instruction stringlengths 32 27.2k |
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Say party A wants to prove that it has seen the entirety of a public, big message m. Providing the hash of m is not good enough, because a third party could provide A with the hash. IIUC, signing the message with A's private key would be in principe ok, but most/all signature schemes work by first hashing m, so then ag... |
I run an open source project implementing some RipeMD and SHA hashes, one day I got nerdy and threw together my own Sponge function. I have now tested it with the dieharder 3.31.1 test suite. Is it acceptable to use as an PRNG for cryptography? This is the results:
> dieharder -a -f IdeaProjects/angelos-project-crypt/s... |
When a modulo is 0, the result of squaring or multiplying modulo will always be 0 as well. Therefore the loop could break and return 0.
It can be a mean to compute faster the result of square and multiply modular exponentiation at a negligible cost of comparing the modulo to 0.
Perhaps, using large prime numbers like f... |
this is my first question.
I've been into classical cryptography for about a year or so, but I am getting started with cryptanalysis of these ciphers. I am trying to figure out how to reconstruct the Polybius square when performing a known-plaintext attack on the Bifid. Can you all help me out when it comes to this?
|
I developed an application that stores large files. Those files are stored in plain text. Now the project owner wants those files be encrypted on storage, he wants confidentiality, integrity, and authenticity.
The application is written in C# using .NET Framework 4.8. There are no authenticated encryption stream cypher... |
Suppose that $k$ is the key for a block cipher. I am interested in the security of key schedules of the form $(k_0,\dots,k_n)$ where $k=k_0$ and $k_{j+1}=A_jk_j+b_j$ where each $A_j$ is some constant invertible matrix and $b_j$ is a constant vector and where $k_0=k_n$ so that the final round key is the original key. In... |
I have an assignment where I have to understand a protocol proposed in a research paper. The first step involves computing Per-XOR, but I can't seem to understand the explanation given. Below is the explanation given, along with solved question:
"Permute (transposition) the string ‘’ according to
the string ‘’, by chec... |
In the spirit of Are curve secp256k1 ECDSA signatures distinguishable from random data?
Are RSA signatures distinguishable from random data?
What if you don't know the message?
What if you have many common datasets you can do analysis across?
|
I'm trying to understand a protocol proposed in a research paper. There is a step that involves computing inverse Per-XOR. The explanation along with solved example is given below:
"Perform inverse permutation in a sequential manner to get the
concealed string ‘’. For inverse permutation, we use one
pointer/indexer () ... |
There exist two such question but I have noticed my question is fundamentally different as it asks for mapping between two different curves, rather two different prime field like this.
Given a finite field $\mathbb{F}_{103}$ we have two elliptic curves defined over it. The equations of the curves are $y^2 =x^3$ and $y^... |
I'm working on a secret sharing scheme and facing a challenge in detecting cheaters among the shareholders. Here's the setup:
There's a decoder $D$, a set of $2T$ shareholders, and a combiner/detective $C$.
Within the set of shareholders, there are $T$ known cheaters.
The combiner can provide the decoder with any secr... |
Sometimes if we have an attacker who's able to solve decision-LWE problem then we can use them (as a sub-routine) to solve (search) LWE problem, i.e., $\mathsf{sLWE} \leq \mathsf{dLWE}$.
Conversely, sometimes if we have an attacker who's able to solve (search) LWE problem then we can use them (as a sub-routine) to sol... |
Assuming we have fixed pairing friendly elliptic curve groups $G_1$, $G_2$ and $G_T$ where for $a \in G_1$ and $b \in G_T$ it holds $e(a,b) \in G_T$.
Let's put some more context and we are working in bls12-381. what is a standard way to compute $e(a,b)*r$, where r is a random bit string. Putting in another way how do ... |
I would like to find the fastest way to derive G for secp256k1 and secq256k1 curves, does anyone know the method, equation?
Edit:
I'm interested to know how can this happen, when we use n/2 of secp256k1 we would get this as our x coordinate
0x3b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63
However, half of the secq256k1 gro... |
Suppose that $F: \{0,1\}^n\times \{0,1\}^n\rightarrow \{0,1\}^n$ is a strongly pseudorandom permutation. Let $\hat{F}(k,x):=F(k,k)\oplus F(k,x)$. I know that $\hat{F}$ can't be a strongly pseudorandom permutation. How to prove that $\hat{F}$ is a normal PRP? This is the problem 6.20 in the joy of cryptography.
I want ... |
Good afternoon! I'm trying to write a code for a lattice based scheme (based on the SIS problem).
