proceeds in the computation, MBBC-delivering messages and computing the protocol’s messages to P2P-send in the subsequent round. 28 It starts by wiping the data structure that collects the message to subse-quently P2P-send and by updating the round index by majority (the rc value may have been previously altered by an
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agent). Subsequently, if valid SEND message is received, then the related ECHO message is computed and enqueued to be P2P-send. For all the ECHO messages received, if a process has received the one associated with a specific MBBC instance from a suf-ficient number of distinct processes (a quorum), then the READY message is computed and enqueued, if such a number is not sufficient but includes at least a currently correct process, then the ABORT message is generated. If it is sure that the ABORT message associated with a MBBC instance has been sent by at least a correct process, then the received READY messages associated with the same instance are discarded in order to preserve the Agreement property. If a sufficient number of READY messages associated with a MBBC instance have been received and specific conditions are met, then the message is delivered. These conditions are met at most once for every process, namely three rounds after the MBBC-Broadcast beginning or at the first subsequent round when a process get correct, for the mini-mum round label (making it irrelevant to the primitive). Furthermore, if a sufficient amount of READY messages is received, then the same message is enqueued to P2P-send, in order to guarantee that processes that are faulty three rounds after the MBBC-broadcast will MBBC-deliver the as-sociated payload when correct. Finally, the round index is increased and its value is enqueued to P2P-send. # References Ittai Abraham, Ling Ren, and Zhuolun Xiang. Good-case and bad-case la-tency of unauthenticated byzantine broadcast: A complete categorization. In Quentin Bramas, Vincent Gramoli, and Alessia Milani, editors, 25th International Conference on Principles of Distributed Systems, OPODIS 2021, December 13-15, 2021, Strasbourg, France , volume 217 of LIPIcs ,pages 5:1–5:20. Schloss Dagstuhl - Leibniz-Zentrum f¨ ur Informatik, 2021. doi:10.4230/LIPIcs.OPODIS.2021.5 . Nicolas Alhaddad, Sourav Das,
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Title: URL Source: Markdown Content: # Byzantine Reliable Broadcast with O(nL + kn + n2 log n) # Communication ## Sisi Duan 1 and Haibin Zhang 21Tsinghua University, duansisi@tsinghua.edu.cn > 2 ## Beijing Institute of Technology, haibin@bit.edu.cn Abstract Byzantine reliable broadcast (BRB) is one of the most fundamental primitives in fault-tolerant distributed computing. It is well-known that the best BRB protocol one can hope for has O(nL + n2) communication. It is unclear if this bound is achievable. This paper provides a novel BRB protocol—BRB1, which achieves O(nL + kn + n2 log n)communication, where n, L, and k are the number of replicas, the message length, and the security parameter, respectively. Our protocol is efficient, because the only building blocks we need are threshold signatures which have been used in various Byzantine fault-tolerant (BFT) protocols (e.g., SBFT, HoneyBadgerBFT, HotStuff). Our protocol is the first asynchronous BRB protocol that breaks the known O(nL + kn 2) bound. # 1 Introduction Byzantine reliable broadcast (BRB) is a fundamental tool in fault-tolerant distributed comput-ing, ensuring that all replicas in a distributed system deliver the same message from a designated sender (even if some replicas, including the sender, are Byzantine). First, BRB itself is powerful enough to build killer applications such as online payment systems [16, 26]. More importantly, BRB is a popular building block for high-level protocols, such as Byzantine fault-tolerant state machine replication (BFT) protocols (e.g., HoneyBadgerBFT , BEAT , Dumbo , DAG-Rider , PACE , WaterBear , MiB ), and multi-party computation . This paper introduces a novel BRB protocol reducing the communication complexity of BRB protocols, thereby improving upon all the above-mentioned protocols immediately. A brief history of BRB. Bracha’s broadcast [11, 12] is the first BRB protocol proposed and is one of the most classic protocols
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in fault-tolerant distributed computing. It has 3 steps, O(n2)messages, and achieves O(nL 2) communication. Bracha’s broadcast is information-theoretically secure (assuming authenticated channels only). Note the message complexity of O(n2) for Bracha’s broadcast is optimal, and one cannot expect to achieve anything better. Hence, the epicenter of BRB research is to reduce the communication complexity of BRB protocols. Assuming hash functions, Cachin, Kursawe, Petzold, and Shoup describe a BRB protocol aiming to improve Bracha’s BRB in an optimistic manner: if faulty replicas are not actively inter-fering with the protocol execution, the communication complexity of the protocol is O(nL + kn 2), 1where k is the size of the hash function output; in the worst case, it has O(n2(L+k)) communication (no better than Bracha’s broadcast). Still assuming hash functions, Cachin and Tessaro (CT) design an erasure-coded BRB protocol that achieves O(nL + kn 2 log n) communication. CT BRB is highly efficient, as it assumes hash functions and has been widely used in many practical asynchronous BFT protocols using BRB (e.g., HoneyBadgerBFT , BEAT , Dumbo ). Assuming trusted setup, Nayak, Ren, Shi, Vaidya, and Xiang (NRSVX) propose an erasure-coded BRB protocol achieving a communication cost of O(Ln + kn 2) . Recently, Das, Xiang, and Ren (DXR) propose a new BRB protocol achieving the same communication, assuming hash functions only . DXR BRB explores the idea of online error correction (OEC) due to Ben-Or, Canetti, and Goldreich . Later, Alhaddad, Duan, Varia, and Zhang (ADVZ) have shown another BRB protocol using erasure coding proof system . ADVZ BRB achieves the same communication as DXR BRB but assumes trusted setup. The benefit of this ADVZ BRB, however, is that it uses fewer steps than NRSVX but slightly less concrete communication than DXR BRB. What we can hope for BRB? BRB requires
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validity and agreement. Validity means that if a correct replica p broadcasts a message M of length L, then all replicas eventually delivers M .Agreements means that if some correct replica delivers a message M , then every correct replica eventually delivers M . Validity implies the need of transmitting at least nL bits, as all replicas need to possess M . Agreement implies the need of broadcast (i.e., n2 messages and at least n2 bits needed), as a linear communication would not be possible to ensure agreement in the presence of failures in a constant number of rounds. Therefore, the best communication complexity can hope for a BRB protocol is O(nL + n2). However, the above “best” bound is difficult, if not impossible, to achieve, as one would typically need to cryptography (e.g., hashes, commitments, signatures) or more advanced cryptographic building blocks to: 1) compress input, 2) authenticate data and ensure data transferability, or 3) ensure data consistency (if just sending the erasure-coded fragments instead of the input data itself). Doing so would seem to need agreeing on the underlying cryptographic tool, which at least incurs kn 2 communication, where k is the length of the underlying cryptographic primitive. So intuitively, what one could reasonably hope for a practical BRB protocol achieves O(nL + kn 2)communication. Indeed, attaining O(nL + kn 2) communication has already proven tricky: only very recently (after 2020), NRSVX BRB , DXR BRB , and ADVZ BRB have achieved the goal, via different techniques (see Table 1). This paper demonstrates a somewhat surprising result: we can construct BRB protocols with lower communication. In particular, our BRB protocol eliminates the cubic term which may easily dominate the communication with a large n or a small L. ## 1.1 Our Contributions This paper provides a novel
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BRB protocol that achieves O(nL + kn + n2 log n) communication, where n, L, and k are the number of replicas, the message length, and the security parameter, respectively. BRB1 breaks the symmetry in designing BRB protocols. Our protocol uses threshold signatures [9, 10] and authenticated channels. We begin with a half-baked construction satisfying validity but not agreement. Then we present BRB1 that tackles the problem retroactively in the sense that we simply allow the agreement problem to happen in the middle but fix the problem before the end of the protocol. 2protocol setup asymptotic communication Bracha’s BRB none O(n2L)CT BRB none O(nL + kn 2 log n)NRSVX BRB trusted O(Ln + kn 2)DXR BRB none O(nL + kn 2)ADVZ BRB trusted O(nL + kn 2)BRB1 (this work) trusted O(nL + kn + n2 log n) Table 1: Comparison of BRB protocols. Trusted setup means that a trusted party is responsible for generating public parameters for the system, say, the public key for threshold signatures. PKI means public-key infrastructure. L is the input length and k is the security parameter. Note our BRB protocol has better communication complexity than DXR and ADVZ BRB protocols, as k + n ≪ kn (for a given k, e.g., 128). Our protocol has strictly lower communication than existing BRB protocols that have O(nL + kn 2) communication, as long as one would not be “crazy” to use an exponentially large system with n = O(2 k). In practice, for major BRB applications, such as online payment systems [16, 26] and asynchronous BFT systems [38, 19, 27, 32, 20], the message length is much longer than the security parameter (e.g., 128 bit), as these applications use message batching extensively for high system performance. (Meanwhile, it is possible that our
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BRB protocol is indeed optimal, as it is unclear if the O(nL + n2) bound is achievable.) It is also trivial to replace threshold signatures using aggregate signatures, so the resulting protocol maintains the same complexity while working in the PKI model. Discussion. This paper provides a new BRB protocol, BRB1 that uses the trusted setup model, relying on threshold signatures. In applications where trusted setup is permitted (for instance, all known asynchronous BFT protocols implemented using BRB), one can directly use our BRB protocol. In applications where trusted setup is not allowed, one may run a distributed key gener-ation (DKG) algorithm to generate the needed public parameters: various DKG algorithms have been proposed in the synchronous setting [5, 23, 28], the partially synchronous setting , and the asynchronous setting (e.g., [17, 33, 1]). Lastly, while our BRB protocol has better communication than DXR BRB, DXR BRB relies on hash functions only and does not assume trusted setup or PKI. So all those protocols are interesting and useful in their own regard. One possible reaction to this work is to say: forget it, the improvement is small . Such a viewpoint underestimates the importance of the work. On the one hand, our protocol removes the cube term (i.e., kn 2) which is easily the bottleneck of the protocol when n is reasonably large or L is small. On the other hand, from the theoretical perspective, even just a “small” improvement would prove significant for BRB, because BRB is one of the most fundamental primitives in distributed computing: before this work, we do not even know if the bound of O(Ln + kn 2) is the best we can hope for among BRB protocols using cryptography. Versions of the paper. The early version of the paper contains a different BRB protocol
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that has more steps than BRB1. As there is no reason to favor that one, so we remove it. 32 System Model and Problem Statement A Byzantine reliable broadcast (BRB) protocol consists of n replicas, where f out of them replicas may fail arbitrarily (Byzantine failures). We assume the existence of point-to-point authenticated channels between each pair of replicas. We consider asynchronous systems making no timing assumptions on message processing or transmission delays. This paper considers adaptive corruption, where the adversary can choose its set of corrupted replicas at any moment during the execution of the protocol, based on the information it accumu-lated thus far. Note that the static corruption is weaker, as the adversary is restricted to choose its set of corrupted replicas at the start of the protocol and cannot change this set later on. All protocols we consider assume that f is a constant fraction of n with f ≤ ⌊ n−13 ⌋, which is optimal. A (Byzantine) quorum is a set of ⌈ n+f +1 2 ⌉ replicas. Without loss of generality, this paper may assume n = 3 f + 1 and a quorum size of 2 f + 1. Byzantine reliable broadcast (BRB). We review the definition of Byzantine reliable broadcast (BRB). A BRB protocol is specified by two protocols r-broadcast and r-deliver such that the following properties hold: • Validity : If a correct replica p r-broadcasts a message M , then p eventually r-delivers M . • Agreement : If some correct replica r-delivers a message M , then every correct replica eventually r-delivers M . • Integrity : For any message M , every correct replica r-delivers M at most once. Moreover, if a replica r-delivers a message M with sender ps, then M was previously broadcast by replica ps. Identifying
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protocol instances. We assume each protocol instance is associated with a unique tag id . For each step of the protocol, we provide a unique step name (e.g., cbc-send , disperse )which will help readers better distinguish different steps. # 3 Building Blocks Reed-Solomon code. An ( m, n ) Reed-Solomon code consists of an encode algorithm and a decode algorithm. The encode algorithm takes as input m, n, and a data block M with m data fragments and uses those as m coefficients to produce a polynomial P of degree m − 1. Then the encode algorithm outputs n points ( coded fragments ) by evaluating P on n different points. The decode algorithm takes as input m, a set T of coded fragments, and the number of incorrect coded fragments r, and outputs a degree m − 1 polynomial (coefficients as data fragments) by correcting up to r failures (incorrect fragments) in T . It is known that as long as |T | ≥ m + 2 r, decode can correct up to r failures in T and decode the original block [37, 44, 22]. Online error correcting (OEC) algorithm. Online error correcting algorithm due to Ben-Or, Canetti, and Goldreich allows one to decode efficiently from a growing set T that keeps receiving coded fragments, where up to f out of |T | coded fragments are incorrect. For our purpose, fixing an ( f + 1 , n ) Reed-Solomon code where n = 3 f + 1, let M be the original data block with m data fragments. There are at most n coded fragments, and up to f coded fragments may be replaced with arbitrary (incorrect) fragments. Suppose T be a set that keeps receiving these coded fragments, one after another. The OEC algorithm performs
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at most f +1 trials of the decode algorithm. In the r-th trial (0 ≤ r ≤ f ), the recipient waits until it receives 4fragments from 2 f + r + 1 replicas and then attempts to decode. In particular, the OEC algorithm has the first trial when |T | ≥ 2f + r + 1 for r = 0. If not successful, then it keeps waiting for new fragments and then runs the decode algorithm for 1 ≤ r ≤ f until decode for some r is successful and outputs the data fragments. (For Reed-Solomon codes, if the reconstructed polynomial agree with 2 f + 1 points in T , then decode outputs the coefficients of the reconstructed polynomial.) Note that the OEC algorithm must be successful when r = f , because the decode algorithm can correct f arbitrary failures among |T | = 3 f + 1 coded fragments. The the decode algorithm may well output before the trial for r = f . Asynchronous data dissemination. Das, Xiang, and Ren propose asynchronous data dissemination (ADD) which allow f + 1 correct replicas to disseminate a message to all correct replicas in an asynchronous network, where f is the upper bound on the number of faulty replicas in the system. The ADD construction introduced by Das, Xiang, and Ren is as follows: in the first step, all replicas holding M send coded fragments to all replicas; in the second step, upon receiving f + 1 matching fragments di, a replica pi fixes its fragment as di and broadcasts di. Then replicas wait to receive fragments and use OEC algorithm to decode the original block M . ADD is information-theoretical and does not use any cryptographic tools, and the communication cost of ADD is O(nL +
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n2 log n). (Reed-Solomon code has a field size of at least n, so each symbol has at least O(log n) bits. Each data symbol is of size O(max( L/n, log n)), and therefore all-to-all sending the symbols incurs O(n2 · max( L/n, log n)) = O(nL + n2 log n).) While this paper uses ADD, we did not use it in a black-box manner. So in some sense, readers do not need to understand ADD to understand our protocols. In fact, knowing OEC is good enough for our constructions. We do, however, use ADD as an abstraction to motivate our constructions. Signatures and threshold signatures. We use a conventional signature scheme consisting of three algorithms ( siggen , sigsign , sigverify ). siggen outputs a pair of public/secret keys ( pk, sk ). A signature signing algorithm sigsign takes as input a message M and a private key sk and outputs a signature σ. A signature verification algorithm sigverify takes as input pk , a message M , and a signature σ, and outputs a bit. We require the conventional unforgeability property for signatures. A ( t, n ) threshold signature scheme [9, 42] consists of the following algorithms ( tgen , tsign , shareverify , tcombine , tverfiy ). tgen outputs a system public key known to anyone and a vector of n private keys. A partial signature signing algorithm tsign takes as input a message M and a private key sk i and outputs a partial signature σi. A combining algorithm tcombine takes as input pk , a message M , and a set of t valid partial signatures, and outputs a signature σ. A signature verification algorithm tverify takes as input pk , a message M , and a signature σ, and outputs a bit. We
