instruction
stringlengths
15
30k
Alice has a master private key scalar $a$, with corresponding public key $A=aG$. $G$ is a well-known base point on the curve. Alice deterministically creates a new identity associated with a particular message $m$. She calculates the private key $b = HKDF_s(a, m)$, where $\operatorname{HKDF_s}$ means to use HKDF to ...
Alice has a master private key scalar $a$, with corresponding public key $A=aG$. $G$ is a well-known base point on the curve. Alice deterministically creates a new identity associated with a particular message $m$. She calculates the private key $b = HKDF_s(a, m)$, where $\operatorname{HKDF_s}$ means to use HKDF to ...
I asked [this question on StackOverflow][1] but it seems like it's more appropriate for this Crypto community. I am using the browser built in SubtleCrypto library in javascript to generate public and private keys as such: let keyPair = await crypto.subtle.generateKey( { name: "ECDSA", ...
JavaScript SubtleCrypto - Is there a way to convert the ECDSA keys into a more "portable" format and preferably shorter?
Are you aware of papers proposing secure multiparty computation protocols for stable matching problems such as [Stable Roommates](https://en.wikipedia.org/wiki/Stable_roommates_problem) and [Stable Marriage](https://en.wikipedia.org/wiki/Stable_marriage_problem) problems? Specifically, I would like the ranking of each...
Secure multiparty computation protocols for stable matching?
Suppose you have a message $m$ and you want to design a protocol that produces an encrypted message $c$ such that it cannot be decrypted before a certain time $t$ has passed from the encryption. How would you realize this? What assumptions do you need? I am just curious about it and I would like to discuss ideas...
Are you aware of papers proposing secure multiparty computation protocols for stable matching problems such as [Stable Roommates](https://en.wikipedia.org/wiki/Stable_roommates_problem) and [Stable Marriage](https://en.wikipedia.org/wiki/Stable_marriage_problem) problems? Specifically, I would like the ranking of ea...
I am reading the [`Lightweight Introduction to Lattices`](https://www.cryptool.org/download/ctb/CTB-Chapter_Lattice-Introduction_en.pdf) and it is a problem [Challenge 8](https://www.cryptool.org/download/ctb/CTB-Chapter_Lattice-Introduction_en.pdf#challenge.8) that makes me quite struggle. Basically, the problem give ...
I am reading the [`Lightweight Introduction to Lattices`](https://www.cryptool.org/download/ctb/CTB-Chapter_Lattice-Introduction_en.pdf) and it is a problem [Challenge 8](https://www.cryptool.org/download/ctb/CTB-Chapter_Lattice-Introduction_en.pdf#challenge.8) that makes me quite struggle. Basically, the problem give ...
Is this what you were looking for? [ Secure Stable Matching at Scale](https://eprint.iacr.org/2016/861) by Jack Doerner, David Evans, and abhi shelat.
I understand that we need 2-to-power cyclotomic ring to show that the solving decision RLWE is as hard as solving search RLWE. Is there any chance to prove it without 'cyclotomic' property? For example, in NTRU prime, using Z[x]/(x^p-x-1), can we show worst case reduction from LWE?
There is much more structure to this problem than a generic substitution cipher, and consequently much more that can benefit an attacker. As this is for the purposes of an exercise, I shall only suggest lines of enquiry rather than a complete answer. Please do ask for additional help if required. In the meantime, pleas...
I'm Trying to create a zk-proof of a neural network in [https://github.com/berendjan/zk-neural-network](https://github.com/berendjan/zk-neural-network) using [ZoKrates](https://zokrates.github.io) and PyTorch. The steps to reproduce are in the README.md However when computing the witness I run into errors ```bash ...
What are the computational limitations of ZkProofs using ZoKrates?
Since this is a survey, I assume that the submissions do not need to be publicly verifiable. A simple approach you can use is Verifiable Oblivious Pseudorandom Functions ([VOPRF][1]). This is the technique behind the [Privacy Pass][2] protocol. The conductor of the survey publicly publishes a (private, public) EC...
