Split (1)

train · 97.2k rows

instruction stringlengths 15 30k
When I have been in this situation, I have found it helpful to find someone else's implementation, and instrument it with print statements. It's not clear what langauge you are using, but it never hurts to get exposed to a new one anyway :). Take this example in C perhaps? https://github.com/h5p9sl/hmac_sha256/blob/ma...
I am a student in the process of creating a firewall circumvention program based on smuggling data inside of legitimate HTTP. I have limited cryptographic knowledge. I need a way to encrypt my higher-level protocol such that I get a random bytestream indistinguishable from random data that can then be disguised as i...
Fully-encrypted (non-fingerprintable) symmetric encryption algorithm?
1) For authenticated disk encryption, there are extra data such as IV or tag that need to be stored for all the alternative mods that are placed in Table 1. For these data, it will be necessary to use a sector other than the sector where the encrypted data is located. Consumed space by extra storage of tags or ...
I'm trying to implement HMAC SHA256 (I've implemented SHA256 successfully). I am trying to find examples where they show the results after each HMAC stage (XOR, append, H etc). Does anyone know of any resources which contain examples with the results from each step?
I am trying to understand how OpenSSL adds points on an elliptic curve. I have understood from [here](https://stackoverflow.com/questions/76712735/where-is-the-definition-of-add-located-in-openssl) that [ossl_ec_GFp_simple_add()](https://github.com/openssl/openssl/blob/a024ab984e540bff65d25407496c34b3567b55a7/crypto/ec...
Can anyone explain the algorithm that OpenSSL uses to add two points on an elliptic curve?
I want a family of efficiently computable random-ish bijections $f_{k,n} : [0..n) \to [0..n)$ for $n \le 2048$. We cannot make the $f_{k,n}$ be secure for encryption at this domain size of course, but I really only need the set $f_{k,n}\big( [0..n/3) \big)$ to be distributed somewhat randomly. In particular, those se...
I want a family of efficiently computable random-ish bijections $f_{k,n} : [0..n) \to [0..n)$ for $n \le 2048$. We cannot make the $f_{k,n}$ be secure for encryption at this domain size of course, but I really only need the set $f_{k,n}\big( [0..n/3) \big)$ to be distributed somewhat randomly. In particular, those se...
Actually, I'd advise you to reconsider the "shuffle $[0,n)$ solution; such a permutation table (packed) would fit in 2816 bytes (for $n \le 2048$); that's well within the L1 dcache on most non-lowend CPUs (and well within the L2 cache). And, I would personally suspect that a full cache miss (of both the L1 and the L2 ...
Actually, I'd advise you to reconsider the "shuffle $[0,n)$ solution; such a permutation table (packed) would fit in 2816 bytes (for $n \le 2048$); that's well within the L1 dcache on most non-lowend CPUs (and well within the L2 cache). And, I would personally suspect that a full cache miss (of both the L1 and the L2 ...
This is most likely a dumb question. I'm doing a mathematical research project that overflowed a bit into cryptography. It got me thinking about something. Can the following cryptosystem work? Let Alice and Bob share a private key $d$ using the Diffie Hellman key exchange, where $d\in \mathbb{F}_p$ for some prime $p...
What's the catch with this Diffie-Hellman based cryptosystem?
I am reading the paper [Pseudorandom Quantum States][1],where the following candidate was shown to be a Pseudorandom state, called the complex random phase state:\ $PRF_k:X → X$ be a keyed pseudorandom function where $X = \{0, 1, 2, . . . , N − 1\}$ and $N = 2^n$ with $n$ being the security parameter. The family of ps...
Let's temporarily work upon the assumption that proper KBKDF functions do not exist, for the sake of argument. Would keccak256 be a secure choice for a KBKDF that derives 256-bit keys from a 256-bit master secret $k$ with an arbitrary-length derivation path $p$? And is this true in general for hash functions that ha...
Is keccak256 (and similar hash functions) a suitable KBKDF for 256-bit keys?
Let's temporarily work upon the assumption that proper KBKDF functions do not exist, for the sake of argument. Would keccak256 be a secure choice for a KBKDF that derives 256-bit keys from a 256-bit master secret $k$ with an arbitrary-length derivation path $p$? And is this true in general for hash functions that ha...
I am reading the paper [Pseudorandom Quantum States][1],where the following candidate was shown to be a Pseudorandom state, called the complex random phase state:\ $\mathrm{PRF}_k:X → X$ be a keyed pseudorandom function where $X = \{0, 1, 2, . . . , N − 1\}$ and $N = 2^n$ with $n$ being the security parameter. The fam...