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require the conventional robustness and unforgeability properties for threshold signatures. We simply omit the public keys, private keys, and key generation algorithms when no ambiguity arises. We may leave the verification of partial signatures and threshold signatures implicit when describing algorithms. Consistent broadcast (CBC). We review the definition of consistent broadcast (CBC) [40, 14]. A CBC protocol is specified by c-broadcast and c-deliver such that the following properties hold: • Validity : If a correct replica p c-broadcasts a message M , then p eventually c-delivers M . • Consistency : If two correct replicas c-deliver two messages M and M ′, then M = M ′. • Integrity : For any message M , every correct replica c-delivers M at most once. Moreover, if the sender is correct, then M was previously c-broadcast by the sender. A verifiable CBC (VCBC) protocol is a CBC protocol with an additional verifiability 5CBC-SEND CBC-ECHO CBC-FINAL DISPERSE RECONSTRUCT CBC Figure 1: A half-baked idea. property: when a correct replica has c-delivered a message M , then it can produce a single protocol message P that may be sent to other parties such that any other correct party will immediately deliver P once receiving P . VCBC can be used as a building block for high-level protocols . Steps and phases. We use the standard notation of steps , where a step consists of receiving a message from some party, running a local computation (optional), and sending a message to some party. We also use the notation of phases, where a phase consists of a fixed number of steps. In our notation, a protocol has several phases, and each phase has several steps. Of course, it makes sense to directly count how many steps a protocol has. # 4 Technical Paths Review of
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DXR BRB. Das, Xiang, and Ren use OEC to build DXR BRB protocol with O(nL + kn 2) communication. 1 The idea is simple and efficient, following the three-step pattern of Bracha’s broadcast. In the first step, the sender broadcasts the whole message m instead of sending individual coded fragments. In the second step, replicas echo replicas different coded fragments and a hash of m denoted as h. In the third step, upon receiving 2 f + 1 matching echo messages, replicas send ready messages with coded fragments and h; upon receiving f + 1 ready messages with the same h, replicas wait for f + 1 matching echo messages with the same h and then send ready messages (the ”amplification” step). The replicas keep all ready messages with the same h in a set and run OEC algorithm until successfully reconstructing some data m′. The replica delivers m′ only if it matches h. Apparently, the second step and the third step involves all-to-all broadcast of hashes, incurring O(kn 2) communication. A half-baked idea: breaking the symmetry for BRB design. Our first idea is to break the symmetry in designing BRB protocols. Indeed, when designing efficient BRB protocols, one typically follows a symmetric design approach: in the first step, the sender sends some data (either the whole input message M or a coded fragment) to every replica; in the following steps, replicas all broadcast fragments and/or short cryptographic proofs to each other in order to achieve agreement. In our new design, we break BRB constructions into a linear communication phase and a broadcast phase. We use cryptography in the first linear communication phase, while the broadcast phase explicitly rules out cryptography. > 1Note that the authors also provide a 5-step BRB protocol which may be viewed as a less
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efficient variant of the DXB BRB. 6Our starting protocol works as follows. In the first linear communication phase, our goal is to disperse the input to ensure that f +1 correct replicas to have consistent data, a goal that consistent broadcast (CBC) [40, 14] or its information dispersal version may achieve; in the second broadcast phase, our idea is to “amplify” consistent data from f + 1 correct replicas to all replicas, a goal that asynchronous data dissemination (ADD) may achieve. Such a construction is depicted in Figure 1. We use CBC and ADD in a black-box manner. For the above construction, the first phase has O(nL + kn ) communication, while the second phase has O(nL + n2) communication. Adding them together, we have a construction with O(nL + nk + n2). Unfortunately, the construction only achieves validity but not agreement. Indeed, it is easy to show that some correct replicas r-deliver message M , while some other replicas do not r-deliver any message, violating agreement. As an example, a faulty sender may make only one correct replica deliver the message in the CBC phase and enter the second phase. All f faulty replicas collude and disseminate correct fragments to f + 1 correct replicas. Together with the fragment from the correct replica, each of the f + 1 correct replicas receive f + 1 matching fragments, share their fragments, complete ADD, and deliver the corresponding message. The rest f correct replicas, however, cannot deliver the message, since they fail to start ADD. Some trivial modifications of the above construction suffer from a similar problem. One such modification could be illustrated as follows: whether receiving a threshold signature from the sender to start ADD, replicas immediately broadcast fragments once receiving fragments. This approach does not work either, because
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it is still possible that some correct replicas r-deliver a message M ,while other correct replicas do not deliver anything. Below, we outline how we solve the agreement problem, by providing an approach to handling the issue retroactively . BRB1 (Figure 2). In BRB1, our idea is simply to let the agreement issue occur and then fix it retroactively. We add one more ready step after the ADD phase and ask replicas to r-deliver a message M only if it receives enough ready messages. The most interesting part is that an amplification step is now introduced, going back to the very first step of the broadcast phase ,instead of the beginning of the same step. To our knowledge, our novel amplification technique is in contrast to all other known amplification steps ever used in BRB and even fault-tolerant distributed computing. Strikingly, the ready step and the ”unconventional” amplification step are all we need for a secure BRB construction. # 5 BRB1 This section describes BRB1, a BRB protocol that has six steps. BRB1 uses a strategy that is different from BRB1. We show the workflow of BRB1 in Figure 2 and pseudocode in Algorithm 1. BRB1 consists of two phases: a linear CBC phase and a broadcast phase. CBC phase (Algorithm 1: line 4-15). This phase runs a standard CBC. In particular, the sender ps broadcasts an ( id, cbc-send , M ) message. Upon receiving an ( id, cbc-send , M ) message, each replica generates a partial signature σi and sends an ( id, cbc-rep , M, σ i) message to ps. If ps receives n − f partial signatures, it combines them into a threshold signature σ and broadcasts an (id, cbc-final , M, σ ) message to all replicas. Upon receiving an ( id, cbc-final ,
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M, σ ) message, each replica sets msg as M and proof 1 as σ and completes CBC. 7CBC-SEND CBC-ECHO CBC-FINAL READY DISPERSE RECONSTRUCT CBC amplification Figure 2: BRB1 workflow. Broadcast phase (Algorithm 1: line 16-33). The broadcast phase consists of three steps: disperse , reconstruct , and ready . The first two steps are similar to those in . In particular, upon the completion of CBC, each replica pi encodes its msg into coded fragments d. For each replica pj , pi sends it an ( id, disperse , d j ) message. Upon receiving f + 1 matching ( id, disperse , d ∗ > i )messages, pi fixes d∗ > i and broadcasts ( id, reconstruct , d ∗ > i ). Upon receiving at least n − f recon-struct messages, each replica starts to decode the message using OEC. This process may continue until OEC outputs a message M . A local parameter output is then set as M .But this is not the last step of the BRB1. When OEC outputs M , each replica broadcasts an ( id, ready ) message. Furthermore, if replica pi previously has not sent a disperse message, it disperses the coded fragments, i.e, pi encodes M and sends pj (for any j ∈ { 0, · · · n − 1}) an (id, disperse , d j ) message. Each replica waits for n − f (id, ready ) messages and then delivers message output (message output by OEC). Analysis. The crucial step for BRB1 to achieve agreement is the amplification step after message M is output by OEC. In particular, if the OEC outputs M and a replica has not previously sent a disperse message, the replica encodes M and sends the coded fragments via a disperse message
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to the replicas. If a replica r-delivers M , it has received n−f (id, ready ) messages and at least f +1 correct replicas have completed the OEC. These correct replicas will send their coded fragments via the disperse message. Accordingly, it is guaranteed that all correct replicas eventually decode M , broadcast the ready messages, and r-deliver M .The consistency property of CBC guarantees that no correct replicas will broadcast inconsistent coded fragments, as each replica only disperses the coded fragments upon the completion of CBC. An adversary cannot force any correct replicas to receive f + 1 matching but incorrect fragments in the disperse step. Therefore, OEC can correct the errors and ensure that all correct replicas r-deliver the same message M .Let us analyze the communication complexity of BRB1. First, the first linear CBC phase has O(Ln + kn ) communication. The disperse and reconstruct steps both have O(Ln + n2 log n)communication. The ready phase does not carry bulk data and has O(n2) communication only. Therefore, the communication complexity for is O(Ln + kn + n2 log n). ## 5.1 Proof of BRB1 Theorem 1. Assuming a secure threshold signature and authenticated channels, BRB1 satisfies validity, agreement, and integrity. 8Algorithm 1 BRB1 with identifier id and sender ps. Code shown for replica pi. > 1: Initialization > 2: (pk, sk ) ← tgen (1 k) {threshold signature key generation; pk is the public key and sk is a vector of n private keys } > 3: proof 1 ← ⊥ , msg ← ⊥ , output ← ⊥ , pset 1 ← ∅ , T ← ∅ {initialize the parameters } > 4: upon r-broadcast (M ) > 5: msg ← M > 6: broadcast ( id, cbc-send , M ) {cbc-send step } > 7:
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upon receiving ( id, cbc-send , M ) from ps do {cbc-rep step } > 8: msg ← M , σi ← tsign (id, M ) > 9: send ( id, cbc-rep , M, σ i) to ps > 10: upon receiving ( id, cbc-rep , M, σ j ) from pj and pi = ps do {cbc-final step } > 11: if shareverify (( id, M ), σ j ) and M = msg > 12: add σj to pset 1 > 13: if |pset 1| ≥ n − f > 14: σ ← tcombine (( id, M ), pset 1), broadcast ( id, cbc-final , M, σ ) > 15: upon receiving ( id, cbc-final , M, σ ) from ps do {disperse step } > 16: if tverify (( id, M ), σ ) and M = msg > 17: proof 1 ← σ, d ← encode (f + 1 , n, msg ) > 18: for j ∈ { 0, · · · n − 1} > 19: send ( id, disperse , d j ) to pj > 20: upon receiving f + 1 matching ( id, disperse , d ∗ > i ) do > 21: fix d∗ > i , broadcast ( id, reconstruct , d ∗ > i ) {reconstruct step } > 22: upon receiving ( id, reconstruct , d j ) from pj do > 23: add dj to T > 24: for 0 ≤ r ≤ f do > 25: wait until |T | ≥ 2f + r + 1 > 26: if decode (f + 1 , T, r ) = M {send ( ready ) and execute the amplification step } > 27: output ← M > 28: broadcast ( id, ready ) > 29: if (disperse
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) has not been sent > 30: d ← encode (f + 1 , n, M ) > 31: for j ∈ { 0, · · · n − 1}, send ( id, disperse , d j ) to pj > 32: upon receiving n − f (id, ready ) do {ready step } > 33: if output ̸ = ⊥, r-deliver output Proof. We first provide the following three lemmas. Lemma 2. If a correct replica sends a disperse message with fragments encoded from message M , at least one correct replica has completed CBC and received M from the sender. Proof. Each correct replica sends a disperse message with fragments encoded from M for two cases: 1) It completes CBC and receives M from the sender; 2) It completes the reconstruct step and obtains M . We show that in both cases, at least one correct replica has completed CBC and receives M from the sender. For the first case, trivial. For the second case, if a correct replica completes the reconstruct step, it must have received at least n − f reconstruct messages, among which at least f + 1 are sent by correct replicas. For any of the correct replicas, it must 9have also received f + 1 matching disperse messages. As there are at most f faulty replicas, there must exist at least one correct replica that sends the disperse message after it completes CBC and receives M . Lemma 3. If a correct replica pi sends an ( id, reconstruct , d ∗ > i ) message and a correct replica pj sends an ( id, reconstruct , d ∗ > j ) message, d∗ > i and d∗ > j are both encoded from the same message M .Proof. Let d∗ > i
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be a coded fragment encoded from message M . If a correct replica pi sends an (id, reconstruct , d ∗ > i ) message, it must have received f + 1 matching ( id, disperse , d ∗ > i ) messages, among which at least one is sent by a correct replica. Among them, at least one correct replica has sent a disperse message. According to Lemma 2, at least one correct replica completes CBC and receives message M from the sender. Let d∗ > j be a coded fragment encoded from message fM . If pj sends an ( id, reconstruct , d ∗ > j )message, according to Lemma 2, at least one correct replica completes CBC and receives message fM . This violates the consistency property of CBC. Thus, it holds M = fM . Lemma 4. If a correct replica r-delivers M , the sender ps has previously broadcast M and at least one correct replica has received a valid threshold signature proof 1 = σ.Proof. If a correct replica pi r-delivers M , it receives n − f (id, ready ) messages. Furthermore, in the reconstruct step, the OEC outputs a decoded message M . Accordingly, pi must have received at least 2 f + 1 ( id, reconstruct , d j ) messages, among which at least f + 1 are sent by correct replicas. According to Lemma 3, the f + 1 correct replicas only send coded fragments encoded from the same message M ′. Therefore, the reconstructed f -degree polynomial for M must agree with f + 1 fragments from correct replicas. It must hold that M = M ′.If pi r-delivers M , it has received at least 2 f +1 ready messages and also 2 f +1 reconstruct
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messages, among which at least f + 1 are sent by correct replicas. According to Lemma 2, at least one correct replica has completed CBC and received a valid threshold signature proof 1 for M , and meanwhile the sender ps has sent M .In the following, we prove that BRB1 satisfies validity, agreement, and integrity. Validity. If a correct replica ps r-broadcasts M , all correct replicas complete CBC, according to the validity property of CBC. Therefore, all correct replicas will send the disperse messages for the same M , receive f + 1 matching disperse messages, and broadcast the reconstruct messages. No correct replica can receive f + 1 matching ( id, disperse , d i) for M ′̸ = M . Each correct replica will then send a ( id, reconstruct , d i) messages such that di is encoded from M . Thus, all correct replicas will receive 2 f + 1 reconstruct messages from all correct replicas, output some value and then send the ( id, ready ) messages. All correct replicas, including the sender, will then receive n − f (id, ready ) messages and r-deliver some message. Furthermore, as shown in Lemma 4, if any correct replica r-delivers M ′̸ = M , ps has previously sent M ′, contradicting the fact that ps is a correct replica and r-broadcasts M . Therefore, all correct replicas will r-deliver the original message M . Agreement. The proof of agreement consists of two parts: 1) if a correct replica pi r-delivers M and a correct replica pj r-delivers M ′, then M = M ′; 2) if a correct replica pi r-delivers M , any correct replica will eventually r-deliver some message. 10 We prove the first part. If a correct replica pi r-delivers M
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, according to Lemma 4, at least one correct replica has completed CBC and possessed a valid threshold signature for M . Furthermore, If pj r-delivers M ′, at least one correct replica has completed CBC and possessed a valid threshold signature for M ′. This violates the consistency property of CBC. Thus, M = M ′.Then we prove the second part. If a correct replica pi r-delivers M , it has received n − f ready messages, among which at least f + 1 are sent by correct replicas. The f + 1 correct replicas must all output M by OEC, as proved in the first part. Furthermore, for each of the f + 1 correct replicas, if it has not previously sent a disperse message, it will encode message M and broadcast the disperse messages according to our protocol. Therefore, each correct replica eventually receives at least f + 1 matching disperse messages. Eventually, all correct replicas will receive at least n − f reconstruct messages. According to Lemma 3, each correct replica sends a fragment ( id, reconstruct , d i) such that di is encoded from the same message M . Therefore, each correct replica eventually outputs some message. Finally, each correct replica will eventually send an ( id, ready ) message, receive n − f (id, ready ) messages, and r-deliver the value. Integrity. According to the protocol, a replica does not participate in the protocol after it r-delivers . Hence, each correct replica r-delivers at most once. Furthermore, as proved in Lemma 4, if a replica r-delivers a message M with sender ps, M was previously broadcast by ps. # 6 Related Work AVID vs. BRB. Asynchronous verifiable information dispersal (AVID), introduced by Cachin and Tessaro , is a primitive closely related to BRB.