There are two papers that propose oblivious transfer protocols, both claiming to be universally composable (UC). The first protocol is more complex, and I am convinced that it is indeed UC. The second protocol is simple, but reminds me of the so-called "simplest OT protocol" of Chou and Orlandi, which is well-known to ...
Claims about universally composable oblivious transfer, which ones are correct?
I found [information][1], that it is **possible to construct a hash and signature that look valid** if the hash is not computed within the contract itself (we are talking about ECDSA/ecrecover here). So, the task is to construct a hash + v, r, s that would resolve to a particular address using ecrecover(). I have ac...
Imagine this scenario: * On a particular PC is a service that provides cryptographic functions -- in particular AES-CBC and ECC (ECIES/ECDSA). * The service provides access to a single key stored in an HSM -- the key itself is never visible to any software on the PC (including the service itself). * Copying the serv...
In lemma4.5, it says that we can construct a polynomial protocol P* with an S-ranged polynomial protocol P. However, in my opinion, I think it constructed P using P* in the proof. Specifically, in the last step of the construction, the verifier queries the identity of a polynomial(not in a range S), so it is invoking...
Suppose it is an Army Enigma I. Choose a reflector from UKW-B or UKW-C and choose three rotors from I, II, III, IV and V. For each of the 120 reflector/rotors permutations, there are 17,576 starting indicator positions to test. Menu ---- Ciphertext $\tt RRHKJ \ KNJXE \ UWNFO \ T$ has 16 characters. Crib $\tt WET...
Summary: The operation of the Enigma Bombe is well documented. I manage to use it and a candidate checking machine to recover the plugboard pairs and the ring setting for the fast rotor. I struggle to recover ring settings for the slow and the middle rotors. Question: Where can I find out more technical details on t...
This is a followup to my recent question [https://crypto.stackexchange.com/questions/106513/discrete-logarithm-challenges-and-records][1]. I am interested in confirming my understandings from the answer to that question, stated below: 1. For a discrete logarithm problem in a generic group of size $N$ with no sp...
I'm trying to create a zk-proof of a neural network in [https://github.com/berendjan/zk-neural-network](https://github.com/berendjan/zk-neural-network) using [ZoKrates](https://zokrates.github.io) and PyTorch. The steps to reproduce are in the README.md However, when computing the witness I run into errors ```bash...
In the [NIST 800-56A rev3][1] "Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography" in section 6.1.1.2 "(Cofactor) Full Unified Model, C(2e, 2s, ECC CDH) Scheme" the shared secret is calculated as follows: Party U Calculates: 1. $Z_s = d_{s,U} Q_{s,V}$ 1. $Z_e = d_{e,U} Q...
Why NIST 800-56A rev3 does not use cross secret calculation in C(2e, 2s, ECC CDH) scheme?
There is a random scalar seed $s$ which we may call a master secret. There are 2 public strings or scalars: $m1, m2$ and 2 corresponding EC keypairs: $a, A=a*G$ and $b, B=b*G$ $a$ and $b$ are somehow securely derived from $(s, m1)$ and $(s, m2)$ respectfully. It might be $a = HKDF(s, m1)$ or $a = s + m1$, or s...
This is a followup to my recent question [https://crypto.stackexchange.com/questions/106513/discrete-logarithm-challenges-and-records][1]. I am interested in confirming my understandings from the answer to that question, stated below: 1. For a discrete logarithm problem in a generic group of size $N$ with no sp...
Suppose it is an Army Enigma I. Choose a reflector from UKW-B or UKW-C and choose three rotors from I, II, III, IV and V. For each of the 120 reflector/rotors permutations, there are 17,576 starting indicator positions to test. Menu ---- Ciphertext $\tt RRHKJ \ KNJXE \ UWNFO \ T$ has 16 characters. Crib $\tt WET...
No. CBC decryption has a neat feature that allows recovery from errors. [![enter image description here][1]][1] Not having the IV is essentially an error and only corrupts the first block. So if an attacker decrypts using an all zero IV, they don't get the first block (since they don't know the secret IV to XOR it ...