I'm looking for a library that may help me in this task without taking care of the implementation of the trapdoor generation's algorithm. Moreover, I'm searching for a method helpful to set the SIS parameters according to... |
is there an encryption algorithm where no key is wrong, but only one key is right?
essentially, if I encrypt some data with key X, any random "key" can "decrypt" the text, but using a random key essentially returns some random rata, and not the actual data that was encrypted using the key X.
The objective is essentiall... |
I am working with point addition and scalar multiplication on the secp256k1 curve for points $(x,y)$ or public keys to derive the next public key scalar k times further from it. Actually when I use a larger scalar then it loops back due to the cyclic nature of curve or arithmetic operations. I want such a way to stop i... |
Finally caving and asking for help...I'm not in the field, just doing random CTF challenges to learn more and I've really been enjoying it in general. However, I'm totally stuck on this puzzle at the moment. If you see the answer, please don't tell me but please just give a bit of a hint or something.
Here's what I kno... |
Are there situations currently where a PRNG just will not do? Are there current situations where only a TRNG will be useful?
What about if someone uses a cryptographically secure PRNG?
What is the biggest use case (in terms of magnitude) for a TRNG that a PRNG can't solve.
|
Some protocols employ ephemeral ECC key exchanges throughout the session. Such as the Noise framework.
Is the rationale to do this simply because you can do it efficiently?
To provide future secrecy wouldn't all you need is a simple hash function to ratchet the symmetric encryption key?
Seems like the only value for re... |
I am using the NIST suite to test the randomness of binary numbers and I have a 64KB dataset. I am confused with the results in finalAnalysisReport.txt.
I have the following questions:
does the test pass only if there is no "*" in both "p-value" and "proportion" columns?
example:
12
5
7
3
5
4
5
3
4
2
0.108791
45/... |
The problem
Let the following function be a collision reisistant hash function
$$H=\{H_s:\{0,1\}^{2n} \rightarrow \{0,1\}^{n} \}$$
Let the following function be a PRG
$$G:\{0,1\}^{n+1} \rightarrow \{0,1\}^{2n}$$
Is the following costrunction a collision resistant hash function?
$$H^*(x) = H_s(G(x))$$
My solution
My int... |
In DES encryption, the IP table is shown. If the input
given in hexadecimal is "0020 0940 0000 F008", which
are the bit positions of "1" after the IP stage ?
|
How good is blake3 for generating pseudo-random bitstrings in comparison to a random oracle?
Let's say we generated an arbitrarily long pseudo-random bitstring by concatenating blake3 hashes together in the following manner:
blake3(seed) || blake3(seed + 1) || blake3(seed + 2) || ... || blake3(seed + n)
How good (in t... |
I have implemented the following code for SHA3-224 which uses "shortmessage" in bit oriented mode, the message length is 47 bits and I am not able to get correct message digest which is supposed to be "6a1cdc94a6d676d598d7dd51be9461598bd931b6a8c45d6b34dfa6bb":
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
... |
I was reading CRYSTALS-Kyber design. They have used compress_q(x,d) to scale an element of $\mathbb{Z}_q$ to $[ 0,1,...,2^d-1 ]$. The definitions of compress_q(x,d) and decompress_q(x,d) are as follows:
$$
Compress_q(x,d) = \left\lfloor (2^d/q)\cdot x\right\rceil mod^{+}2^d
$$
$$
Decompress_q(x,d) = \left\lfloor (q/2^d... |
i created a function in javascript that creates my a for the DH exchange like this:
function createSecretKeyArray(){
let BigNumber = require('bignumber.js');
let numberArray = [];
const multiplier = 1;
for(let i=0; i<32; i++){
let randomNumber = BigNumber.random(multiplier);
let MulConstant = new ... |
I see a lot of references to the Davies-Meyer construction for one-way compression functions.
But I can't find any citation to the original paper.
Does anyone have it?
|
I am trying to compare various encryption algorithms in terms of encryption duration, decryption duration, information entropy, NPCR, UACI, and correlation coefficients.
I used a Lena 256x256 grayscale PNG image as the test image, and ran my Python code on macOS X with an i7 CPU and 8 GiB RAM. I found and used implemen... |
I'm working to use Differential Zero Knowledge proof on client local data before sharing with server. May I know which parameters need to be established at server side as to verify that the client is not cheating?