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The original AVID constructions are both AVID and BRB protocols. The difference between these two distributed systems primitives is that BRB requires that replicas store a full copy of message, but AVID may only ask replicas to store erasure-coded fragments in a consistent manner. Erasure codes and error correcting codes in fault-tolerant distributed systems. Erasure codes and error correcting codes are fundamental tools in fault-tolerant distributed computing pro-tocols. Besides BRB, they have been used in various other primitives with Byzantine failures, such as asynchronous verifiable information dispersal (AVID) [15, 30], multi-valued validated Byzantine agreement (MVBA) , multi-valued Byzantine agreement , read/write storage [18, 4, 29], and BFT storage . Definitions and constructions for reliable broadcast (in the crash failure model). The properties of reliable broadcast have been (somewhat informally) captured in SIFT . Schneider, Gries, and Schlichting formally define reliable broadcast as well as implement a protocol in the crash failure model . Crash fault-tolerant reliable broadcast becomes widely known through the ISIS system due to Birman and Joseph . Note that the definition of BRB is identical to that in the crash failure model: the only difference lies in the failure assumption, where BRB considers Byzantine failures, and crash fault-tolerant reliable broadcast considers crash failures. Byzantine consistent broadcast (CBC). Byzantine consistent broadcast may be viewed as BRB without the totality property. The notion has been implicitly discussed in [43, 12] and more formally by Reiter and Cachin, Kursawe, Petzold, and Shoup (CKPS) . The CBC construction is due to Cachin, Kursawe, Petzold, and Shoup . BRB extensions. BRB has also been explored in some extended settings (e.g., probabilistic 11 BRB , BRB with dynamic membership ). Good-case latency. Abraham, Nayak, Ren, and Xiang provide a complete categorization for Byzantine broadcast and BRB in terms of the good-case latency
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which measures the time one takes for all correct replicas to commit when the broadcaster is correct . # 7 Conclusion We propose a novel BRB protocol with O(nL + kn + n2 log n) communication, where n, L, and k are the number of replicas, the message length, and the security parameter, respectively. Our protocol is the first asynchronous BRB protocol that breaks the known O(nL + kn 2) bound. # Acknowledgement We are indebted to Nicolas Alhaddad and Mayank Varia for the helpful discussion and insightful comments that lead to the paper. We thank the PODC reviewers for their insightful comments. Many thanks to Zhuolun Xiang for kindly clarifying the fact that the communication of ADD, strictly speaking, is O(nL + n2 log n) instead of O(nL + n2). # References I. Abraham, P. Jovanovic, M. Maller, S. Meiklejohn, G. Stern, and A. Tomescu. Reaching consensus for asynchronous distributed key generation. In PODC ’21: ACM Symposium on Principles of Distributed Computing, Virtual Event, Italy, July 26-30, 2021 , pages 363–373. ACM, 2021. I. Abraham, K. Nayak, L. Ren, and Z. Xiang. Good-case latency of byzantine broadcast: A complete categorization. PODC’21. N. Alhaddad, S. Duan, M. Varia, and H. Zhang. Succinct erasure coding proof systems. Cryptology ePrint Archive , 2021. E. Androulaki, C. Cachin, D. Dobre, and M. Vukolic. Erasure-coded byzantine storage with separate metadata. In Principles of Distributed Systems - 18th International Conference , 2014. M. J. B. Libert and M. Yung. Born and raised distributively: Fully distributed non-interactive adaptively-secure threshold signatures with short shares. In Theoretical Computer Science ,2016. M. Ben-Or, R. Canetti, and O. Goldreich. Asynchronous secure computation. In STOC , pages 52–61. ACM, 1993. M. Ben-Or, R. Canetti, and O. Goldreich. Asynchronous secure computation. In Proceedings of the
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twenty-fifth annual ACM symposium on Theory of computing , pages 52–61, 1993. K. P. Birman and T. A. Joseph. Reliable communication in the presence of failures. ACM Transactions on Computer Systems (TOCS) , 5(1):47–76, 1987. 12 A. Boldyreva. Threshold signatures, multisignatures and blind signatures based on the gap-diffie-hellman-group signature scheme. In Public Key Cryptography — PKC 2003 , 2002. D. Boneh, B. Lynn, and H. Shacham. Short signatures from the weil pairing. Journal of cryptology , 17(4):297–319, 2004. G. Bracha. An asynchronous [(n-1)/3]-resilient consensus protocol. In Proceedings of the third annual ACM symposium on Principles of distributed computing , pages 154–162. ACM, 1984. G. Bracha. Asynchronous byzantine agreement protocols. Information and Computation ,75(2):130–143, 1987. C. Cachin, R. Guerraoui, and L. Rodrigues. Introduction to Reliable and Secure Distributed Programming . 2nd edition, 2011. C. Cachin, K. Kursawe, F. Petzold, and V. Shoup. Secure and efficient asynchronous broadcast protocols. In Annual International Cryptology Conference , pages 524–541. Springer, 2001. C. Cachin and S. Tessaro. Asynchronous verifiable information dispersal. In SRDS , pages 191–201. IEEE, 2005. D. Collins, R. Guerraoui, J. Komatovic, P. Kuznetsov, M. Monti, M. Pavlovic, Y.-A. Pignolet, D.-A. Seredinschi, A. Tonkikh, and A. Xygkis. Online payments by merely broadcasting messages. In 2020 50th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN) , pages 26–38. IEEE, 2020. S. Das, Z. Xiang, and L. Ren. Asynchronous data dissemination and its applications. CCS ’21. D. Dobre, G. O. Karame, W. Li, M. Majuntke, N. Suri, and M. Vukolic. Proofs of writing for robust storage. IEEE Trans. Parallel Distributed Syst. , 30(11):2547–2566, 2019. S. Duan, M. K. Reiter, and H. Zhang. Beat: Asynchronous bft made practical. In CCS , pages 2028–2041. ACM, 2018. S. Duan and H. Zhang. Pace:
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Fully parallelizable bft from reproposable byzantine agreement. Cryptology ePrint Archive , 2022. S. Duan, H. Zhang, and B. Zhao. Waterbear: Information-theoretic asynchronous bft made practical. Cryptology ePrint Archive , 2022. S. Gao. A new algorithm for decoding reed-solomon codes. In Communications, information and network security . 2003. R. Gennaro, S. Jarecki, H. Krawczyk, and T. Rabin. Secure distributed key generation for discrete-log based cryptosystems. Journal of Cryptology , 20(1):51–83, 2007. R. Guerraoui, J. Komatovic, P. Kuznetsov, Y.-A. Pignolet, D.-A. Seredinschi, and A. Tonkikh. Dynamic byzantine reliable broadcast. In OPODIS 2020 , 2021. R. Guerraoui, P. Kuznetsov, M. Monti, M. Pavlovic, and D. Seredinschi. Scalable byzantine reliable broadcast. In DISC 2019 , 2019. 13 R. Guerraoui, P. Kuznetsov, M. Monti, M. Pavloviˇ c, and D.-A. Seredinschi. The consensus number of a cryptocurrency. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing , pages 307–316, 2019. B. Guo, Z. Lu, Q. Tang, J. Xu, and Z. Zhang. Dumbo: Faster asynchronous bft protocols. In CCS , 2020. K. Gurkan, P. Jovanovic, M. Maller, S. Meiklejohn, G. Stern, and A. Tomescu. Aggregatable distributed key generation. In A. Canteaut and F. Standaert, editors, Advances in Cryptology - EUROCRYPT 2021 , volume 12696, pages 147–176. Springer, 2021. J. Hendricks, G. R. Ganger, and M. K. Reiter. Low-overhead byzantine fault-tolerant storage. In T. C. Bressoud and M. F. Kaashoek, editors, SOSP , pages 73–86, 2007. J. Hendricks, G. R. Ganger, and M. K. Reiter. Verifying distributed erasure-coded data. In PODC , 2007. A. Kate and I. Goldberg. Distributed key generation for the internet. In 2009 29th IEEE International Conference on Distributed Computing Systems , pages 119–128. IEEE, 2009. I. Keidar, E. Kokoris-Kogias, O. Naor, and A. Spiegelman. All you need is DAG.
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In PODC ,pages 165–175. ACM, 2021. E. Kokoris Kogias, D. Malkhi, and A. Spiegelman. Asynchronous distributed key generation for computationally-secure randomness, consensus, and threshold signatures. In Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security , pages 1751–1767, 2020. C. Liu, S. Duan, and H. Zhang. Mib: Asynchronous bft with more replicas. arXiv preprint arXiv:2108.04488 , 2021. D. Lu, T. Yurek, S. Kulshreshtha, R. Govind, A. Kate, and A. Miller. Honeybadgermpc and asynchromix: Practical asynchronous mpc and its application to anonymous communication. In CCS ’19 , 2019. Y. Lu, Z. Lu, Q. Tang, and G. Wang. Dumbo-mvba: Optimal multi-valued validated asyn-chronous byzantine agreement, revisited. In PODC , 2020. F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes , volume 16. Elsevier, 1977. A. Miller, Y. Xia, K. Croman, E. Shi, and D. Song. The honey badger of BFT protocols. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Secu-rity , pages 31–42. ACM, 2016. K. Nayak, L. Ren, E. Shi, N. H. Vaidya, and Z. Xiang. Improved extension protocols for byzantine broadcast and agreement. In H. Attiya, editor, 34th International Symposium on Distributed Computing, DISC 2020 .14 M. K. Reiter. Secure agreement protocols: Reliable and atomic group multicast in rampart. In Proceedings of the 2nd ACM Conference on Computer and Communications Security , pages 68–80, 1994. F. B. Schneider, D. Gries, and R. D. Schlichting. Fault-tolerant broadcasts. Science of Com-puter Programming , 4(1):1–15, 1984. V. Shoup. Practical threshold signatures. In Advances in Cryptology — EUROCRYPT 2000 ,2000. S. Toueg. Randomized byzantine agreements. In Proceedings of the third annual ACM sym-posium on Principles of distributed computing , pages 163–178, 1984. L. R. Welch and E. R. Berlekamp. Error
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correction for algebraic block codes, 1986. US Patent 4,633,470. J. H. Wensley, L. Lamport, J. Goldberg, M. W. Green, K. N. Levitt, P. M. Melliar-Smith, R. E. Shostak, and C. B. Weinstock. Sift: Design and analysis of a fault-tolerant computer for aircraft control. Proceedings of the IEEE , 66(10):1240–1255, 1978. 15
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Title: The Life-Changing Loaf of Bread URL Source: Published Time: 2013-02-12T17:16:31+00:00 Markdown Content: Skip to content FACEBOOK INSTAGRAM PINTEREST MAIL How to make healthy choices every day HOME RECIPES ONLINE CLASSES COOKBOOKS SHOP WORK WITH ME ABOUT CONTACT THE LIFE-CHANGING LOAF OF BREAD It took me a long time to settle on the title for this post. Why? Because it’s quite a statement to suggest that a humble loaf of bread will change your life… but the Life-Changing Loaf of Bread will do just that. I am willing to be so bold. When I began eating healthier, bread was definitely on my hit list. Not because bread is inherently “bad” (in my books nothing is that black and white), but that I knew when I was basing three meals a day around a loaf of crusty, white French loaf, something had to give. I realized that if I replaced a few slices of bread a day, I could make room for things like greens, fresh fruits, legumes, and that I would be getting more nutrients from the same amount of calories. Light bulb moment. Now, that isn’t to say that my love affair with bread ended there. Oh no. When I moved to Denmark four years ago I fell head-over-heels for bread all over again, except this time, it wasn’t light and fluffy – it was kind of like the weather – dark, deep, and intense. The Danes are excellent bread makers, especially when it comes to sourdoughs and of course, rye. Bread here is hearty, filling, and a single slice is almost like a meal in itself. I love going to the bakery on Saturday morning and getting a loaf of rye that has naturally risen for days, been baked for 24 hours, and looks and feels like
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a brick. People often ask me why I don’t bake my own bread, and the answer is simple: the Danes just do it better. And I like the ritual of walking down the canal to the bakery (rye bread is one of the few things I actually purchase “ready-made”). This way I appreciate bread on a whole other level and it becomes special. I savour every slice instead of making it every meal. It wasn’t until I went for lunch at a friend’s place a couple weeks ago that my life changed. When I walked into her apartment I could smell it. Something malty and definitely baked, toasty, nutty…when I rounded the corner to her kitchen, there it was. A very beautiful loaf of bread, pretty as a picture, studded with sunflower seeds, chia and almonds, golden around the corners and begging me to slice into it. She served it with a number of spreads; pesto, lentil hummus, some veggie pate. It magically seemed to compliment everything I slathered across its speckled flesh. Moist, dense, chewy. Hints of sea salt here and there, nestled between the oats, around the corner from a golden flax seed. So beautiful and more than tasty, this was a revelation. “Please tell me this is good for me!” I begged her. She smiled. FRIENDLY FIBER: PSYLLIUM SEED HUSKS You’re probably asking yourself how the heck this bread holds itself together without any flour. Nice observation, and the answer is psyllium seed husks. Psyllium seed husks are one of nature’s most absorbent fibers, able to suck up over ten times their weight in water. Psyllium come from the plant Plantago ovata and is related to the common garden dweller Plantain (not to be confused with the fruit!). For this reason, you’ll often find psyllium in over-the-counter
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laxatives, stool-bulking agents and colon cleansing kits; basically anything having to do with poo. I just came back from running a detox course in Lisbon where I got all the participants in-the-know about this amazing little supplement that also helps to reduce cholesterol levels, aid digestion and weight loss, and alleviate diarrhea and constipation. Psyllium seed husks contain both soluble and insoluble fiber. The soluble fiber dissolves in water and soothes the digestive tract with its mucilaginous properties, while the insoluble fiber acts like a broom to sweep the colon free of toxins. Taken during a detox, juice cleanse, or fast, psyllium can greatly improve the body’s ability to eliminate impurities. But the good news is, you can take it anytime – many people find that a daily dose of a teaspoon or two in a glass of water really helps them get their bowels moving, (or slow them down if necessary).* But what does this have to do with bread? Well, the idea here is to use psyllium to bind all these lovely ingredients together without resorting to flour. There have been some low-carb bread recipes floating around the ‘net as of late that take advantage of psyllium and I think it’s a great idea. Eat delicious bread, have good poops. I’m in! Psyllium is available at health food stores and most pharmacies. It comes in two forms, the raw husks themselves, and powdered, which are just the husks that have been pulverized. It is easier to take the powdered form as it dissolves easier in water, but that is not important in the case of this bread – either type work just fine. NOW, ALLOW ME TO EXPLAIN THE TITLE. I know you’re just burning for me to back this up with a few good reasons, so here