Let's temporarily work upon the assumption that proper KBKDF functions do not exist, for the sake of argument. Would keccak256 be a secure choice for a KBKDF that derives 256-bit keys from a 256-bit master secret $k_{256}$ with an arbitrary-length derivation path $p$? And is this true in general for hash functions t...
Let's temporarily work upon the assumption that proper KBKDF functions do not exist, for the sake of argument. Would keccak256 be a secure choice for a KBKDF that derives 256-bit keys from a 256-bit master secret $k_{256}$ with an arbitrary-length derivation path $p$? And is this true in general for hash functions t...
Let's temporarily work upon the assumption that proper KBKDF functions do not exist, for the sake of argument. Would keccak256 be a secure choice for a KBKDF that derives 256-bit keys from a 256-bit master secret $k_{256}$ with an arbitrary-length derivation path $p$? And is this true in general for hash functions t...
Let's temporarily work upon the assumption that proper KBKDF functions do not exist, for the sake of argument. Would keccak256 be a secure choice for a KBKDF that derives 256-bit keys from a 256-bit master secret $k_{256}$ with an arbitrary-length derivation path $p$? And is this true in general for hash functions t...
Do any parallelizable cryptographic hash algorithms that allow for quick—preferably constant-time—recalculation of a hash result upon updating a portion of the data input exist? I know that BLAKE3 is called "parallelizable", but a Merkle tree doesn't seem like it's what I'm looking for when the time taken to recalc...
I have several mathematical operations on binary numbers that are special cases of more general arithmetic operations. I am wondering whether there exist more specialized algorithms purpose-made for these edge cases that are faster than the general algorithm. Could someone point me to such algorithms if they exist?...
Special algorithms for edge cases of binary arithmetic?
I have several mathematical operations on binary numbers that are special cases of more general arithmetic operations. I am wondering whether there exist more specialized algorithms purpose-made for these edge cases that are faster than the general algorithm. Could someone point me to such algorithms if they exist?...
> If a hacker was to crack this cryptosystem, it would essentially be the same difficulty as cracking Diffie-Hellman, right? Well, the answer to that comes down to the meaning of "crack"; cryptographers give a different meaning to that then lay people do. What a cryptographer means by "crack" an encryption system...
The LWE assumption states that it is hard to distinguish LWE samples from uniformly distributed samples. That is, the distinction $(A,b)$ with $A$ and $b$ uniformly distributed, is hard to distinguish from $(A,b=As+e)$, where $A$, $s$ are uniformly distributed and $e$ follows a different distribution. However, in c...
> If a hacker was to crack this cryptosystem, it would essentially be the same difficulty as cracking Diffie-Hellman, right? Well, the answer to that comes down to the meaning of "crack"; cryptographers give a different meaning to that then lay people do. What a cryptographer means by "crack" an encryption system...
$\bullet$ What does private-key functional encryption mean? Or functional encryption in private-key setting?\ Wasn't functional encryption a generalization of public key encryption? So now, why do we have private-key functional encryption?! It's a little confusing.\ I've seen a few sentences in [Romain Gay][1]'s ...
It's studied Diffie-Hellman in (the multiplicative subgroup of the finite field $\mathbb F_p$, followed by encryption in $\mathbb F_p$. That is, appropriate prime $p$ and some $g\in\mathbb F_p$ are publicly agreed upon, e.g. the [3072-bit MODP Group of RFC 3526][1]. Then sending $x\in[0,p)$ from $A$ to $B$ goes: ...
It's studied Diffie-Hellman in the multiplicative subgroup of the finite field $\mathbb F_p$, followed by encryption in $\mathbb F_p$. That is, appropriate prime $p$ and some $g\in\mathbb F_p$ are publicly agreed upon, e.g. the [3072-bit MODP Group of RFC 3526][1]. Then sending $x\in[0,p)$ from $A$ to $B$ goes: -...
It's studied Diffie-Hellman in the multiplicative subgroup of the finite field $\mathbb F_p$, followed by encryption in $\mathbb F_p$. That is, appropriate prime $p$ and some $g\in\mathbb F_p$ are publicly agreed upon, e.g. the [3072-bit MODP Group of RFC 3526][1]. Then sending a confidential message $x\in[0,p)$ f...
The Pedersen hash is a low constraints friendly hash for Zk-Snarks. Unlike many algorithms, the Pedersen hash returns a point `P = (x,y)` on a curve as a hash. Depending on the selected curve, there can exist a fast deterministic way to compute a different input that yields `−P=(x,−y)` using the Weierstrass form...