I've looked at "Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure... |
I am looking for an example of handling bit messages in SHA-3. I have looked at the example for 5-bit here but when I give complete padded msg
D30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000... |
As shown below it explains how generate zetas table and use it. But curious thing is that how KYBER_ROOT_OF_UNITY constant is generated ? I've tried multiple ways to generated it and cannot explain how it is found. Maybe I missed some little point. Let's says prime is 1073692673 how can I find also equivalent root_of_u... |
I am aware that in the Pedersen commitment scheme, the relationship between g and h must be unknown in terms of discrete logarithms. Knowing the relationship would be insecure as it would break the hiding property. I used the following simple "attack" to try and understand:
c = g^m * h*r
The attacker knows g = h^x, so... |
My guess would be that families are more secure. In which way though?
I have seen claims that hash function families can be collision resistant while single hash functions can not be. Is this true? And if so, why?
|
Assume there are two keyed hash-functions $H_1(k_1, m)$ and $H_2(k_2, m)$, with $k_1$ and $k_2$ being independently randomly sampled public keys.
The XOR-combiner is defined as $C_\oplus^{H_1, H_2}:=H_1(k_1, m) \oplus H_2 (k_2, m)$.
Assuming at least one of $H_1$ and $H_2$ is collision resistant, is $C_\oplus^{H_1, H_2... |
The problem
Let the following be a family of PRF functions with key length $2\lambda$
$$\mathbb{F} = \{F_k:\{0,1\}^n\rightarrow\{0,1\}^n\}_{k\in\{0,1\}^{2\lambda}}$$
Assuming one way functions exists, show how to use $\mathbb{F}$ to construct a secure MAC with key length $\lambda$ bits and message length $t*n$ bits for... |
I am looking for a threshold signature scheme (or similar proposals are happily accepted) that suits the following scenario:
One Base Station is transmitting signed broadcast message to all members in a communication cell. Each mobile member can verify the signature only with the key that it holds. If users exit / entr... |
If someone had a very efficient RSA factoring algorithm, would a company or government entity be willing to purchase it? What factoring time would be considered fast, months, days, hours, minutes? After they factor it, what do they do with the 2 primes numbers?
|
I have constructed a quintessential two transistor noise generator typical of what might be found when doing an internet search for such circuits. After laborious tuning I have it adjusted to about the best it's going to get from the analog/circuitry side.
Over relatively short and choice stretches of frequency (say 30... |
I am trying to prove that given two OWF $f$ and $g$ the function $h$ given as:
$$\text{h}(x)=(\text{f}(x),\text{g}(x))$$
is not always OWF. As a counter example I am considering $\text{f}(x) = \text{g}(x) \oplus x$.
For this to work I need to find an example of $\text{f}$ and $\text{g}$ still being OWF. I know that I c... |
In the sponge construction for hash functions, including SHA3 and SHAKE, its used a permutation
$$f:\{0,1\}^r\times\{0,1\}^c\to\{0,1\}^r\times\{0,1\}^c\\
\;\quad(R,C)\quad\quad\mapsto\quad\;(R',C')$$
where $r$ is the rate, $c$ is the capacity (with $r+c=1600$ in SHA3 and SHAKE). Function $f$ is iterated with a $r$-bit ... |
I am trying to understand the signal protocol better. I spend some time trying to understand their codebase (the backend is written in java).
The signal protocol indicates that the user has to upload one prekey at the time of registration (signed using their identity key) and about a 100 unsigned prekeys.
Then when som... |
I understand it is possible to convert a Random OLE (ROLE) into an OLE with desired inputs with some extra communication. My understanding is, Alice and Bob mask their desired input with the random inputs from the ROLE and each send a single message as explained in:
Converting a random OLE (oblivious linear function ev... |
I'm adding password protection/encryption support to a Python package that makes ZIP files (https://github.com/uktrade/stream-zip). I'm opting to not add ZipCrypto support, but instead add WinZip-style AES
From https://www.winzip.com/en/support/aes-encryption/ WinZip has two versions of this, AE-1 and AE-2, and it look... |
In this answer, it is stated
It has actually been shown (by Canetti, Goldreich and Halevi) that
random oracles cannot exist "in all generality" in the following
sense: it is possible to build pathological signature and asymmetric
encryption schemes, which are secure when they internally use a random
oracle, but which ... |
Preface: I am beginner of cryptography and not native English speaker. So I may make terrible mistake (about grammar and cryptography).
I understand that the parameters used for AES-CTR are "key", "nonce" and "counter" in addition to plaintext and ciphertext.
I also understand that it is not a good idea to disclose all... |
If I have a function f(x, y) and g(x, y) and f and g a are constant time, is the following code vulnerable to side channel attacks (assuming the conditional is constant time as well)
if (conditional) {
f(a, b);
g(b, a);
else {
f(b, a);
g(a, b);
}
|
Problem: Given $g, g^a, g^b, g^c \in G$ and an efficient bilinear map $e:G \times G \longrightarrow G_T$, distinguish $g^{abc}$ from a random element of $G$.