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we go. First of all, when I make bread, there are bowls, spoons, measuring cups and flour everywhere. There is always a mess to clean up, and my biggest pet peeve is trying to get the very last bit of dough unstuck from the mixing bowl. Serenity now. The only thing this bread leaves you with is a used spoon and a measuring cup. Everything that you mix, you do so right in the loaf pan. Genius. Secondly, bread almost always requires some kneading, then some waiting, and then perhaps more kneading. Maybe more waiting? I’m confused already. This bread, on the other hand, is kind of brainless. Dump all the ingredients into the loaf pan, stir, and let it sit for a couple hours. Or overnight, all day, or however long or short you find convenient. Whatevs. You rule the bread, not the other way around. Third. Bread recipes are specific. Use this kind of flour, and that kind of yeast… What if I told you that if you don’t have hazelnut, you could use almonds? If you don’t like oats, you could use rolled spelt. Out of maple syrup? Use honey! See where I am going with this? The only thing I will emphasize is to replace the ingredients in the same proportion and with a similar ingredient for the best results. The rest is your call. Fourth, breads require a rising agent, whether that is a sourdough starter (this takes days to make) or commercial yeast (which should really be avoided if possible). This bread doesn’t. Great. Fifth reason, your typical loaf of packaged grocery-store bread is not really that healthy. It uses flour, which has often been stripped of much of its fiber, bran, essential fats, and unless milled mere hours before baking has lost most
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of its nutrients through oxidation. It is high in refined carbohydrates and most times, low in protein and healthy fats. Most breads require gluten-containing flours for texture and leavening, which many are trying to eat less of . And sometimes bread has kooky ingredients like corn syrup and food colouring. Seriously. Read those labels. The Life-Changing Loaf of Bread features whole grains, nuts, and seeds. High in protein, incredibly high in fiber, and it is gluten-free and vegan. Everything gets soaked for optimal nutrition and digestion. I will go so far as to say that this bread is good for you. SIXTH, THIS BREAD MAKES THE BEST TOAST. EVER. 4.81 from 46 votes THE LIFE-CHANGING LOAF OF BREAD INGREDIENTS 1 cup / 135g sunflower seeds ½ cup / 90g flax seeds ½ cup / 65g hazelnuts or almonds 1 ½ cups / 145g rolled oats 2 Tbsp. chia seeds 4 Tbsp. psyllium seed husks 3 Tbsp. if using psyllium husk powder 1 tsp. fine grain sea salt add ½ tsp. if using coarse salt 1 Tbsp. maple syrup for sugar-free diets, use a pinch of stevia 3 Tbsp. melted coconut oil or ghee 1 ½ cups / 350ml water INSTRUCTIONS In a flexible, silicon loaf pan combine all dry ingredients, stirring well. Whisk maple syrup, oil and water together in a measuring cup. Add this to the dry ingredients and mix very well until everything is completely soaked and dough becomes very thick (if the dough is too thick to stir, add one or two teaspoons of water until the dough is manageable). Smooth out the top with the back of a spoon. Let sit out on the counter for at least 2 hours, or all day or overnight. To ensure the dough is ready, it should retain its shape
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even when you pull the sides of the loaf pan away from it it. Preheat oven to 350°F / 175°C. Place loaf pan in the oven on the middle rack, and bake for 20 minutes. Remove bread from loaf pan, place it upside down directly on the rack and bake for another 30-40 minutes. Bread is done when it sounds hollow when tapped. Let cool completely before slicing (difficult, but important). Store bread in a tightly sealed container for up to five days. Freezes well too – slice before freezing for quick and easy toast! NOTES Makes 1 loaf Sarah Britton Click here to print this recipe I realize that few pleasures in life will ever be able to compete with tearing open a fresh baguette, or slicing into a thick-crusted country levain, and I am not suggesting that those pleasures be forgotten. On the contrary, let’s let those things be what they are and enjoy them from time to time. And for now, and hopefully the better part of your bread-munching days, I offer my latest and greatest pleasure to you; the Life-Changing Loaf of Bread with no down-side, a bread with personality, a triumphant flag raised high exclaiming that deliciousness and health are not exclusive. This bread changed my life. Will it change yours too? For the visual learners out there and for those who’d like to come hang with me in my kitchen, the Life-Changing Loaf of Bread is just one of many cooking classes both live and recorded featured on my wellness platform, My New Roots Grow. Check it out! LEARN MORE ABOUT MY CLASSES Q & A I’d love to answer the number of questions about substitutions for the Life-Changing Loaf of Bread coming into the comments section! Please be advised that I cannot guarantee
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any results beyond the recipe above. To help out, if you do make a successful substitution, let me know in the comments! Thanks! 1. There is no substitute for the psyllium husks. Whenever I write a post about a specific ingredient, it is because THAT is the point of the recipe and I like to highlight one way you can use it. For those of you who can’t find psyllium, buy it online. It’s cheap. 2. For nut substitutions, the bulk of this bread is nuts and seeds so you’ll have to skip the recipe. If it is JUST a nut allergy and seeds are okay, replace the nuts with seeds. 3. You can use ground flax seeds instead of whole, but you’re going to need a lot more water as the ground flax seed is highly absorbent. 4. Substituting the oats with quinoa flakes may work, but again, they absorb a lot more water than oats do. Add more water accordingly. 5. Oats are inherently gluten-free, but if you have a sensitivity to gluten, make sure to purchase certified gluten-free oats. 6. For sugar-free or low-sugar diets, use a pinch stevia to replace the maple syrup. 7. A flexible, silicon loaf pan is best because you can test to see if the dough is holding together, and it’s easy to remove the loaf from the pan, BUT, a regular pan should be fine. 8. This bread is not raw. I haven’t tried drying it out. If you want to make it raw I suggest *trying* to slice it before you bake it and dehydrating the slices individually. * if you are interested in taking a dietary psyllium supplement, please read the instructions carefully. Do not give psyllium to young children, as it can be a choking hazard. THE BEST
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COCONUT SOUP, EVER CRISPY CORNMEAL SWEET POTATO FRIES 2,621 THOUGHTS ON “THE LIFE-CHANGING LOAF OF BREAD” KEKSIG February 26, 2025 at 5:59 pm This bread is absolutely delicious! Thank you! Reply FLORA PETAL February 25, 2025 at 8:27 pm After trying the original recipe, I’ve made some adaptations. 1. I use a mixture of different nuts and seeds. 2. Instead of water, I use kefir or buttermilk or coconut milk. 3. I add raisins or dried blueberries and skip the salt. 4. Instead of a loaf pan, I press the dough into muffin pans (makes 24). I freeze them and they are superb when reheated, eaten with a bit of butter. Reply DONA January 19, 2025 at 12:07 pm Question… I just discovered this bread and love it! My second has just come out of the oven from whence I baked it the whole time in a glass bread pan with a parchment sling. I’m totally satisfied with the results, however, I’m curious. I took the liberty of not taking it out of the pan 1/2 way through and my question is , why. Why the instruction to, “Remove bread from loaf pan, place it upside down directly on the rack and bake for another 30-40 minutes.” How does this change the baking or the texture or ??? Reply Pingback: Super Chunk Gingerbread Granola - My New Roots CARROLL COUNTY RECKLESS DRIVING December 19, 2024 at 1:26 am I recently tried making the Life-Changing Loaf of Bread recipe, and I have to say, it truly lives up to its name! This bread is not only delicious but also packed with nutrients and fiber. I love how easy it is to make, and the fact that it’s gluten-free is a huge bonus for me. It’s so satisfying to enjoy a slice
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of this bread with some avocado or nut butter spread on top. I highly recommend giving this recipe a try if you’re looking to add more wholesome ingredients to your diet. It’s definitely become a staple in my weekly meal prep routine! Reply NINA January 16, 2024 at 4:55 pm I love this recipe and have made it many times over the years. I’m curious about the phytonutrients from the soaked nuts.. is it possible to soak the nuts, discard the water, and then make the loaf? How do you think I would need to adjust the recipe? Reply HOLLY November 20, 2023 at 10:53 am Hi, What size silicone loaf pan do you recommend using? Also, has anyone used a glass loaf pan and it worked out just fine popping it out of the pan? Third, what do ya’ll prefer using–psyllium seed husks or the powder and why? Thanks! Holly Reply SARAH BRITTON November 21, 2023 at 6:21 pm Hi Holly! We sent an email as well, but a standard 9×5 loaf pan works great, and we have no trouble not using a silicone so long as you grease the whole thing and at least parchment paper the bottom of the pan. We have made with both types of psyllium, though we use the powder most often! Hope this helps 🙂 Reply I JUST MADE MY FIRST LOAF IN A GLASS PAN LINED WITH PARCHMENT PAPER. IT COMES OUT PERFECTLY. LOVE THIS BREAD. September 29, 2024 at 10:16 am This is so easy and delicious, especially warm. Reply Pingback: Discovering the Calories in Sweet Bread - A Tasty Revelation! DUBAI SIM September 17, 2023 at 11:38 pm The Life-Changing Loaf of Bread has truly transformed my relationship with food. It’s not just bread; it’s a revelation! This wholesome, hearty
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creation has become a staple in my daily routine, providing sustenance and satisfaction like no other. It’s more than a recipe; it’s a game-changer for anyone seeking a healthier, more fulfilling way to enjoy bread. I’m forever grateful for this culinary gem! Reply PRESTIGE PARK GROVE September 1, 2023 at 1:24 am Thank you for sharing Reply TOIMISTOTILA HELSINKI August 18, 2023 at 12:34 pm Thanks a bunch for such fantastic recipes. <3 Reply SARAH BRITTON September 6, 2023 at 11:40 pm xoxo! Reply TOIMISTOTILA HELSINKI August 18, 2023 at 12:33 pm Thank you so much for your beautiful blog and your delicious recipes. <3 Reply SARAH BRITTON September 6, 2023 at 11:39 pm Thank you for reading! Reply YENI MEDYA July 20, 2023 at 3:33 pm This is a very fantastic and delicious recipe. Reply DANIELLE July 19, 2023 at 3:38 pm Love this recipe! I swapped out nuts for pumpkin seeds and it worked really well. My only issue is that I can never flip it on the rack after the first cooking period. I tend to have to get to 40-45 mins before it won’t fall through the cracks :). I’m hoping to try a smaller pan in the future because my current attempts have not been tall enough to put anything on it (although I love eating it plain!). One thing I’ve noticed that seemed odd was, right out of the oven the ghee taste comes through really well but when I reheat the frozen pieces that flavor fades. Still tasty, but I miss the buttery taste. Anyone have any ideas? Reply FIONA SV January 17, 2024 at 1:03 am Delicious!! I was extra chuffed that I had all the ingredients in the cupboard already so no shopping required. I’ll definitely be mKing this again! Reply
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SESLICHAT July 14, 2023 at 6:33 pm Excellent share, well done Reply ELENA SMITH July 14, 2023 at 10:25 am Wow! This article is simply amazing !!! Reply BIANCA July 12, 2023 at 4:01 am I think I have never been so invested in an article about bread :’) This is wonderful. Also the photos. I’ve made bread myself once or twice, but usually i find it quite boring and prefer cakes or more “fun stuff”. But this one – i will give it a try. Thanks for sharing! Greetings from Berlin Reply Pingback: Nut and Seed Bread - Angela Warburton - Transformational Coaching and Mindfulness in Toronto RWCUPDATES July 10, 2023 at 3:21 pm Thank you for your sweet and interesting content Reply BUILDER LANE COVE July 10, 2023 at 10:44 am “The Life-Changing Loaf of Bread” is an incredibly popular recipe from the website “My New Roots”, where it has garnered a huge following of health-conscious individuals who are seeking a nutritious and delicious alternative to traditional bread. Reply Pingback: Life Changing Bread - Katharina Gantenberg FRASES PARA FOTO SOZINHA July 8, 2023 at 12:07 pm “I just had to leave a comment and express how much I enjoyed this blog post. Your writing not only educates but also entertains. It’s rare to find a blog that strikes the perfect balance between informative and engaging. Keep up the fantastic work!” Reply SAMIRO MUNO June 28, 2023 at 2:41 pm Wow! This homemade recipe is simply amazing!!! Reply JO June 17, 2023 at 6:42 am I love this recipe and have made it many times over the years. I wondered if you could cook in an air fryer? Reply SESLI MUHABBET SOHBET SITELERI May 21, 2023 at 8:58 pm very nice sharing thanks Reply JAN HEALEY June 11, 2023
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at 1:37 am Made exactly as recipe said and it is so delicious Reply SARAH BRITTON September 7, 2023 at 12:05 am Yay!! Glad to hear it 🙂 CHERYL May 7, 2023 at 12:12 pm I make this bread once a month. My husband and I love it. I occasionally substitute the nuts depending on what I have on hand. It does freeze so easy. Reply Pingback: Links: Bread, Cake and Marmalade + the Bee's Wrap Winner – Food in Jars Pingback: Spread the Love: Elevate Your Snacks with Homemade Nut and Seed Butter – Bulletproof Survival Pantry JO BUSCK April 5, 2023 at 9:33 am Hi Sarah, I have made this many times over the years and it has indeed been life changing – inherently due to its deliciousness! My husband now has to go Grain Free and is missing bread terribly. I had forgotten about this wee gem and am now wondering if you might have a suggestion for the oats please that would still ensure the bread worked? Thank you so much. Warm wishes, Jo Reply ANNA B June 27, 2023 at 12:40 pm I am wondering if you figured it out. I am starting grain free diet soon and would like to find the substitute for oats. Reply PAULA July 11, 2023 at 4:56 pm I use quinoa flakes instead if oats for a grain free loaf, works really well Reply JENNIFER MASON December 3, 2023 at 2:49 pm Do you find you need to add more water using quinoa flakes? Glad to hear your make it this way – excited to try this recipe 🙂 TALA February 26, 2024 at 8:22 am Are you able to toast the bread in a toaster. Does it work well for sandwiches? WILLOW January 11, 2024 at 9:11 pm
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Jo & others Perhaps try cassava flour &/or tigernut flour. Both are actually tubers, and I use them in the AutoImmune Protocol/the Autoimmune Paleo foods I eat. Reply Pingback: What Are The 'Healthiest' Breads? - Kim Pearson NATACHA March 26, 2023 at 7:09 am I’m baking it right now but… I realised I put the wrong quantities ! I speak french and I thought that tbsp meant teaspoon (I know, why the b then ?) instead of the big spoon. Well… I hope it doesn’t crumble too much.. next time I’ll get the measuring right :p Reply ERIN March 22, 2023 at 2:41 am Was expecting this to be closer to the texture of vollkornbrot. Not so much. Ingredients were all very expensive where we live. Maybe I’ll try pulsing in the food processor a few times before adding the wet ingredients, just too big of pieces in it. Reply EMILY March 18, 2023 at 9:41 am My loaf is extremely flat. I used psyllium seed husk powder, but otherwise everything exactly the same. Soaked it overnight. Baked more than recommended, and is still very crumbly. Any thought? Reply SARAH BRITTON April 3, 2023 at 11:09 am Hi Emily! Thanks for leaving your comment. The loaf is not intended to rise much with no leaving agent, but if you’d like it to be thicker, you could try a deeper / shorter pan. As for the crumbly texture, since you’re soaking overnight, the ingredients may be absorbing more liquid. You could try adding a few extra splashes of water, shorten the soak, or add a bit more psyllium husk powder (1/2 Tbsp at a time). The bread should look well-hydrated before baking, if not, I would add more water. I hope this helps! Reply MONA May 17, 2023 at 12:52 pm