No. CBC decryption has a neat feature that allows recovery from errors. [![enter image description here][1]][1] Not having the IV is essentially an error and only corrupts the first block. So if an attacker decrypts using an all zero IV, they don't get the first block (since they don't know the secret IV to XOR it ...
No. CBC decryption has a neat feature that allows recovery from errors. [![enter image description here][1]][1] Not having the IV is essentially an error and only corrupts the first block. So if an attacker decrypts using an all zero IV, they don't get the first block (since they don't know the secret IV to XOR it ...
No. CBC decryption has a neat feature that allows recovery from errors. [![enter image description here][1]][1] Not having the IV is essentially an error and only corrupts the first block. So if an attacker decrypts using an all zero IV, they don't get the first block (since they don't know the secret IV to XOR it ...
No. CBC decryption has a neat feature that allows recovery from errors. [![enter image description here][1]][1] Not having the IV is essentially an error and only corrupts the first block. So if an attacker decrypts using an all zero IV, they don't get the first block (since they don't know the secret IV to XOR it ...
No. CBC decryption has a neat feature that allows recovery from errors. [![enter image description here][1]][1] Not having the IV is essentially an error and only corrupts the first block. So if an attacker decrypts using an all zero IV, they don't get the first block (since they don't know the secret IV to XOR it ...
I recently started to learn about Shamir secret sharing and [Feldman's VSS Scheme][1]. I know the concepts But I can't figure out how it works. mostly because many of modulates are with "p" and some of them are with "q". I can't find a good sample that helps me understand it better. here's the example I am working ...
Let's say there's Alice and Bob. 1. Let Alice and Bob agree on a message $M_1$, a tag $T_1$, and a function $HMAC$. 2. Alice proves to Bob that she knows a key $K$ such that $T_1 = HMAC(M_1, K)$ without revealing what $K$ is, using a zero knowledge proof. 3. Alice sends Bob some cryptographic object $MysteryBox$. 4...
This is a rather simple question, but answers are nowhere to be found. Are there any variants of Poly-n hsahing algorithms which provide bigger outputs (like 32 instead of 16 bytes)? Or, is there any research which discusses the variability of the constant $2^{130}+5$, why this number is special or whether there are ot...
Poly1305 variants with bigger output?
This is a rather simple question, but answers are nowhere to be found. Are there any variants of Poly-n hsahing algorithms which provide bigger outputs (like 32 instead of 16 bytes)? Or, is there any research which discusses the variability of the constant $2^{130}+5$, why this number is special or whether there are ot...
I'm working on solving a encryption task, and I'm a bit stuck. I want to clarify that I'm only seeking hints and not direct answers since I want to solve it myself. The goal is to solve it on my own; otherwise, it wouldn't make sense. Therefore, I'm just looking for hints to help me progress from where I'm stuck or any...
This is a rather simple question, but answers are nowhere to be found. Are there any variants of Poly-n hsahing algorithms which provide bigger outputs (like 32 instead of 16 bytes)? Or, is there any research which discusses the variability of the constant $2^{130}-5$, why this number is special or whether there are ot...
I'm working on solving a encryption task, and I'm a bit stuck. I want to clarify that I'm only seeking hints and not direct answers since I want to solve it myself. The goal is to solve it on my own; otherwise, it wouldn't make sense. Therefore, I'm just looking for hints to help me progress from where I'm stuck or any...
Let's start with what got me wondering about this issue: It's a curious construction, that while most digital signature schemes come from public-key encryption (Impagliazzo's cryptomania), there are constructions like SPHINCS that construct secure signature out of a hash function (Impagliazzo's minicrypt). Now ther...