Is it a hard problem?
|
Does anyone know if CertificateVerify is sent in TLS_DH_RSA with client authentication? Does anyone know the RFC or could explain the meaning of it? With TLS_RSA, a hash is normally calculated with the private RSA key at this point. And with DH?
|
Known conditions:
The block size of this algorithm is 16 bytes.
If there are multiple encryption modes, then it is limited to ECB mode.
Always use only one immutable key.
Since only ECB encryption mode is used, things like segment size, IV, and counter will not come in handy.
Due to the fact that symmetric encryption... |
In my current project we will have to encrypt a lot of S3 objects (a few billions) with AWS KMS.
Our security department requires that we use KMS keys backed by CloudHSM. But since CloudHSM incurs some non-negligible extra charges in terms of pricing and key management (key rotation particularly), I was wondering if it... |
Is keystream reuse a meaningful concern in AES-256 encrypted ZIP files that adhere to the AE-2 spec? From “Attacking and Repairing the WinZip Encryption Scheme” by Tadayoshi Kohno
when using 256-bit AES keys, we expect collisions after encrypting 2^64 files
This seems extremely high to me. So high that I'm wondering ... |
I'm studying for a cryptography exam, I have this question from a past exam:
Consider the MAC with key $k$, based on a block cipher $E_{(k)}$ with block size $n$, and a collision-resistant hash function $h$ with output size $n$.
The MAC on a message m is calculated as:
$$ \text{MAC}(m) = E_{h(m)}(k) $$
Discuss the sec... |
With a use of almost MDS the Midori cipher provides a good diffusion. But why $S_b$ is used as S-box and what is its actual importance?
|
In the book Cryptography Engineering, Design Principles and Practical Applications, by Niels Ferguson, Bruce Schneier and Tadayoshi Kohno, in a section discussing multiplicative groups, the authors assert, “For any element $g$ [of a multiplicative group $G$ modulo $p$], the order of $g$ is a divisor of $p-1$. This isn’... |
In the Montgomery Curve $y^2=x^3+486662x^2+x$, $A=486662$. So, why when applying its code in Python or another programming language, $A=121665$?
import os
import binascii
P = 2 ** 255 - 19
A24 = 121665
def cswap(swap, x_2, x_3):
dummy = swap * ((x_2 - x_3) % P)
x_2 = x_2 - dummy
x_2 %= P
x_3 = x_3 + d... |
Assume the input linear mask is $a$, and output mask is $b$，for a block cipher $F$ with $r$ round,How to accurately and quickly estimate the bias of linear cryptanalysis? which is
\begin{equation*}
Prob\{a\cdot x+b\cdot F(x)=0 \}
\end{equation*}
is there any good algorithm？
Same question for differential cryptanalysis ... |
AES256 is said to be around 20% slower than AES128 (at least it was on my own benchmark). Is it slower only because of increased computation cost or does it also involve disk access?
Let's say I upgrade my laptop to have twice as powerful a CPU but the disk has the same specs. I have been using AES128 on the old laptop... |
The tag of a file is generated by the user's private key, which includes the file data, the file identifier and other contents. Is there any signature algorithm that can modify the file identifier information and regenerate the file signature under the original user's private key without disturbing the user?
I've seen ... |
In Montgomery Curve $By^2=x^3+Ax^2+x$, B $\neq$ 0, A $\neq$ +2 or -2. First case:
If $x_{1}$=$x_{2}$ and $y_{1}$=$y_{2}$$\neq$0: then s=($3(x_{1})^2$+$2Ax_{1}$)/(2B$v_{1}$). If $x_{1}$$\neq$$x_{2}$: then s=($y_{1}-y_{2}$)/($x_{1}-x_{2}$).
In both:
$x_{3}= Bs^2-A-x_{1}-x_{2}$ and $y_{3}=s(x_{1}-x_{3})-v_{1}$ Second ca... |
Assume I have a private key, priv_k, a public key pub_key and a message, msg, along with its hash, hash. I can produce a ECDSA signature, S, of hash using priv_k, and verify the signature with pub_key, msg and S.
It is possible to split priv_k into shares, priv_share1, priv_share2, such that I can:
sign hash with priv... |
In AES, while Converting Plain text to HEX in this image, how is X 23 and not 17 while all others are in Hex state.
|
I've made an implementation of a linear RNG. It has two constants: b and p. Every time new value of a is generated. Every time a value of x is also generated secretly.