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Hi Sarah, Would love to know if you have nutritional information for this bread. Its lovely and is definitely changing my life! Thanks in advance. Mona KAY July 24, 2023 at 11:18 am Psyllium husk and psyllium husk powder cannot be substituted in equal quantitites.. SARAH BRITTON September 28, 2023 at 1:51 pm Hello! That’s correct, it’s either 4 Tbsp. psyllium seed husks or 3 Tbsp. if using psyllium husk powder, hope this helps! DEBORAH HARNER March 3, 2023 at 10:02 am Just made this recipe this morning exactly as described. Turned out perfectly. Prior to baking, I let it soak about 7 1/2 hours (overnight). Sliced beautifully although I will take one commenter’s advice to slice a bit more thickly to avoid a bit of crumbling. I will be making this again. Reply BED AND BOARD DIVORCE IN NEW JERSEY February 25, 2023 at 4:52 am Thank you for the wonderful recipes. bed and board divorce in new jersey Reply Pingback: Green & Groovy Pizza With A Dairy Free Broccoli Crust - A Tasty Love Story Pingback: ‘Life Changing’ Loaf – Becoming Healthy HEATHER MITCHELL December 18, 2022 at 5:02 pm A friend referred me to this recipe when she found out I needed to go gluten free. I love it, mostly I have toasted it. Made it in regular metal loaf pan, as do not have silicone one, and just greased it really well with coconut oil and it worked well. I wonder how stevia liquid would work instead of powder, I have just added stevia liquid to my kitchen, but not used to how it works. Reply SARAH BRITTON April 3, 2023 at 11:16 am Hi Heather, great idea! I haven’t tried liquid stevia in this recipe, but it could work! To replace 1 Tbsp of maple
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syrup, I would use 6-9 drops to start. You can add it right along with the other ingredients. Let me know if you give it a go. 😊 Reply Pingback: Soooo Many Good Things Just For You - Melani Marx Pingback: BLOG POSTS I LOVE – Nourish & Inspire Me – Best Recipes Ever MADHAVI October 27, 2022 at 1:12 am This bread is absolutely delicious — thank you! I have a question about the texture, though: the inside of the bread was a bit soft even after the baking was done. Should I soak it for longer before putting it into the oven (I did only the bare minimum of 2 hours because I was so eager to eat it!), or should I bake it for longer in order to make it more solid and less crumbly?Thanks. Reply TANIA SHILLAM March 30, 2023 at 10:10 am I love this but have the same question about the sense that the middle is uncooked. I tried making the bread in Brownie tins, but I’m really not sure what to do about it. I guess adding baking powder wouldn’t work because flour isn’t the base… Reply DANIEL J ALTNETHER DDS October 17, 2022 at 12:10 pm Loved this loaf. I used pumpkin seeds and almonds. It had a yield of 12 slices at 198 cal per slice using a recipe nutrition calculator. Reply KAY YVONNE March 4, 2023 at 6:23 pm just the loaf I have been looking for. I love it Reply RYLEE GREGOIRE October 12, 2022 at 8:17 am Great recipe, my partner and I make it all the time. But where is the nutritional information? I see others reference it in the comments but I can’t find it. Reply CONNIE September 24, 2022 at 2:10 pm Can you substitute
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extra virgin olive oil for the coconut oil? Reply SARAH BRITTON September 26, 2022 at 3:53 pm Hello! Yes, absolutely! Reply Pingback: What I Eat as a Vegan: Easy Spring Meals - Happy Apples Recipes Pingback: Life-Changing Bread | Kim Sunée Pingback: Gluten Free Nut And Seed Loaf - Lavender and Lime BIGG NUTRITION August 5, 2022 at 8:48 am You have shared really good information, Thanks Reply KATHLEEN August 1, 2022 at 10:13 am I get best results when using a bowl to mix ingredients. The mixture is periodically stirred until no liquid remains at the bottom of the bowl. This ensures even rehydration. Then it goes into a small, parchment-lined bread pan (4.5″ x 8.5″) to rest overnight. The longer time, opposed to a 2-hour rest, further ensures complete hydration. Be sure that when baking is done, you hear a hollow sound when the bread is thumped on the bottom. If there is no hollow sound, bake longer. Slice thickly, not thinly. All of this results in a non-crumbly bread. My son just asked me for the recipe. Thanks! . Reply CAMILA GREGOIRE July 27, 2022 at 2:23 am Waw! After reading this I went to the kitchen to make this no-bread immediately! My family loved it a lot. Reply Pingback: GUEST POST – 4 Tips for Raising Eager Eaters | Well Beyond the Kitchen Pingback: How To Go Gluten Free (Includes product suggestions!) - Hälsa Health SARA LEANDRO June 4, 2022 at 2:51 pm I appreciate your post. And I tried the recipe, and it was absolutely incredible. My family love it too. Thank you for sharing this post. Reply KIRSTEN HALLING January 13, 2022 at 1:05 pm I accidentally substituted Konjac root powder (glucomannan) for the psyllium husk powder because somehow I bought it a while
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ago and was dumb enough to not check the label. That being said, the bread held together beautifully and the Konjac root seems to have similar properties to the psyllium husk. This is my new favorite breakfast for on-the-go nutrition. Thank you so much for this recipe! Reply Pingback: life changing loaf & sweet potato gnocchi (with burnt butter sage( – in search of angophoras ANGIE December 5, 2021 at 11:39 am Would this bread help lower cholesterol ??? Reply VIVE January 23, 2022 at 7:13 pm I am answering this question as a non-medical person, but I can tell you that my husband’s cholesterol went down 50 points after eating this bread regularly. Three of the main ingredients — oats, psyllium, and flax seed — are all associated with lowering cholesterol and a host of other benefits to the health, so it’s worth a try. Reply ASTRO December 3, 2021 at 5:25 pm Delicious bread recipe for sure! Looking at your writing though: “…while the insoluble fiber acts like a broom to sweep the colon free of toxins. Taken during a detox, juice cleanse, or fast, psyllium can greatly improve the body’s ability to eliminate impurities.” As a medical professional I can confirm that nothing of that sort actually happens in the body. There’s no such thing as ‘detoxing’. In medical terms, it’s a nonsense. It’s a pseudo-medical concept designed to sell you things. The healthy body has kidneys, a liver, skin, even lungs that are detoxifying at all times. There is no known way – certainly not through detox treatments – to make something that works perfectly well in a healthy body work better. If toxins did build up in a way your body couldn’t excrete, you’d likely be dead or in need of serious medical intervention. Reply
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ERIN March 22, 2023 at 2:33 am THIS! THANK YOU! Needed to be called out! Reply RACHEAL BROWN November 24, 2021 at 6:51 am These breads are healthy as well as tasty, yesterday I had made them and trust me they were delicious. I suggest everyone should try this . Reply SABINE November 11, 2021 at 2:43 pm Thank you for this recipe; I’ve made hundreds of loaves throughout the years since you first shared it. I typically swap out the nuts for almond milk pulp and adjust the liquid ratio to get the right consistency for the dough. It’s a wholesome and satisfying loaf that is a favourite in our home. Reply SARAH BRITTON November 12, 2021 at 3:45 pm Hi Sabine! Thanks so much for writing and so happy to hear you’re enjoying again and again. Stay well! Reply CHRIS October 20, 2021 at 2:10 pm I’m not a vegan. I’m not orthorexic. I don’t “detox” or do cleanses. I don’t hold with much of the woo stuff. But I needed to use up some ingredients and, on searching, found this recipe. It’s great! Amazed I hadn’t come across it before. I look forward to tinkering with it and making lots of different versions in future: sweet, savoury, with raising agents, ground smooth, with added fruit/veg, substituting the various nuts and seeds etc. It’s a winner. Congratulations to your Danish friend! Reply JEAN October 19, 2021 at 7:19 am This is wonderful bread and so very easy to make. I made the odd alteration – oil (light taste olive oil) instead of coconut oil, no nuts but added pumpkin seeds and also a bit of millet and a little less psyllium but added a little ground flax seed. I do have a query – I wondered if the
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time (overnight) this lovely loaf sits prior to baking plus the amount of water allows the flax seeds to soak and soften enough to release their benefits – from what I understand soaked flax seeds are as digestible as ground flax seeds …………… or perhaps they need soaking separately and then adding. I wonder if you have any idea regarding this Thank you so much for posting this wonderful recipe. Reply MICHELE February 7, 2022 at 12:37 pm Hi, I don’t use silicone bakeware. Can I use a glass loaf pan with or without parchment paper? Can’t wait to try this recipe! Reply KATHLEEN July 7, 2023 at 7:34 pm I use aluminum loaf pans because that’s what I have, and it bakes beautifully. GAB July 25, 2023 at 3:41 am I was wondering the same thing! Pingback: 14 Vegan Sandwich Ideas – Desiree Nielsen – Medline Pingback: Easy Bread baking for busy people - Holiday-Golightly Pingback: Savoury Wednesday: Fitness-Nuss Brot ohne Mehl - Food Ebony Recipe Pingback: September Reading Update | the Little Red Reviewer KARVIE August 4, 2021 at 3:50 pm This bread is amazing and I have been making it every other week! I like how a small slice is enough to keep me full and satisfied. The only thing I have tweaked was reducing sunflower seed to 1/2 cup, replaced hazelnut/almond with pumpkin seed, added a handful of black sesame seed and seasoning (ground turmeric, ginger, cinnamon and black pepper). Since I was baking it in a toaster oven, I began baking the loaf at 350F for the initial 20 mins as instructed then reduced to 300F until it’s done. Thank you for sharing this recipe!! Reply Pingback: Adventure Bread Recipe (gluten free, vegan) - Dishing Up Balance ELIZABETH July 26, 2021 at 6:46 am Thank
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you for the information. Reply Pingback: The healthiest bread yet? The genius Ezekiel x Life-Changing Loaf of Bread Mash-up - Holiday-Golightly Pingback: Gesundes Nutella Rezept Zum Löffeln - Ohne Schlechtes Gewissen - Julie Christin Boenig THE ORDINARY NIACINAMIDE 10 ZINC 1 July 16, 2021 at 6:06 pm Nice information! Thanks for this article Reply Pingback: Life Changing Bread - Brot mit Gelinggarantie | Bewusstwärts Pingback: My version of the ‘Life Changing Loaf of Bread’ – Saskia Griffiths Pingback: Saskia’s version of the ‘Life Changing Loaf of Bread’ – Saskia Griffiths MITAL June 29, 2021 at 7:26 am Hi I just wanted to say thank you for this recipe. I make it almost every week – have a loaf in the oven now! We all love it. I do not eat oats so I alternate the recipe with different flours like Quinoa (which works really well – I add a little less than the amount of oats) and Teff. Thanks again! Reply SARAH BRITTON July 1, 2021 at 11:57 am Sounds beautiful. So happy you’ve modified to make it work for you and your loved ones — that’s what it’s all about! Reply SANDRA HANSCOMB July 24, 2021 at 4:51 am Hi can you tell me the carbohydrate content of their lovely bread, I’m on a reduced carb diet allowing 45 g a day of carbs . I want a healthy loaf this tastes define but I’m sure I can’t have much of it even though it’s very healthy! SARAH BRITTON July 26, 2021 at 4:10 pm Hi Sandra! I don’t run nutritional panels on my recipes though I recommend plugging this one into a nutritional website (just google!) and you should get the information you’re after 🙂 Be well! CLARISSA December 22, 2022 at 12:10 pm Do you sub out
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exactly the same amount of teff flour or quinoa flour for the oats? 1 1/2 cups? I’d like to replace the oats with something. Thank you! Reply Pingback: Adventure Bread – J & S Quality Bakery Pingback: Joanne Lee Health | Bread without the Bloat Pingback: What I Eat as a Vegan: Easy Spring Meals Dublin - Justgrocerys.com MAHI PATEL May 26, 2021 at 12:34 pm Whenever we praise someone, we give him a number, like if I appreciate your post from one to 10, I would like to give you the full number of 10 because you wrote your post very well. The word is very beautiful. I hope you will keep writing such excellent posts in your life and we will definitely comment by reading these posts. Reply Pingback: 50 Best Vegan Blogs That's Actually Worth Following Pingback: Life-Changing Rezepte - Manuela Richter CHRIS April 17, 2021 at 7:33 pm This bread was a delight to eat. I did need to sub hemp seed powder for the psyllium husks as that is what I had and it is similar. I followed the recipe for everything else. Thank you for the great recipe. I will make this again. Reply BRIAN April 1, 2021 at 12:48 am This is really an excellent bread! In its texture, it’s like a dense German Vollkornbrot, but gluten-free. It’s easy to put together, and delicious…. just what I’ve been looking for over the last few years of missing decent gluten-free bread. Thanks for publishing this recipe! Reply SARAH BRITTON April 1, 2021 at 11:51 am You’re so welcome! Happy you found it — enjoy 🙂 Reply JESSICA March 30, 2021 at 7:45 pm Hi, I am looking for informaiton on the recipe variations including the cinnamon raisin and garlic versions of this Life Changing
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Loaf. I read in the comments about it but I cannot find any information on how to make these variations. Thank you! Reply SARAH BRITTON April 1, 2021 at 11:56 am Hi Jessica! I’d add 1/4 cup or so of raisins or currants to the mix with 1 Tbsp. of cinnamon (adjust up or down to suit your tastes!) and for a garlic / savoury version check out the Everything Bagel Spice Loaf recipe on The Substitute Baker. Reply CATHY JIMENEZ April 9, 2021 at 10:26 pm I am using grams to measure out the ingredients. Just curious…using cups measuring seems like less quantity?? Would the results be the same? How can 90g and 65g both be 1/2 cup? Reply LINDA DAVIES May 28, 2021 at 4:11 pm It is a comparison of volume and weight. So the 90 g ingredient weighs more, with the same amount of volume as a 65 g half cup PAULA WARD January 16, 2022 at 2:27 pm I substituted blackstrap molasses for the honey and added a few raisins, and it was delicious. The raisins got a little burned on top, so next time I will try pushing any on top down into the dough. I also vary the types of nuts and seeds I use (some in our family are sensitive to almonds (subbed pecans and sesame seeds) and sunflower seeds (subbed pumpkin seeds). All delicious. I will try different dried fruits next. Reply Pingback: Lockdown Lunches, Desk Dinners – hanny please CHRISTINA GEORGE March 27, 2021 at 5:13 pm Hello! I have a quick question about storing the bread after it has baked and cooled. The recipe in My New Roots states to store in a tightly closed container in the refrigerator but the recipe here doesn’t mention refrigeration. I suspect the