No. CBC decryption has a neat feature that allows recovery from errors. [![enter image description here][1]][1] Not having the IV is essentially an error and only corrupts the first block. So if an attacker decrypts using an all zero IV, they don't get the first block (since they don't know the secret IV to XOR it ...
eprint.iacr.org/2019/953.pdf In lemma4.5, it says that we can construct a polynomial protocol P* with an S-ranged polynomial protocol P. However, in my opinion, I think it constructed P using P* in the proof. Specifically, in the last step of the construction, the verifier queries the identity of a polynomial(not in ...
In lemma4.5, of [PlonK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge][1] they claim that we can construct a polynomial protocol $P^*$ with an $S$-ranged polynomial protocol $P$. However, in my opinion, I think it constructed $P$ using $P^*$ in the proof. Specifically, ...
I encountered a question while reading an article. My understanding is that fully homomorphic encryption supports ciphertext addition and multiplication. Why does the basic protocol given in this article include ciphertext subtracted by plaintext? [![enter image description here][1]][1] [1]: https://i.stack.img...
Let `E` be an elliptic curve of prime order `n`. If we assume that Alice and Bob both know a scalar value `z`, is there a known zero-knowledge protocol (ideally a Sigma protocol) that allows Bob to convince Alice that he knows some point `R` such that `zR` satisfies some equation? The context of this is as follows....
Is there a ZKP that proves knowledge of a particular elliptic curve point?
Since this is a survey, I assume that the submissions do not need to be publicly verifiable. A simple approach you can use is Verifiable Oblivious Pseudorandom Functions ([VOPRF][1]). This is the technique behind the [Privacy Pass][2] protocol. The conductor of the survey publicly publishes a (private, public) EC...
Since this is a survey, I assume that the submissions do not need to be publicly verifiable. A simple approach you can use is Verifiable Oblivious Pseudorandom Functions ([VOPRF][1]). This is the technique behind the [Privacy Pass][2] protocol. The conductor of the survey publicly publishes a (private, public) EC...
Suppose it is an Army Enigma I. Choose reflector UKW-B or UKW-C. Choose three rotors from I, II, III, IV and V. For each of the 120 reflector/rotors permutations, there are 17,576 starting indicator positions to test. Menu ---- Ciphertext $\tt RRHKJ \ KNJXE \ UWNFO \ T$ has 16 characters. Crib $\tt WETTE \ RVORH...
I'm learning OQS OpenSSL and I'd like to create a certificate with dilithium in C, using liboqs and OQS OpenSSL. This is my code (based on https://stackoverflow.com/questions/256405/programmatically-create-x509-certificate-using-openssl and a lite bit of chagpt): ```c #include <stdio.h> #include <stdlib.h> #inclu...
I am looking for references for the most basic secret sharing and MPC arithmetic algorithms for generic rings or prime fields. Problem: >Suppose there are $m$ parties $P_1, \ldots, P_m$ which wish to do arithmetic over a ring. > >They hold some secret shared values $[x], [y]$ and they wish to compute $[x+y]$ and ...
I am looking for references for the most basic secret sharing and MPC arithmetic algorithms for generic rings or prime fields. Problem: >Suppose there are $m$ parties $P_1, \ldots, P_m$ which wish to do arithmetic over a ring. > >They hold some secret shared values $[x], [y]$ and they wish to compute $[x+y]$ and ...
I have been wondering if sending audio fragments over a phone call would be considered a form of cryptology. Let's say that you own two mobile phones and say that one of your phones is one the Verizon network and the other is on the AT&T network. You have a friend who also owns two mobile phones. Say that one of hi...
Would sending audio fragments over a phone call be considered a form of cryptology?
I have been wondering if sending audio fragments over a phone call would be considered a form of cryptology. Let's say that you own two mobile phones and say that one of your phones is on the Verizon network and the other is on the AT&T network. You have a friend who also owns two mobile phones. Say that one of his...
I'll take that challenge for Kyber, but I fear that a simplification of Dilithium could more easily lead to a dangerous understanding. I'm going to describe a cryptographic design, **mini-Kyber**, that is closely related to Kyber, but before that I'm going to have to describe a few new ways of doing sums. ### Clo...