Pedersen Hash : when truncating the hash to keep only the X coordinate, is it possible to compute a collision when the Babyjubjub curve is used?
I've developed an algorithm for fast modular exponentiation modulo composite numbers with known factorization. I'm not very well versed in cryptography, so I'm wondering if any of you know of an application of this algorithm to some cryptosystem. Even if there is no cryptosystem where this can be used, I'm also interes...
Let $r(b,t)$ denote the bitstring $b$ rotated to the left by $t$ bits: for example, $$r(00110101,5)=10100110.$$ Let $m(b_1,b_2,b_3)$ denote the [majority function](https://en.wikipedia.org/wiki/Majority_function): for example, $$m(10010111,00101110,10100000)=10100110.$$ Consider the following game. Player...
I have come across the TenSEAL tutorial on implementing homomorphic encryption (HE) and they mention the global_scale parameter. (https://github.com/OpenMined/TenSEAL/blob/main/tutorials/Tutorial%202%20-%20Working%20with%20Approximate%20Numbers.ipynb) global_scale: the scaling factor, here set to 2^40. I am st...
What is meant by the scaling factor in homomorphic encryption?
Why does TFHE/Concrete only support <8 Bit numbers?
From the [PLONK paper](https://eprint.iacr.org/2019/953.pdf). Page 18 > We describe an optimization by Mary Maller to reduce the number of F-elements in the proof from $M$. We begin with an illustrating example. Suppose $V$ wishes to check the identity $h1(X) \cdot h2(X) − h3(X) \equiv 0$. The compilation describ...
From the [PLONK paper](https://eprint.iacr.org/2019/953.pdf). Page 18 > We describe an optimization by Mary Maller to reduce the number of $F$-elements in the proof from $M$. We begin with an illustrating example. Suppose $V$ wishes to check the identity $h1(X) \cdot h2(X) − h3(X) \equiv 0$. The compilation descr...
0 I have two questions: 1. Can someone point me to some solution providing multi-party {t,n}-threshold ECDSA? 2. I imagine that such scehemes works first by creating an ECDSA private key then sharding it to n subkeys, t of which subkeys are required to generate the initial ECDSA private key. Am I r...
I have come across the TenSEAL tutorial on implementing homomorphic encryption (HE) and they mention the global_scale parameter. (https://github.com/OpenMined/TenSEAL/blob/main/tutorials/Tutorial%202%20-%20Working%20with%20Approximate%20Numbers.ipynb) global_scale: the scaling factor, here set to 2^40. I am st...
Relationship between the scaling factor and polynomial degree in homomorphic encryption?
Relationship between the scaling factor and polynomial degree in CKKS variant of homomorphic encryption?
The Pedersen hash is a low constraints friendly hash for Zk-Snarks. Unlike many algorithms, the Pedersen hash returns a point `P = (x,y)` on a curve as a hash. Depending on the selected curve, there can exist a fast deterministic way to compute a different input that yields `−P=(x,−y)` using the Weierstrass form or ...
Is it possible to get the negative point with −x in that version of the Pedersen hash over the BaybyJubJub curve?
I've been experimenting in python with different approaches to cryptographically secure pseudo random number generators, comparing them using the NIST testsuite implemented by https://github.com/InsaneMonster/NistRng/tree/master. My requirements are: * must be cryptographically secure, so its output is suitable as...
$\bullet$ What does private-key functional encryption mean? Or functional encryption in private-key setting?\ Wasn't functional encryption a generalization of public key encryption? So now, why do we have private-key functional encryption?! It's a little confusing.\ I've seen a few sentences in [Romain Gay][1]'s ...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with example. We will stick to standard (quadratic) multiplication, but will integrate modular reduction with the multiplication; that's the so-called interleaved modular reduction. It's not the [most commonly described][1...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with example. We'll make the example $7510\times 8431\times 2143\bmod9137$ for reasons in [comment][3], with operands in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with example. We'll make the example $7510\times 8431\times 2143\bmod9137$ for reasons in [comment][3], with operands in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\times 8431\times 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit ...
In general, I want to encourage experimentation like this, as long as you aren't using it in a production environment. Everyone needs to start somewhere, and playing with these sorts of toy constructs is a great way to learn. I don't want to discourage that. My biggest problem with your approach is that it doesn't a...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\times 8431\times 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit ...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\times 8431\times 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit ...