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moist kalamata olives make it a prime candidate for refrigeration however, I am wondering your opinion / experience on leaving it out so long as it is not steamy weather. I’d like to send a loaf to a friend (who serendipitously gave me your cookbook!) and am wondering if it could withstand a couple of days in the post. Many thanks!! Reply SARAH BRITTON April 1, 2021 at 11:59 am Hi Christina! It can withstand a couple days in the post wrapped well (and without olives, correct!). Under normal circumstances I do keep it in the refrigerator or sliced in the freezer just to extend the shelf-life but if we’re talking 2-4 days it should be okay in the post as long as the portions not eaten right away are frozen upon arrival. Hope this helps 🙂 All love to you! Reply ANDREA MEEHAN March 22, 2021 at 8:05 pm I love this. It forgave me for only having half the amount of psyllium and flax and compensating with extra chia. I loved the whole almonds. Maple syrup is expensive in Australia so I used golden syrup! I’m looking forward to trying with no sweetener and less oil like others have done. Thank you Reply Pingback: How to turn your teen into a lean mean eating machine - Fulham Osteopaths Pingback: Debbie's & Roy's Favorite Things 2016 | Mindful Family Medicine Pingback: Sourdough Life-changing bread - Our Gabled Home Pingback: Oat & Seed Cracker Bread | Katie's Conscious Kitchen GREENER GOODS March 4, 2021 at 1:02 pm I posted almost 4 years ago and back to say THANK YOU again for this amazing, versatile,forgiving recipe! I share it every time I make it on media and get lots of thank you’s! Just remember to use psyllium! And, I have never
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owned a silicone baking device and have always used a well-oiled glass bread pan. The loaf pops out easily (run a knife around sides, invert–it pops right out). I then bake it in the oven. After it cools, I slice it and freeze the slices. Pop in toaster or oven and it’s wonderful! Today, I used the full amount of psyllium, and I found Konsyl carries ORGANIC psyllium, which I just ordered from their website. It’s way more finely powdered, and has lighter flavor, than the red-capped Konsyl they have in stores (not organic). Anyway! I used more water, because it seemed to want it, and this time used the maple syrup I said I don’t bother to use because why not? Maple syrup is delicous, and I am not skerred of any ingredients since I have a new, deep appreciation for experiences, foods and activities during COVID. So, I used 2 T of maple syrup and 2 T of organic Carapelli unfiltered extra-virgin olive oil in lieu of 3 T of coconut oil. It’s on counter awaiting baking. Thank you again for this marvelous recipe. I have it bookmarked but should probably save the page and email it to myself for extra-safekeeping. Please let us know if you’re still enjoying the loaf as well. Stay well, healthy and happy everyone. P.S. DO NOT eat more than two then slices. This is like a supercoloncleanser and thus healthy for our systems. Meant to be rationed a bit and enjoyed. Easy to put together another loaf 🙂 Reply JOHANNA March 10, 2021 at 12:39 am Hello! I’m so excited to eat my first loaf, having just transitioned to a wheat free diet! Unfortunately, the loaf kind of fell apart in places – I couldn’t put it on the rack directly. Too
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much water? Not enough water? I followed all the ingredients and instructions! Reply MORIE FORD July 24, 2021 at 12:27 pm Johanna – that happened to me the first time too! Here is how I tried it the second time around and it didn’t happen again. I love this bread! Once mixed, I let the mixture sit overnight before baking. Also increased the baking time to 30 -35 minutes for the first half. Not sure which of these two things makes it work, so I continue to do both and it really works for us. Sometimes we even do 35 minutes for the last half – if we want extra crunch. LISA February 18, 2021 at 8:58 am I tried this recipe today and what can I say: I LOVE it! I didn’t expect that it would taste this good! I don’t need margarine or any kind of spread with it – it’s delicious, flavorful and rich! My loaf gave 16 slices and I had to stop myself after 2! I made some minor alterations: I didn’t add the syrup/any sweetener or the oil and just added an additional splash of water. For “65g of hazelnuts or almonds” I added half whole hazelnuts and half ground almonds and for the flax seed I added half whole and half ground flax seeds. I let it sit for about for about 10h and baked it for a total of 50min. It came out perfect – it’s holing together very well, it’s slightly crunchy on the outside and soft, chewy on the inside. Thanks for this recipe! Reply MAREE KNIEST March 3, 2021 at 12:29 pm I made this recently and I love it! It is so much better than the pricy similar things I’m seeing in the fancy shops these days. SO
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MUCH BETTER. I will say I did not use a silicon pan and that WAS A HUGE MISTAKE as you may imagine. I will be investing in one as I plan to make this often. Reply Pingback: Chleb zmieniający życie – bez mąki BRIGITTE February 13, 2021 at 4:47 pm Made it today for first time. Added 1 mashed banana, 2 shredded carrots and some almond flour. Came out perfect. Just not sure why we’re calling it bread. Looks and taste more to me like a granola bar? Reply GREENER GOODS March 4, 2021 at 1:07 pm Your carrots and banana sound lovely! I think it’s called a nut loaf, or bread, beacuase it simply can be a “bread”–although not a typical but delicious one–as it can be sliced, toasted and otherwise enjoyed as a bread with a spread of avocado, butter or meat/fruit/veg of choice. I’ll let the author speak though–but that was my assumption in reading through her article. Some say it could more aptly be categorized as a nut loaf. The psyllium adds moisture, as would your banana and carrots, but mine has never turned out dry enough to be even remotely like a granola bar…it’s a bread for sure…like a German sunflower seeded bread or hearty banana walnut bread texture, in my experience…. but like a true bread. I slice and freeze mine though to enjoy whenever I want–pop in toaster oven for a few minutes, flip over once…delicious and yummy. I’m going to note your recipe because I love carrots and using banana. Thank you! Reply Pingback: Lentil Vegetable Soup with Ham • anatomy of a pineapple ANDREA February 2, 2021 at 11:33 pm This is a very fantastic and delicious recipe. I will try at home. Thank you for sharing this post. Reply MICHAELA
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January 30, 2021 at 6:34 pm Hello? I have a question: Psyllium seed husk is it the seed, or the peel of the seed. Here in germany you can buy both (Flohsamenschalen and Flohsamen) they have different properties. The google translation isn’t helpful . So i don’t know what you mean… Greetings Michaela Reply SARAH BRITTON March 1, 2021 at 4:42 pm Hello! This recipe used the husk and we have access to the psyllium husk in both a flaked and powdered form. Either work for the recipe but in different quantities noted in the recipe! Hope this helps you. Reply ANNIKA November 19, 2022 at 4:46 pm A very late reply: it should be Flohsamenschalen, since the husk is the peel of the seed. Reply ARAICA January 23, 2021 at 11:58 am I’ve given up counting how many times I’ve made this and am so grateful I stumbled across the recipe years ago. I always use seeds and not nuts so my son can take it as a school safe snack. The two favourite flavour variations in my house are cinnamon raisin and garlic. I just throw a little powdered garlic in, sometimes with herbs or a little cinnamon, nutmeg and raisins (I typically add an extra tbsp or so of water for the raisins to soak up) The base recipe is still my favourite with a little honey and variations are favourites for quick lunch and school snacks. Thank you so much for such a great and versatile recipe! Reply TASHI January 8, 2021 at 2:47 pm Amazing recipe – i never make it the same way twice. I like to add buckwheat and millet. Recently tried it with some baking powder with good fluffier results. To help hold the bread together i blender about 1/4 of the
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flax, buckwheat and oats into flour. Curious if anyone has tried yeast or fermentation on this bread. That might be my next experiment. Reply SARAH BRITTON January 14, 2021 at 12:46 pm Hello! I have added about 2 Tbsp. of a sourdough starter to the loaf as it rests before baking and I love the result! Let me know how it goes for you! Reply LEXI January 31, 2021 at 6:38 am Hey Sarah! I have sourdough starter at home, did the loaf raise more when you added it? And it did you just add it at the end? SARAH BRITTON March 1, 2021 at 4:40 pm Hello! I stirred a couple tablespoons into the base mix before it sat out to rest and it did add a bit of levity to the loaf! GEMMA February 4, 2021 at 5:42 pm I first made this bread 7 years ago after my mom raved about it and I love that so many people are still coming to discover it for themselves. This recipe (and you) are what inspired me to try a plant based diet and I’ve never felt better. Thank you so much! LISA January 20, 2021 at 10:49 pm Hi Tash, first time bread baker : ) – it is cooling and I’m looking forward to trying. like the idea of if being a little fluffier. How much baking soda did you add? Reply WENDY March 6, 2021 at 8:17 pm Hi, Keen to try this recipe and wondered if I could use normal melted butter LINDA January 6, 2021 at 1:06 am Good article . The way how you explain this strategies. Is very professional. Reply LINDA January 4, 2021 at 3:37 am Thank you for sharing your great information. I read your blog daily . It give
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me so much knowledge and ideas. Reply GRELIA DAVIES ALBÁN December 28, 2020 at 9:20 pm Hello. This recipe Is amazing. Can I replace the rolled oaks for almond flour? Reply SARAH BRITTON January 14, 2021 at 12:50 pm Hello! Though I have not tried, I do know others have experimented quite a bit! Reply TRACY December 20, 2020 at 8:28 am Wow – the interest in this recipe has real longevity! I’m just stumbling across it and will make today. My question is : what about pumpkin seeds? Sounds like substitutions are pretty liberal. So – are there any cautions around subbing some pumpkin seeds (pepitas) for the sunflower seeds? Thanks! Tracy Reply SARAH BRITTON January 14, 2021 at 12:53 pm Hi Tracy! Not at all sub some or all of the sunflower seeds for pumpkin seeds or for a nut-free version use pumpkin seeds instead of the nuts — all add-ins can be easily mixed and matched! Reply Pingback: Weihnachtsmenü Teil II - Süsskartoffel-Hummus & Rote-Bete Walnuss-Dip * FreiStyle Pingback: nut free seeded loaf (vegan & gluten-free) - blue border BOXSTREM November 9, 2020 at 2:32 am thanks for recipe Reply Pingback: Bezglutenowy chleb życia | Smakowity chleb MICHELLE October 20, 2020 at 5:28 pm I didn’t think this was going to work. I live at 8300 ft altitude and any bread that requires rising usually flops, badly. This bread worked great, tastes amazing and is super healthy. All things I love!!! Reply Pingback: Nut free, gluten free, 'Life Changing fruit Loaf' - Georgeats KYLE SWEENEY October 11, 2020 at 6:20 pm Hi, I am intolerant to oats 🙁 is there something I could sub that would still make this bread work? Thanks so much! Reply SARAH BRITTON October 12, 2020 at 11:27 am Hi Kyle! There are
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countless comments on this post with people’s updated recipes, you should check them out! I do know some have had success with quinoa / barley flakes — good luck! Reply EILEEN October 13, 2020 at 6:49 pm I’ve made this many times using equal amount of sliced tigernuts instead of oats, works very well Reply LAURA November 1, 2020 at 3:50 am I have substituted rolled oats with similar amount of rolled buckwheat. Reply ANDREA IRVIN January 8, 2021 at 2:59 am I just made it for the first time and subbed in ground almond flour. Works perfectly. Reply TERESA April 14, 2021 at 3:50 pm What did you substitute the almond flour for? LISA October 9, 2020 at 11:21 pm This has become a staple in my house from when you first posted it and I can’t tell you how many times I’ve been asked for this recipe from friends and I’ve shared your link. I prefer hazelnuts to almonds. At times I’ve substituted olive oil for coconut oil and chickpea flour, sweet potato flour , and cassava/manioc flour for the oats. They have all worked and are good. Thank you for this amazing recipe! Reply JAYESH PATEL January 9, 2021 at 6:38 am Hi, do you use roasted hazelnuts? Reply PUTRA September 10, 2020 at 8:05 pm Thank you so much for your post Reply SALLY D-C September 1, 2020 at 9:45 am This is certainly a life changing loaf of bread. Thank you, Sarah. I love eating something that is so nourishing and tasty at the same time. My second attempt was even better than the first. Both times i part-baked it in the bread maker before up-ending it and completing it stand-alone in the oven as briefed. This time i doubled the quantities (all except for
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the honey, of which i use half the recipe amount as a personal preference) because my bread maker tin is large. I increased the part-cooking to 30 mins and then gave it 30 mins in the oven, expecting it to need more but it didn’t. I also left it to stand for 4 hours beforehand. Each time i’ve used psyllium husk powder, and ground flaxseed, of necessity, but haven’t added extra liquid and both loaves have come out fine. Better than fine. They slice well, they toast well, the slices aren’t crumbly and they go with everything. I’ve eaten them with all sorts of pesto, with banana, with peanut butter and jam, and toasted on their own. With the second loaf i pre-toasted the almonds and hazelnuts (i mixed them in the recipe) and pre-toasted half the sunflower seeds. I love toasted seeds and nuts. I also added a tbsp of tapioca flour ‘just in case the 6 tbsp of the psyllium wasn’t enough to hold it together, but i may not have needed to. I’ll omit it next time and see. So happy. Many thanks indeed. Reply FREDA September 3, 2020 at 2:02 am Hi there I was wondering if anyone knows why the bread I baked has a very weird flavour and smell ? Has anyone had that experience? but otherwise it came out beautiful All the ingredients are super fresh as I use them everyday in my diet therefore it can’t be anything wrong with the ingredients Please help ?? Reply GAIL DAVIES May 13, 2023 at 12:51 pm I wish I had not used coconut oil. It gave a repellent taste and smell. That may be the source of the problem for you too BONNIE October 24, 2020 at 8:53 am Amazing. Loved it. So easy.
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Just swapped olive oil instead of coconut and honey instead of maple syrup as I didn’t have them. Gave some to my friends they loved it. Thanks so much for sharing that great recipe. X Reply ALECIAB July 30, 2020 at 11:43 am I love this bread. Has anyone baked it in a muffin tin? Reply PAMELA July 29, 2020 at 10:06 pm Is it possible to get the life changing loaf of bread recipe with the correct water amount for using ground flax seed? I have read in many places that unground flax passes through undigested so I always use ground. Reply SARAH BRITTON August 12, 2020 at 8:53 am Hi Pamela! That is true. If you chew well you will crunch through some of them and any of them that remain whole will be excellent fiber for digestion. I haven’t tried with the ground but I’m sure someone out there has! 🙂 Reply KRISTINE October 31, 2020 at 10:54 pm I had whole flax and just ran them for a couple of seconds in a coffee grinder I use for herbs. They became partially cracked, in larger pieces, some even still whole, not finely ground like flax meal. DIANA BINGHAM August 31, 2020 at 11:26 am I tried it with ground flax seed and added an extra 1/3 cup of water. It seems to be holding together well after baking a slicing. I let it sit overnight though just in case it was too much water added to give it more time for the loaf to soak up the liquid. Reply DAVID July 26, 2020 at 9:39 am Good share! Reply Pingback: 50 Best Vegan Blogs That's Actually Worth Following (2020) AYLA July 9, 2020 at 5:28 pm First attempt with this recipe and it turned out great.