This is a rather simple question, but answers are nowhere to be found. Are there any variants of Poly-n hashing algorithms which provide bigger outputs (like 32 instead of 16 bytes)? Or, is there any research which discusses the variability of the constant $2^{130}-5$, why this number is special or whether there are ot...
I have been wondering if sending audio fragments over a phone call would be considered a form of cryptology. Let's say that you own two mobile phones and say that one of your phones is on the Verizon network and the other is on the AT&T network. You have a friend who also owns two mobile phones. Say that one of his...
[![Use of a hash function for message authentication][1]][1] [1]: https://i.stack.imgur.com/EO8Et.png In this picture we have a use of a hash function for message authentication. M is plaintext message. H is hash function. E is encryption block with K symmetric key. || is concatenation of plaintext M with ...
Yes, it's starting to be. You're starting along the lines of a manual version of [Frequency Hopping Spread Spectrum][1] techniques. You're using phones in this case, whereas in reality radios would be used. But the effect is the same, and is used for both civilian and military applications. Now imagine instead o...
What are the software tools used for customizing secret sharing and network steganography, which can be used for enhancing secret data transmission?
I'm trying to understand how its represented a ciphertext of CKKS in memory, or the data structure. Here is what I understand, correct me if I'm wrong. I also add some questions. 1. To start with, given a polynomial degree N and and a coefficient modulus, say {60, 40, 40, 60}. This means that the encoding...
Is it possible to forge a RSA signature with a known public key, hardcoded padding, and unlimited oracle information?
One of the kind of attacks that we are trying to prevent here with such mechanisms is called "[Key Compromise Impersonation][1]", where a party **obtained your private key** (not the other party's) and is trying to _impersonate other parties to you_. Now, I'll try to tackle your different questions in a different or...
I am reviewing the ZKP course, represented by the university of Berkley (https://zk-learning.org/). In pages 41 and 42 of lecture 6 that is attached below (https://zk-learning.org/assets/lecture6.pdf), the instructor explains the Poly-commitment based on Bulletproofs scheme. He uses an example for a polynomial with deg...
In this [paper](http://compneuro.uwaterloo.ca/files/publications/voelker.2017.pdf), they shortly introduced how to uniformly sample points from the n-sphere. The points of n-sphere consist with normal variables. My question is .. 1. If I samlpe coefficients of ring using normal distribution, what is differenc...
1. What do you mean by a ring in this context? 2. We prove the general case of the $n$-sphere. We note that the probability density function of an $n$-fold Gaussian distribution is given by $$\frac1{(2\pi)^{n/2}}\exp(-x_1^2/2)\exp(-x_2^2/2)\cdots\exp(-x_n^2/2)=\frac1{(2\pi)^{n/2}}\exp\left(-(x_1^2+x_2^2+\cdots +x_n...
1. What do you mean by a ring in this context? 2. We prove the general case of the $n$-sphere. We note that the probability density function of an $n$-fold Gaussian distribution is given by $$\frac1{(2\pi)^{n/2}}\exp(-x_1^2/2)\exp(-x_2^2/2)\cdots\exp(-x_n^2/2)=\frac1{(2\pi)^{n/2}}\exp\left(-(x_1^2+x_2^2+\cdots +x_n...
Normally, when computing an EC threshold dkg, i have all parties reveal a commitment to the public key, and only reveal their own public key after verifying the commitments. Otherwise it's trivial to produce a public key that gives one member control. In a 2 party, for example, one can just wait for the other's publ...
Normally, when computing an EC threshold DKG, I have all parties reveal a commitment to the public key, and only reveal their own public key after verifying the commitments. Otherwise it's trivial to produce a public key that gives one member control. In a 2 party, for example, one can just wait for the other's publ...