In general, I want to encourage experimentation like this, as long as you aren't using it in a production environment. Everyone needs to start somewhere, and playing with these sorts of toy constructs is a great way to learn. I don't want to discourage that. My biggest problem with your approach is that it doesn't a...
In general, I want to encourage experimentation like this, as long as you aren't using it in a production environment. Everyone needs to start somewhere, and playing with these sorts of toy constructs is a great way to learn. I don't want to discourage that. My biggest problem with your approach is that it doesn't a...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\times 8431\times 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit ...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\times 8431\times 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit ...
The Pedersen hash is a low constraints friendly hash for Zk-Snarks. Unlike many algorithms, the Pedersen hash returns a point `P = (x,y)` on a curve as a hash. Depending on the selected curve, there can exist a fast deterministic way to compute a different input that yields `−P=(x,−y)` using the Weierstrass form or ...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\times 8431\times 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit ...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\times 8431\times 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit ...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\times 8431\times 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit ...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\cdot 8431\cdot 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit or...
For the Substitution Cipher, for functions such as $$f(x) = x^k mod 26$$ or $$f(x) = x^k + k mod 26$$ (functions that consist of x^k), why do the values of k=5 or k=7 or k > 10 have one-to-one mapping? I know 5 and 7 are relatively prime to 26, however, what about 3 or 9? Also why do it map when k > 10?
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\cdot 8431\cdot 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit or...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\cdot 8431\cdot 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit or...
In this answer we study modular multiplications using Montgomery arithmetic, and illustrate it with the example $7510\cdot 8431\cdot 2143\bmod9137$, working in base $\beta=10$ because the question does. But we remain general, thus use _limb_ for _decimal digit_. In practice on a modern computer we could use $32$-bit or...
After reading that about "37% of the 256-bit outputs" of SHA-256 are unreachable when fed only 256-bit inputs [[1][1]] I'm curious & confused. The formula from the proof [here][2] considers a fixed "h-bit" input & output. How does this translate to the maximum number of internal states that are reachable within...
How much of SHA3's internal state can be reached?
> How does this translate to the maximum number of internal states that are reachable within SHA3? No, it does not. Remember, all the rate bits can be set to anything (by setting the next message block appropriately). So, the question is: given that the rate bits can be anything, are there any set of 'capacity...
> How does this translate to the maximum number of internal states that are reachable within SHA3? That depends on what you're asking. If you are considering only 256 bit inputs (which the SHA-256 question did), well, there will be precisely [1] $2^{256}$ states reached (which is far below the 37% value of SHA-25...
> How does this translate to the maximum number of internal states that are reachable within SHA3? That depends on what you're asking. If you are considering only 256 bit inputs (which the SHA-256 question did), well, there will be precisely [1] $2^{256}$ states reached (which is far below the 37% value of SHA-25...
I'm working on a system where I need to sign some data using an ECC private key and share the data and signature over a BLE ADV packet. Since an ADV packet is limited in space, I can't use a full ECDSA signature as the output is too large. As far as I understand, you can't readily truncate an ECDSA signature as you can...
$\bullet$ What does private-key functional encryption mean? Or functional encryption in private-key setting?\ Wasn't functional encryption a generalization of public key encryption? So now, why do we have private-key functional encryption?! It's a little confusing.\ I've seen a few sentences in [Romain Gay][1]'s ...
For the Substitution Cipher, for functions such as $$f(x) = x^k \pmod{26}$$ or $$f(x) = x^k + k \pmod{26}$$ (functions that consist of x^k), why do the values of k=5 or k=7 or k > 10 have one-to-one mapping? I know 5 and 7 are relatively prime to 26, however, what about 3 or 9? Also why do it map when k > 10?
Good morning, I've been struggling with this protocol for the last few days and I'm out of ideas now. The goal is to impersonate Bob by just modifying or dropping packages. The attacker(me) is a Proxy that is between the clients and the servers so any messages are first sent to me and I send relay them to the server...
Good morning, I've been struggling with this protocol for the last few days and I'm out of ideas now. The goal is to impersonate Bob by just modifying or dropping packages. The attacker(me) is a Proxy that is between the clients and the servers so any messages are first sent to me and I send relay them to the server...
``` print(tan(int.from_bytes(open("plain.txt", "rb").read().strip(), "big")).n(1024)) ``` Its sage code. How difficult or easy is it to recover the plaintext from the output of this code? I don't think the hash collision, or second preimage attack will be usefully unless we know the length of the plaintext. I...