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I think I shorted the salt a little as some comments mentioned the bread being salty to their taste. Next time I will reduce the amount of coconut oil a bit and maybe add dates. But absolutely delicious as written too. It’s difficult to not go back for another slice…and another…and another… 🙂 Reply ANITA JARRETT July 19, 2020 at 5:51 pm Is there an alternative to use in this bread instead of coconut oil as I need to lower my cholesterol level,.could I use benecol and if so how much or what would you recommend in place of the coconut oil? Reply JANET HUYTON July 31, 2020 at 12:48 pm Is coconut oil bad for cholesterol? Pingback: Life Changing Bread - Glutenfrei selber machen | Grüne Smoothies Rezepte ANONYMOUS July 6, 2020 at 11:42 pm I not that much of a internet reader to be honest but your blogs really nice, keep it up! I’ll go ahead and bookmark your site to come back in the future. Many thanks Reply MELISSA MISKAVI June 22, 2020 at 10:49 am This bread is truly life changing – I made it with oats and with buckwheat flakes and they both turned out delicious. My husband even loved it! THANK YOU SO MUCH <3 Reply SARAH BRITTON July 2, 2020 at 9:58 pm So happy to hear it! 🙂 Reply IVONNE DIAZ June 12, 2020 at 9:56 pm A friend shared your blog with me in 2014 when I was in Japan feeling homesick. I’ve made this bread countless times since then and love it so much every time. I lovreto have this in my fridge for a quick snack or a quick breakfast. It’s so satisfying especially with butter and jam. Your whole blog is amazing, life-changing, and your food makes me
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feel so good. Thank you for sharing so much and making it accessible to all of us. Being able to use your recipes during these difficult times has given the ability to , in one small way, do something nourishing for my body and soul. Reply SARAH BRITTON July 2, 2020 at 10:07 pm Thank you so much Ivonne! I appreciate your sweet note so very much and hope to continue to create recipes and inspire every body to nourish themselves a little better everyday. Be well, and take good care! Reply ANONYMOUS June 10, 2020 at 2:13 am Usually I don’t learn post on blogs, but I would like to say that this write-up very compelled me to take a look at and do so! Your writing style has been amazed me. Thank you, quite nice post. Reply CAROLYN June 3, 2020 at 9:10 pm Maybe this bread really is life changing! Because I am the queen of messing up recipes and all my bread baking so far has been a real disaster. This one made me laugh, I did it all ‘right’ (substituting lots of things according to what I had in the cupboard, but I was following along the quantities etc), but right at the end I was talking on the phone while I poured in the water and started stirring – what!? Mine was like soup, nothing like how it sounded it should be – I realised i had added 3.5 cups of water not 350ml or 1.5 cups. But I was able to rescue it by adding 1 cup of coconut flour and 1 teaspoon of xanthan gum, and divided it into 2 loaves. I had to bake it for 1 hour all up and the ‘upside down on the rack’ was only possible with
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baking paper underneath, I leave it to you to imagine the mess when I tried without the paper! But, result! The bread is good!! Overall it lacked a bit of salt, probably because I turned 1 loaf into 2. But with butter and vegemite, it’s actually tasting amazing! Thanks so much for the recipe and for giving me something I can feel proud of in my baking! Reply SARAH BRITTON June 11, 2020 at 10:55 am Ha! I’m so glad you were able to act quick and save your precious ingredients 🙂 well done, and enjoy! Reply ANN MARIE BOYLE December 14, 2020 at 5:45 pm You made my day Carolyn, sounds just like me baking ! Reply SERENA PATEL May 25, 2020 at 9:38 pm This recipe is amazing!! I don’t eat bread often because it can leave me bloated, but this one is so delicious, nutritious and high in protein. I love it so much. I’ve had it for breakfast toasted with some coconut yoghurt and chia jam. Even for lunch with some humous and avocado on it. I had to stop myself eating too much! Thanks for a great recipe Reply MAMA LYNN May 31, 2020 at 10:42 am I love this bread, especially when it’s toasted! Has anyone ever made it into muffins? What changes need to be made? Reply CHLOE May 21, 2020 at 8:46 am used and got the following. I need clorie calculator as a diabetic Nutrition Facts Serving size: 1 slice Servings: 8 Amount per serving Calories 334 % Daily Value* Total Fat 23.4g 30% Saturated Fat 4.8g 24% Cholesterol 12mg 4% Sodium 12mg 1% Total Carbohydrate 25.2g 9% Dietary Fiber 12.1g 43% Total Sugars 1.1g Protein 10.3g Vitamin D 0mcg 0% Calcium 73mg 6% Iron 5mg 30% Potassium 342mg 7%
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Reply MAMA LYNN May 30, 2020 at 11:59 pm Love this bread! Especially toasted! Has anyone ever made this into muffins? Suggestions for doing so??? Reply RUTH HAWE June 8, 2020 at 4:48 am how can there be any cholesterol in a vegan product? Reply CHARLIE June 14, 2020 at 12:25 am Because there was an option to use ghee instead of coconut oil. I suppose they added the ghee ALICE February 20, 2024 at 4:27 am I love this recipe, so I recreated a recipe using nutriely recipe builder and got the following nutritional values. You can check more details on the recipe here – I used all vegan ingredients, so this recipe is vegan (as to my liking). Serving size: 94 grams (loaf of bread sliced in 10 pieces). Energy 297kcal (1,244 kj) 18% Carbohydrates 10g 5% Protein 8g 8% Fat 22g 44% Fatty acids, total polyunsaturated 8 g Fatty acids, total monounsaturated cis 6 g Fatty acids, total saturated 5 g Cholesterol (gc) 0 mg Sterols 61 mg Alcohol 0g 0% Water 38g 2% Iron 2mg 25% Calcium 70mg 7% Chromium 4ug 11% Sodium 204mg 14% Iodine 15ug 10% Copper 0mg 0% Salt 520mg 23% Selenium 6ug 11% Zinc 2mg 18% Manganese 1mg 43% Magnesium 133mg 33% Potassium 314mg 10% Fluoride (fluerine) 0mg 0% Phosphorus 297mg 42% Molybdenum 0mg 0% Vitamin d 0ug 0% Vitamin e alphatocopherol 6mg 40% Vitamin c (ascorbic acid) 0mg 0% Vitamin b-12 (cobalamin) 0ug 0% Vitamin a retinol activity equivalents 0ug 0% Thiamin (vitamin b1) 0mg 0% Riboflavine (vitamin b2) 0mg 0% Vitamin b6 pyridoxine (hydrochloride) 0mg 0% Vitamin k 2ug 2% Niacin equivalents, total 3mg 19% Folate 28ug 7% Fibre, total 11g 3% Starch 8g Polyols 0g 0% Reply LEA BARRIOS May 18, 2020 at 11:32 am Among all of
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these positive comments about this bread I feel alone because I am one of the few whose life this bread did not change. After I saw it on the archives of Meghan Markle’s old blog, The Tig, I had to try it. And I did. Three times as a matter of fact. I made it twice with coconut oil and once with ghee. The first two times it came out like soft bread, it crumbled and had seeds flaking from it with every move. The third time it came out more dry and held together which is how it looked in the pictures and how I hoped it would come out but I still didn’t like it. Maybe it’s my spoiled tastebuds but I didn’t enjoy eating it. I imagined myself replacing the baguette I get from Raley’s with this bread that everyone adored but it didn’t work for me. I spent about $70, more or less, on the ingredients like ghee and psyllium husks that I don’t see myself using any time soon. Everyone’s comments made me so excited for this bread and I really wanted it to work so bad that I made it three times. Oh well, I hope it works for everyone else. Reply SARAH BRITTON May 19, 2020 at 10:56 am Hello! Sorry to hear that it wasn’t what you were hoping for. Hardly a replacement for a baguette, the texture and flavor are quite different but certainly delicious and nutritious. Did you use weights for your measurements? That may help a bit if you decide to give it another go! Best of luck, thanks for trying 🙂 Reply LEA BARRIOS June 4, 2020 at 7:23 pm Yes, I did make the recipe with measuring cups and by using a scale to weigh the ingredients.
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It never once sounded hollow though. The last time I made it I pressed on it to make it firm and it helped but still no hollow sound. SARAH BRITTON June 11, 2020 at 10:54 am Hmmm… yes, the packing is a must so happy that helped! Maybe try cooking a bit longer? GRACIE June 18, 2020 at 1:17 pm May be a stupid question but are Steel Cut Oats the same as rolled oats? Can I use the steel cut oats? Thank you! SARAH BRITTON July 2, 2020 at 10:10 pm Hello! Steel cut oats are the whole oat groat that is chopped (they look ragged and chunky) whereas rolled oats are the whole oat groat that has been rolled flat. You want to look for the rolled oats (and not the quick-cooking ones!) for this recipe! STEVE SIVELL November 25, 2020 at 1:42 pm Yes it did change my life and the lives of those I introduce to it. Thank you ? Reply KARINA RAUFF MEISTRUP May 14, 2020 at 5:05 am Hello, I’m a huge fan of this bread and have made it many times. But now I started soaking the nuts and seeds before use, and I find it difficult to determine how much water I should use. Have any tried with pre soaked nuts and seeds before? Cheers Reply LIZ July 31, 2020 at 10:50 pm Did you ever figure this out? I would like to pre-soak the nuts and seeds and oats as well, in more water than the recipe calls for. Then strain them. But then I’m not sure how much water to use! Reply BIANCA May 11, 2020 at 8:00 am Hi there! This recipe truly looks life changing and I really want to make it. I have run out of oats…
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can I sub buckwheat groats/flour for the oats or would this not work? Reply SARAH BRITTON May 13, 2020 at 2:13 pm Hi Bianca! Oats are very much integral to the recipe but buckwheat flakes could work? Groats or flour wouldn’t work here, I suggest you make as written on your first attempt and then play to suit your needs and taste from there! Reply BERTA May 14, 2020 at 12:25 am Hi Bianca, scroll down, you will find at least 2 recipes with buckwheat. I myself replace just some of the oats with buckwheat. Good luck Reply BERTA April 29, 2020 at 5:50 am Thank you very much for this Sarah 1 I have made this loaf many times meanwhile and toasted slices are absolutely delicious! All in all I do follow this recipe. I wonder why oil and some sweet is added. What are the thoughts behind adding the two to this loaf? I made many kinds of bread from baguette to pizza, tortilla , chapati and more. On some, oil helps to make the bread softer, what is desired. However, for pizza or flat bread, oil is not needed. So why here? I will try anyway. Thanks for any input. Berta Reply SARAH BRITTON May 4, 2020 at 12:07 pm Hello Berta! The oil keeps the bread moist and tender, and the maple is there to add balance to the flavour. I have tried without the syrup but never without the oil. Do let me know if you try and how it goes 🙂 Reply BERTA May 8, 2020 at 2:19 am Hello Sarah and all, made it witout oil and without sugar. Changed it a bit: roasted the hazelnuts and 30g of buckwheat for 10 minutes at 200°C. Crushed the hazelnuts coarse in a blender. Mixed
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the water with psyllium seed husks and chia seeds and salt( as described further down ), using a whisk, and added the buckwheat. Let it soak for maybe 5 minutes. Add the well mixed rest to it, subtracting the 30g of buckwheat from the rolled oats. Baked it the next day for 70 minutes at 180°C, and 5 minutes at 250°C. Compared a “classic” loaf (I replaced maple syrup with palm sugar, since I am in Thailand) with this one. Both slices I toasted for 10 minutes (oven) until crip. The “classic” loaf is a bit softer and it tastes a bit more balanced. However we (my friend and I) did not really miss the oil or the balance(sugar). We both enjoyed the even more nutty taste added by the roasted buckwheat. We both are in favor of the better mixed ingredients by desolving the psyllium seed husks and chia seeds first, no cracks at all with less mixing. Conclusion: next time I will add oil and palm sugar (15g) again and we both love the extra crunch added by the roasted buckwheat. Stay well and thanx again BERTA May 11, 2020 at 8:43 pm Now after we have finished that loaf, I will go back using oil, my friend prefers that and 15g of palm sugar, it suits me better. Had to try it 🙂 SARAH BRITTON May 13, 2020 at 2:00 pm Thanks for following up! Great to know 🙂 MARGARET May 12, 2020 at 4:31 pm Hi Sarah, just wanted to say thank you, it’s certainly life changing for me. I have been feeling terrible that I couldn’t seem to make a bread substitute for my egg, gluten, peanut, milk (& some other foods) intolerant 10 year old daughter. I used almondmeal instead of oats and omitted
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the sweetener as she is on a strict diet to try heal her digestive tract…(high protein, keto type avoiding triggers). She can finally have avocado toast with the family again! thank you. SARAH BRITTON May 13, 2020 at 2:00 pm Ohh that’s so nice, so touching! So happy to hear this and that you are able to enjoy a shared meal together. MAGGIE April 23, 2020 at 3:11 pm So, in your post you mention that commercial yeasts should be avoided at all costs (either a quote or paraphrase, going from memory here cause I’m so far down on the page!). Is there a post where you elaborate on this more? As an enthusiast of bread and baking and all of it, I’d love to know more about your thoughts on the matter. I’m learning about sourdough but the easy access of commercial dried yeast is hard to resist, although I have to admit to a similar amount of confusion regarding the kneading and waiting that you referenced, and a huge amount of mess as well! Are other leavening agents also topics of concern, for quick breads and baking? Reply KEITH RICHARDSON April 12, 2020 at 4:45 pm Wonderful recipe Sarah, thank you, it is better than the loaves I’ve been buying from the local Polish grocery shop. I branched out and made an Easter “Simnel” version adding: 125g of rasins; almonds instead of hazelnuts, 50 g of cut mixed peel; 4 Tbsp of Stevia; an extra 1 1/2 Tbsp of psyllium husk; 2 Tsp almond extract; a little extra water and a pack of marzipan. I mixed everything (except the marzipan) up in a bowl and put half in the loaf tin followed by 1/2 the marzipan in a layer. Then put the remaining mixture in and left it
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for about 6 hours. I baked for 25 minutes in the tin then 40 out of it. I then topped it with another layer of marzipan and the apostles. It turned out OK, to the extent that my wife ate a whole chunk. I think I would probably bake at a lower temperature for a little longer next time. Thanks again, delicious! Reply SUE May 7, 2020 at 9:38 am Apostles?? What is that? Reply Pingback: SeedSational Bread KATHLEEN KAHL April 2, 2020 at 12:29 pm If you cannot have or don’t like oats you can use quinoas flakes. You just have to double the water because they really suck the water up. Reply SARAH BRITTON April 9, 2020 at 12:34 pm Thanks for the testing and tip! Reply KASIA April 1, 2020 at 7:41 pm Love this bread and I made it multiple times but I have the same problem every time: when I flip it over after 20 minutes, it’s stuck in my pan. I end up baking it still in the pan (because I can’t take it out) for another 30-40 minutes and when it’s baked, some of it is still stuck to it so there are some pieces. I use US measurements. Any idea what may be going on? Reply SARAH BRITTON April 9, 2020 at 12:35 pm I would line the bottom of your pan with parchment–should come right out! Reply STEVE WATERS April 20, 2020 at 6:38 pm I just received the Lekue bread bowl 100% silicone Check it out You can mix, knead, proof and bake in it. Worth its weight in gold I still use my kitchen aid for the mixing ? Reply BECKY April 28, 2020 at 2:04 pm I made the loaf in a metal bread pan, and was able
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to keep it from sticking was by mixing it in a bowl, and then pouring it into the very well greased pan to set up before baking. Maybe this would help? Reply CHRISTIE July 22, 2021 at 1:07 am My loaf gets stuck in the tin too, I just cook it in there and don’t worry about flipping. I do line my tin with baking paper though. I love this bread, it’s the 4th time I’ve made it now 🙂 Reply Pingback: I made the Life Changing Loaf of Bread – Anti Candida Kitchen AURÉLIA March 12, 2020 at 6:57 am Hey ! Do you know how much calories ? Fot the chole bread or per 100gr ? Love this bread <3 Thx a lot 🙂 Reply SARAH BRITTON March 12, 2020 at 8:26 am Hello! Though I don’t recommend getting too caught up on calorie counts–especially when it comes to something as delicious and nutritious as the LCLOB–there are online tools that you can use to approximate the nutritional facts. So happy to hear you love the bread! Reply ROSIE MCLAUCHLAN March 8, 2020 at 5:58 pm Hi 🙂 If not using a silicon loaf pan, would I need to line and/or grease a regular loaf pan? Or would it be ok without either of those? Thanks so much! Can’t wait to make this on the weekend Reply SARAH BRITTON March 9, 2020 at 11:42 am Hello! I would suggest lining at least the bottom with parchment as it will make the process seamless–enjoy! Reply CORNELLE ELLIS March 7, 2020 at 7:57 am This is my FAVOURITE bread – thank you for an amazing recipe! I like to slice the whole loaf and keep it in the freezer for toast – amazing with hummus, avo and a slice of