I've used OpenSSL to generate an RSA-PSS keypair. ``` -----BEGIN PRIVATE KEY----- MIIBUgIBADALBgkqhkiG9w0BAQoEggE+MIIBOgIBAAJBAKjJmhflBebbRJt0JNWe elk9w32jGxvZrvxO7kdpvNFWCgXIXSU0zC26R2Rca1w81sY4MpKfKl0baIK06Dbp F6cCAwEAAQJANfamrocJeQKXj7/1WtrdMRT/IHb6XtAdEwvFQM28kYyUU4QuIxGO cJ90rX99FdhOouUtbeYVXfnR7+I4NL6C+QI...
May RSA-PSS DB MSB be 1?
An Elgamal-like bit commitment scheme:\ Let $\langle g \rangle$ be a group of order $n$, where $n$ is a large prime.\ Let $h\in_{R}\langle g \rangle\setminus\{1\}$ denotes a random group element such that $\log_{g} h$ is not know to any party, neither the sender nor the receiver.\ $commit(u,x):=(g^{x},h^{u+x})$, whe...
This might be a stupid question, so bear with me. I was wondering if LLM embeddings can be used to anonymize input text. I couldn't find any information online that says that embeddings can be 1:1 decoded back to the original text. An example: A user wants to check some metadata about a query with an external A...
I'll use [PKCS#1v2.2][1] (RSA Laboratories edition) as a reference. Looking a the [private key with an ASN.1 decoder][4], the public modulus $n$ is 512-bit, thus in [RSASSA-PSS-VERIFY][2] we have $modBits\,=\,512$, $k=64$. Thus in [EMSA-PSS-VERIFY][3] we have $emBits\,=\,modBits\,-\,1\,=\,511$. $EM$ is the questi...
I'll use [PKCS#1v2.2][1] (RSA Laboratories edition) as a reference. Looking a the [private key with an ASN.1 decoder][4], the public modulus $n$ is 512-bit, thus in [RSASSA-PSS-VERIFY][2] we have $modBits\,=\,512$, $k=64$. Thus in [EMSA-PSS-VERIFY][3] we have $emBits\,=\,modBits\,-\,1\,=\,511$. $EM$ is the questi...
I'll use [PKCS#1v2.2][1] (RSA Laboratories edition) as a reference. Looking a the [private key with an ASN.1 decoder][4], the public modulus $n$ is 512-bit, thus in [RSASSA-PSS-VERIFY][2] we have $modBits\,=\,512$, $k=64$. Thus in [EMSA-PSS-VERIFY][3] we have $emBits\,=\,modBits\;-\,1\,=\,511$. $EM$ is the questi...
I'll use [PKCS#1v2.2][1] (RSA Laboratories edition) as a reference. Looking a the [private key with an ASN.1 decoder][4], the public modulus $n$ is 512-bit, thus in [RSASSA-PSS-VERIFY][2] we have $modBits\,=\,512$, $k=64$. Thus in [EMSA-PSS-VERIFY][3] we have $emBits\,=\,modBits\;-\,1\,=\,511$. &nbsp;$EM$ is the ...
I'll use [PKCS#1v2.2][1] (RSA Laboratories edition) as a reference. Looking a the [private key with an ASN.1 decoder][2], the public modulus $n$ is 512-bit, thus in [RSASSA-PSS-VERIFY][3] we have $modBits\,=\,512$, $k=64$. Thus in [EMSA-PSS-VERIFY][4] we have $emBits\,=\,modBits\;-\,1\,=\,511$. &nbsp;$EM$ is the ...
I'll use [PKCS#1v2.2][1] (RSA Laboratories edition) as a reference. Looking a the [private key with an ASN.1 decoder][2], the public modulus $n$ is 512-bit, thus in [RSASSA-PSS-VERIFY][3] we have $modBits\,=\,512$, $k=64$. Thus in [EMSA-PSS-VERIFY][4] we have $emBits\,=\,modBits\;-\,1\,=\,511$. &nbsp;$EM$ is the ...