We (collectively) salt passwords, then hash them; maybe even run them through something like PBKDF2 first (depending on how the password will be used). The end result is that we have a string `p` and map it to a fixed-length string `p'` using a surjective transformation with the property that it is difficult to find...
How certain is it that a shorter password can't match the salted hash of a long one?
There's a sister site, crypto.stackexchange.com, that might be better suited to answering your questions about the mathematical properties of hash functions. However, from a practical standpoint: > (Essentially, the attacker is brute forcing a hash collision, not guessing the actual password.) Strictly speaking t...
Let's suppose I have two 2GiB files and I want to encrypt them using One-time pad (Vernam cipher), but I don't want to store two big keys. May I use only one key for the two files if I encrypt the One-time pad key two times with a block cipher with two different keys for block cipher? I mean, take the One-time pad k...
May I use the same One-time pad key two times if I encrypt it with a block cipher using two different block cipher keys?
I have a congruential generator where $$ r_{n+1} = r_n^2 + c\;(mod\;p) $$ known $r_0$, $c$ and $p$ can i get $r_n$ without having to compute all the previous values?
Can I skip ahead with a quadratic congruential generator?
so recently I've been exploring zk-SNARKs algorithm, and I have a maybe stupid question. For example, let's take $x^2+x+1$ and make an algebraic circuit from it: 1) $y=x*x$ 2) $sum=x+1$ 3) $out=sum+y$ <em>(First question: are finite fields needed here?)</em> Now we need to construct a R1CS to each gate. Our v...
I have a congruential generator where $$ r_{n+1} = r_n^2 - c\;(mod\;p) $$ known $r_0$, $c$ and $p$ can i get $r_n$ without having to compute all the previous values?
I am currently trying to solve a training challenge based on AES with CBC. This is the infos I'm given: ``` KEY = "yn9RB3Lr43xJK2██".encode() IV = "████████████████".encode() msg = "AES with CBC is very unbreakable".encode() ``` Those spaces are unknown characters, and I also have the output: ``` c5██████████...
I am currently trying to solve a training challenge based on AES with CBC. This is the infos I'm given: ``` KEY = "yn9RB3Lr43xJK2██".encode() IV = "████████████████".encode() msg = "AES with CBC is very unbreakable".encode() ``` Those spaces are unknown characters, and I also have the output: ``` c5██████████...
In round 4, protocol evaluates `a(zeta), b(zeta), c(zeta), Sσ1(zeta), Sσ2(zeta)`. I know linearisation trick in round 5 implies the identity of other terms. Can we evaluate other term e.g. `Sσ1(zeta), Sσ3(zeta)` instead? Is there any consideration behind these selected terms in paper? ref: 1. PLONK paper: https://e...
The Pedersen hash is a low constraints friendly hash for Zk-Snarks. Unlike many algorithms, the Pedersen hash returns a point `P = (x,y)` on a curve as a hash. Depending on the selected curve, there can exist a fast deterministic way to compute a different input that yields `−P=(x,−y)` using the Weierstrass form or ...
We (collectively) salt passwords, then hash them; maybe even run them through something like PBKDF2 first (depending on how the password will be used). The end result is that we have a string `p` and map it to a fixed-length string `p'` using a surjective transformation with the property that it is difficult to find...
We (collectively) salt passwords, then hash them; maybe even run them through something like PBKDF2 first (depending on how the password will be used). The end result is that we have a string $p$ and map it to a fixed-length string $p'$ using a surjective transformation with the property that it is difficult to find...
\[originally posted on [security-SE][1]\] There's a sister site, crypto.stackexchange.com, that might be better suited to answering your questions about the mathematical properties of hash functions. However, from a practical standpoint: > (Essentially, the attacker is brute forcing a hash collision, not guessing th...
We (collectively) salt passwords, then hash them; maybe even run them through something like PBKDF2 first (depending on how the password will be used). The end result is that we have a string $p$ and map it to a fixed-length string $p'$ using a surjective transformation with the property that it is difficult to find...
\[originally posted on [security.SE][1]\] There's a sister site, crypto.stackexchange.com, that might be better suited to answering your questions about the mathematical properties of hash functions. However, from a practical standpoint: > (Essentially, the attacker is brute forcing a hash collision, not guessing th...
The quoted passage of the Wikipedia article <strike>is wrong</strike> does not at first reading seem to match Blowfish as in Bruce Schneier's _Description of a new variable-length key, 64-bit block cipher (Blowfish)_ ([in proceedings of the first FSE conference, held Dec. 1993][1]) which for this same operation reads: ...

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