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tomato. I’ve made only one small change for myself and that is to roughly chop the hazelnuts otherwise I find they just fall while out of the bread when I slice it (maybe my knife, but anyway saving me some losses). Reply SARAH BRITTON March 9, 2020 at 11:43 am So happy you love it! Reply Pingback: Gezond glutenvrij brood – Femke's Foodies KEVIN CARSON March 2, 2020 at 10:53 am Can I add dried fruit to the recipe, or substitute a mashed ripe banana for some of the water? Reply SARAH BRITTON March 3, 2020 at 11:48 am Hello! Thinking you may be able to cut the maple syrup and add banana but start by reducing the water by only a bit as it is quite a dense, seedy loaf. You can absolutely add dried fruit! Start with small adjustments and work from there–let me know how it turns out 🙂 Reply WANJIRA NJENGA February 29, 2020 at 6:56 pm Hello, I have been making this bread for so long, and love it. My students have asked for the recipe, would it be alright to post it on my FB – of course mention your name and website? Metta, Wanjira Reply SARAH BRITTON March 3, 2020 at 11:50 am Yes, please share the blog link with your students on your Facebook 🙂 Enjoy! Reply WANJIRA NJENGA March 7, 2020 at 7:03 pm Thank you. Will do. Pingback: 20 Best Gluten-Free Bread Recipes | ALTUM Health & Wellness KAREN BETH MARTIN February 10, 2020 at 10:21 am I LOVE this bread and make it often! I made it again last night and did one little thing different and I think it’s better than ever. It was a fluke, really. I couldn’t find my loaf pan (still can’t find it… odd)
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so I made this in an 8×8 baking dish where it spread out flatter. Oh my! I will make it like this every time from now on! It’s crispier and SO delicious! Love it! I also LOVE how versatile this one is! For example, I had brazil nuts instead of almonds and it turned out great. Can’t recommend this bread highly enough! Reply SARAH BRITTON February 29, 2020 at 8:53 am So happy to hear that, and what a happy accident! Sounds like it would be a cross between the loaf and the crackers… what a thought! Thanks for sharing and for your support 🙂 enjoy! Reply LOTUS February 6, 2020 at 6:24 pm Is there any way of making the bread oil free? Reply SARAH BRITTON February 19, 2020 at 5:59 pm Hi Lotus, I would just leave it out, and replace with the same amount of water. I hope that helps! xo, Sarah B Reply KEVIN SMITH February 2, 2020 at 11:44 am ” urdough starter (this takes days to make) or commercial yeast (which should really be avoided if possible). This bread doesn’t. Great. ” Just on this.why should commercial yeast be avoided? Tks Reply Pingback: How to Turn Your Teen Into A Lean Mean Eating Machine KATHLEEN KAHL January 26, 2020 at 12:14 pm I have made this many times with the oats but I am giving them up. I tried it with quinoa flakes. You have to up the water by at least 1/2 cup. I love it this way. Reply SARAH BRITTON February 29, 2020 at 8:59 am Thanks for the tip, Kathleen! So happy that you’ve made it your own. Reply REBECCA January 25, 2020 at 4:30 pm I’ve been making this constantly for several years. I pretty much follow the recipe, but
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I usually use olive oil and honey, not coconut oil and maple syrup, because olive oil is healthier and maple syrup is very expensive where I live. I often swap for walnuts or almonds depending what’s in the cupboard. I sometimes add some dried fruit. I found out that you can make it with ground flax instead of psyllium husk because once I got halfway before I realised the psyllium was finished! That also turned out fine. It’s quite hard to get it wrong, though it turns out much better if you give it a good mix in a bowl and then tip it into the loaf pan. My whole family likes it, even the teenage boys. Reply SARAH BRITTON February 29, 2020 at 9:01 am A family-friendly recipe is a win in my book! So glad that you’ve found substitutions that work with what you have on hand and with your lifestyle and preferences. Enjoy, be well! Reply AJ March 16, 2020 at 1:57 pm Hi Rebecca, what was the proportions you used to replace the psyllium husk with ground flaxseed? How much more water do you add? Can’t find psyllium husk where I live but have a good amount of ground flax seeds and would like to give this recipe a go using what I have on hand at the moment. However, Im open to purchasing psyllium husk online to make the original recipe. Thanks Reply Pingback: Glutenvrij zaden- en pittenbrood – Femke's Foodies Pingback: Everyday Seed Bread (paleo vegan with raw option) | Straits Road Kitchen DIANE January 15, 2020 at 4:26 pm I made this bread several years ago and found that my body COULD NOT tolerate psyllium husk. At all. I finally spent time reading all the comments from your readers, and encouraged by a
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few people who have tried substituting chia for the psyllium husk, I jumped in and tried it. It worked! Here is what I did; Increased chia seeds to 3 tablespoons and subbed 3 tbsp ground chia for the ground psyllium husk. No other changes. It was quite goopy when I put it into the pan but by the next morning it had solidified and baked with no issues. Tastes exactly the same. I’m so thrilled – now on to the Life Changing Crackers!! Yay! Thanks Sarah 🙂 Reply SARAH BRITTON February 29, 2020 at 9:05 am Hi Diane! So happy to hear that the chia substitution worked for you. So honored that the MNR community is open to sharing and commenting, and to making my recipes their own to suit their needs. Good luck with the crackers, hope they’re life-changing 🙂 Reply Pingback: Recipes to Help You Eat More Foods High in Omega 3s - World of Entertainment Pingback: 10 Must-Have Cookbooks for Healthy Food Lovers - The Health Sessions EMMA December 19, 2019 at 9:12 am I stumbled on a cheaper version – however it gave everything a slightly burnt taste and that unpleasant sensation/taste in the back of the throat. I thought it was because the oil may have been off but a friend said it is because it is not sufficiently refined, apparently if you’re cooking with coconut oil get the expensive stuff that doesn’t smell toasted. If soy is not a problem there are some half/half products (kremelta in New Zealand, Copha in Australia) which are odorless and are also cheaper. Reply Pingback: Super Healthy Nut & Seed Bread - Mom Kitchen Recipes HANNA December 9, 2019 at 11:03 am I’m very excited to try making a loaf! Just wondering, can I use molasses instead of
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the maple syrup? 🙂 Reply SARAH BRITTON December 10, 2019 at 3:52 pm Hi Hanna! Sure thing 🙂 The flavour with molasses would probably be quite interesting and delicious! I should also mention that you don’t need to add any sweetener at all. I just like the balance it creates. Hope you enjoy! Sarah B Reply DIANE December 4, 2019 at 12:16 am Obviously very different to ‘normal’ bread but, IMG, so delicious! Thank you for sharing this recipe. It’s a keeper! Reply HILLARY November 26, 2019 at 10:23 am I have made this so many times and it is always a hit! Adding pumpkin seeds is my favorite variation. It is SO easy to make and such a hit. Love it with some quality butter. Love it with greek yogurt, and love it plain! My one note is to mix everything in a bowl then pour into baking pan, and other than that this recipe is perfection. Question regarding amounts on this step: 4 Tbsp. psyllium seed husks (3 Tbsp. if using psyllium husk powder) is that 3 TBSP of Psyllium SEED husk powder, or just the psyllium husk powder? When using Seed Husk Powder should it still be 4 tbsp? I found both Psyllium husk powder and psyllium seed husk powder at my local Natural Grocers/Vitamin Cottage and bought the seed husk powder but was unsure about the amount. Also, can both seed husk powder and husk powder be used interchangeably? Thank you! Reply MONIQUE October 27, 2019 at 8:17 am Rather than use the silicone loaf pan, I use a Fat Daddio push pan . The round loaf is easily sliced into wedges, which I freeze for toasting straight from the freezer. The loaf slips right out of the push pan! Reply SARAH BRITTON October 29, 2019
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at 12:03 pm That’s great to hear, Monique! Thanks for sharing 🙂 xo, Sarah B Reply NILDA November 10, 2019 at 4:06 pm Do you know the approximate dietary value of this bread, such as carbs, calories, protein, etc? By the way, I made this bread and followed the recipe closely. It came out perfect. I do love it. Thanks!!! Reply BOBBI BUTLER January 2, 2020 at 9:12 pm yes I would like very much the nutritional break down since I am diabetic and have to keep check on carbs, fiber etc. LINDA REINER November 10, 2019 at 4:10 pm Am I reading the recipe correctly? When you remove the loaf after 20 minutes of baking, then turn upside down and place directly on the rack…not using a pan? Reply PIPER October 10, 2019 at 11:22 pm Hello! Just wanted to let you know I made this awesome loaf yesterday – but had no psyllium. It was an awesome success anyways 🙂 You actually can replace the psyllium with extra chia seeds. In moisture, they form a sort of gel-like substance. I used three extra tablespoons of chia – one tblspn I ground into powder and chucked in dry ingredients, then the other 2 I added whole to the wet ingredients first. I made the water hot to help the chia goo along – chucked in chia, honey and maple syrup and let stand until cool. I also added a tablespoon of Amaranth flour for density – it’s totally gluten free, and even better than quinoa in healthy content values. The bread held together amazingly well – my hubby even sliced it warm 😀 Absolutely love this recipe – thank you! – it’s going to be part of our staple diet from here on. We live on a boat, so
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all recipe ingredients need to be foreign country friendly and able to withstand long storage – this hits the sweet spot :)) Reply SARAH BRITTON October 21, 2019 at 3:38 pm Hey Piper! That is great to hear! Thank you for sharing 🙂 Your boating adventure sounds like a hoot – thrilled the Loaf can be on bard with you <3 xo, Sarah B Reply JULIA December 27, 2019 at 4:13 am Hi! I just came here to say I made this yesterday without psyllium and saw your post. It came out great. I ground some of the flax seeds and oats and they became very sticky, which held the whole thing together. Reply Pingback: Avocado and Egg Sandwich with Super Seed Bread | The Awesome Green JENNIFER October 3, 2019 at 9:20 pm Should all the nuts and seeds be raw? Reply PRIYANKA September 23, 2019 at 2:11 pm Hi. I tried it today and it came out very sticky. I din’t like it. I baked it for about 1hour and 10 minutes but still it was very gooey and sticky. What should I do please tell me. Reply ANGELIQUE September 18, 2019 at 8:15 pm Baked this and love it! Would it be possible to incorporate some mashed banana? I would love a nut/seed/banana loaf! Reply SARAH BRITTON October 7, 2019 at 9:39 am Hi Angelique, Try it! Maybe sub the oil and maple syrup…let us know how it turns out! xo, Sarah B Reply Pingback: Lebensverändernde Cracker – magentratzerl.de Pingback: Getoastetes Super Seed Power-Brot von Heather aus dem Yum Universe (Vegan, GF) - Rezepte JOSHUA HOWARD August 27, 2019 at 10:53 am Hi! I really like your recipes! Can’t wait to try this one! Reply DEBORA August 24, 2019 at 4:28 pm I’ve got this soaking as
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I type, and it just occurred to me…could the water be substituted with whey from yogurt making? Reply Pingback: The Best Breakfast Bread, Vegan & Gluten-Free - The Colorful Kitchen Pingback: Getoastetes Super Seed Power-Brot von Heather aus dem Yum Universe (Vegan, GF) - Rezepte >Blog KIERSTEN August 4, 2019 at 1:48 pm So this has been life-changing for us and for now I am month I’ve been making this bread every day or every two days. It has become staple. So I don’t want to use a silicone loaf pan, because I don’t really trust the silicon. I have been using parchment paper… But would love to find something that is non-stick and non-toxic. If anybody has any suggestions I’d love to hear them… Do you butter a glass pan? Do you use a stone ware? Do you have to butter or grease? what are your tips? Reply KATHY August 9, 2019 at 6:24 pm I used a glass pan. Oiled it with coconut oil and lined with parchment. It was a bit of trouble but worth it.. Reply JOAN R November 23, 2019 at 4:16 pm You do know that parchment paper is coated with silicone, right? Reply MARIA August 1, 2019 at 8:35 am Hello, I am working on a food-based approach for relieving constipation in my 9-yr old and we need to keep track of fiber intake each day. I would love to know (approximately) how many grams of fiber are in one slice of this bread. Anyone know? I’m following the original recipe for now. Reply LEE LEATHAM August 21, 2019 at 9:05 am I don’t know the answer but it raises the question which crossed my mind which is how big is the tablespoon? In UK it is the largest of the three at
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15ml but in USA I think it is the same as a UK dessertspoon at 10ml. And then is it a rounded or level spoonful, level being half the size of a rounded. I am making this bread for the first time using UK spoon size somewhere between level and rounded to my uncertainty Reply LAURIE August 27, 2019 at 10:46 pm Lee Leatham the measurements are not for “tablespoon/teaspoon” used on the dinner table but rather measuring spoon; we level them off unless it says something like “rounded tablespoon” then it would be just that. I hope this helps VERONICA THOMS December 17, 2019 at 7:32 pm My measuring size tablespoon is 20ml. JOAN SELIX BERMAN July 27, 2019 at 12:28 pm thank you so much for creating this recipe! since my cousin introduced me to this bread several years ago it has become true to its name… and our constant companion, carefully cut and frozen in our freezer for the perfect ready to eat breakfast each day! a friend of mine is GF and grain-free so i adjusted the recipe and now it’s her favorite too… if her husband doesn’t devour it before she has a chance. i love baking for our family and friends and it is always a cherished gift. my adjustments for GF and Grain-Free LCB replace the 1-1/2 cups oat flour with 2 cups Almond Flour (add 1/2 cup for best consistency) add DATES (an israeli friend of ours loved the bread and then suggested this addition… now i always make it with dates,) Raisins bake for 30 minutes in the pan, then flip over on the rack, just as you would the original recipe and bake 25 more minutes or until done. FABULOUS. thanks again so much. Reply CONNIE VAN RIJN November 2,
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2019 at 6:35 pm Thank for the grain free adjustment. The almond flour worked out very well. Cannot have dates or raisins so added walnuts and dried cranberries…absolutely gorgeous! Used a glass loaf pan with parchment paper and coconut oil…very successful. Reply ROSEMARY February 17, 2020 at 5:42 am I have just read your suggestions. However, the recipe calls for rolled oats, and you suggested replacing the “oat flour” with gr almonds. I wonder if the oats should be ground into a flour, as the recipe didnt say to do that. Reply Pingback: Vegan Nut and Seed Bread - Nourished By Nutrition Pingback: 10 Best Sources of Plant-Based Protein - Nourished By Nutrition Pingback: Flourless bread – Peter Helmstedt: the Man… the Enigma… the W@&#er… the Website Pingback: Flourless bread – Peter Helmstedt ALI June 22, 2019 at 5:14 pm I really want to try this recipe but I have intestinal issues and am concerned about using psyllium. I have seen many recipes for Nordic Stone Age bread that this recipe is based on and they all call for eggs as the binder. Aside from the cholesterol factor with eggs, is there another reason why you have chosen psyllium as a binder? I would rather not use eggs but it may be a choice between cholesterol or psyllium side effects in my case. Thank you. Reply DORAINE November 6, 2019 at 9:40 pm I can’t comment on the question of preferring psyllium v. eggs, but if you go with egg the pasture-raised eggs are significantly lower in cholesterol and are more nutrient dense by far than conventional eggs. Some people balk at the price; pastured eggs typically run from $4 to $7 per dozen. Personally I’d way rather spend more for eggs that taste way better, rather than spend more
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