I'll use [PKCS#1v2.2][1] (RSA Laboratories edition) as a reference. Looking a the [private key with an ASN.1 decoder][2], the public modulus $n$ is 512-bit, thus in [RSASSA-PSS-VERIFY][3] we have $modBits\,=\,512$, $k=64$. Thus in [EMSA-PSS-VERIFY][4] we have $emBits\,=\,modBits\;-\,1\,=\,511$. &nbsp;$EM$ is the ...
If there was a not generally unknown shortcut to doing this it would imply either a new serious weakness in AES or in the implementation of CBC on `openssl`. If you knew the IV you could decrypt block by block. To do this you would have had to have supplied the IV yourself. See openssl man page [here][1] >CBC by...
It's asked a theoretical approach, thus I'll suppose the question is not about using existing tools (which would be off-topic), but rather assume custom code. The general sketch is to test candidate passwords by 1. Turning a password into an 256-bit AES key. 2. Testing that key against a portion of the file correspon...
It's asked a theoretical approach, thus I'll suppose the question is not about using existing tools as in [this answer][1], which would be off-topic; but rather I'll assume custom code for the password recovery. The general sketch is to test candidate passwords, approximately from most to least likely, by 1. Turning t...
I'll use [PKCS#1v2.2][1] (RSA Laboratories edition) as a reference. Looking a the [private key with an ASN.1 decoder][2], the public modulus $n$ is 512-bit, thus in [RSASSA-PSS-VERIFY][3] we have $modBits\,=\,512$, $k=64$. Thus in [EMSA-PSS-VERIFY][4] we have $emBits\,=\,modBits\;-\,1\,=\,511$. &nbsp;$EM$ is the ...
It's asked a theoretical approach, thus I'll suppose the question is not about using existing tools as in [this answer][1], which would be off-topic; but rather I'll assume custom code for the password recovery. The general sketch is to test candidate passwords, approximately from most to least likely, by 1. Turning t...
Pretty new to ECC Pairings. I am trying to understand KZG Commitments from multiple sources. I found this [blog][1] beginner friendly and easier to understand. However, I'm stuck at ECC Pairings and having difficulty in order to completely understand it. The blog mentioned: > - Input: 2 points ($P$ and $Q$) on 2 ...
How to find second subgroup for ECC Pairing?
I'll use [PKCS#1v2.2][1] (RSA Laboratories edition) as a reference. Looking a the [private key with an ASN.1 decoder][2], the public modulus $n$ is 512-bit, thus in [RSASSA-PSS-VERIFY][3] we have $modBits\,=\,512$, $k=64$. Thus in [EMSA-PSS-VERIFY][4] we have $emBits\,=\,modBits\;-\,1\,=\,511$. &nbsp;$EM$ is the ...
An Elgamal-like bit commitment scheme:\ Let $\langle g \rangle$ be a group of order $n$, where $n$ is a large prime.\ Let $h\in_{R}\langle g \rangle\setminus\{1\}$ denotes a random group element such that $\log_{g} h$ is not know to any party, neither the sender nor the receiver.\ $commit(u,x):=(g^{u},h^{u+x})$, whe...
In some paper of lattice based cryptography, the matrix norm symbol $||.||_{2}$ is used. Like in paper "Fully Key-Homomorphic Encryption, Arithmetic Circuit ABE, and Compact Garbled Circuits"[\[BGG+'Eurocrypt2014\]][1]. This is a part of preliminaries section:\ PICTURE: [![enter image description here][2]][2] END OF...
Consider a system in which DES is used to encrypt messages in which the first three plaintext Bytes are known by the attacker. How many encrypted messages is it necessary intercept to be reasonably sure of identifying the key used for encryption? I thought about this, but I am not sure: Probability that plainte...
How many ciphertexts should attacker intercepts if he only knows the first 3 bytes of plaintext of each one?
**TL;DR:** Why is there a static-static diffie hellman in the Noise_IK handshake? ______________ Hi, I am currently trying to understand the WireGuard VPN protocol. As you may know, it uses the Noise_IK handshake from the Noise Protocol Framework. This handshake uses two ephemeral-static diffie hellman operat...
Why is static-static diffie hellman needed in Noise_IK?