The generator computes the number c as following:
(a * x + b) mod p == c
All values of a b x p are 256-bit numbers and additionaly p is prime. I assume ... |
I am looking for an alternative to RSA accumulators, and I am wondering if the following option based on function composition might fit the bill. It seems like an obvious tweak on RSA accumulators, which makes me think I'm probably missing something important though.
So I understand that RSA is based on modular exponen... |
I am a self learner and tried to learn AES, so I have a book written in my native language. It has some practical examples about finite fields and AES. It has a question that asks me to calculate the byte substitution process in advanced encryption system in GF($2^8$).
The book ask for 10010011. I know that it is equal... |
I'm not sure if this question belongs here or to StackOverflow. Please flag it if not.
I'm trying to implement a standalone library for finite field arithmetic of prime and prime power order as a way to learn to write safe code. Afterwards I plan to implement some elliptic curve groups on top of it and then some ellipt... |
Is there any cryptanalysis possible if the cipher itself is deterministically derived from key material?
For example, suppose you have n building blocks (ARX primitives, AES ops, other primitives) and parameters to further modulate them (ex. rotation numbers).
How could you even attempt to cryptoanalyze such a cipher?
... |
I have been exploring Bellare and Micciancio's "randomize-then-combine" paradigm for deriving set homomorphic hashing functions. I am particularly interested in grow-only sets, such that elements can be added but not removed from the underlying set (and hash). None of the existing instantiations (AdHash, MuHash, LtHash... |
I am studying the Goldwasser, Micali, Tong theorem about information leakage in RSA. In every book I have searched, there is the following remark $(c = \operatorname{Enc}(x))$:
Note that $\operatorname{loc}(c) = \operatorname{parity}(c \cdot \operatorname{Enc}(2))$ and $\operatorname{parity}(c) = \operatorname{loc}(c ... |
I've got a question regarding the signing algorithm on elliptic curves (EdDSA). In ed25519 signature scheme there is no nonce $k$, instead every message has its own different hash. From what I know the $s$ value of the signature is computed as following:
$$s = r_\mathrm{val} + h(r_\mathrm{val} * G \mathbin\| \mathrm{pu... |
I want to sign a file called data.txt and store its signature in data.txt.sig. To create the signature, I want to use an existing RSA private key, stored in the PEM format within the file RSAPrivate.key. I use the following openssl command:
openssl dgst -sha256 -out data.txt.sig -sign RSAPrivate.key data.txt
But I wou... |
Let's consider a scenario with $k$-secrets, each associated with a user. Every user aims to obscure their respective secret using a $d$-privacy method.
We say a user uses $d$-privacy within a radius $r$ if the distributions of observations or obfuscated secrets from any two locations within a distance of at most $r$ ar... |
In my exploration of zero-knowledge proofs, I have encountered various perspectives on the operational disparities among zk-SNARKs, zk-STARKs, and Bulletproofs, as documented in different blogs and discussions (such as the ones referenced in the provided links).
How do ZK-STARKs, ZK-SNARKs, and Bulletproofs compare in ... |
I'm thinking of cryptographic implementations on garbage-collected (gc) languages/runtimes and that the gc process can be potentially dangerous for an implementation even if the implementation has the "constant-time" property. Imagine the following code for example:
{
x = {big chunk data that are not referenced any... |
We have a set of secrets $S = \{x_1, x_2, \dots, x_n\}$ known to an adversary. Each $x_i \in S$ belongs to user $u_i$ who needs to obfuscate his secret using the notion of $d-$privacy defined in the following.
We assume that we have a numeric function $d(x,x^{\prime})$, giving the distinguishability level between $x,x... |
As you may know, classical ciphers are now often broken with hill-climbing algorithms. The earliest mention of them in cryptography I could find occurs in some 1980s publication mentioning 1979 PhD thesis of M. Hellman's student Dov Andelman titled "Maximum Likelihood Estimation Applied to Cryptanalysis" (available at ... |
I'm reading inner product from generalized sumcheck in baloo paper (P.13), I'm confused with $\lambda_j(0) = N^{-1}$. Can anyone shed some light?
Here's excerpt from the paper
The intuition is that for all Lagrange interpolation polynomials $\{\lambda_j(X)\}_{j=1}^{N}$ corresponding to a multiplicative subgroup H of s... |
We have a set of secrets $S = \{x_1, x_2, \dots, x_n\}$ known to an adversary. Each $x_i \in S$ belongs to user $u_i$ who needs to obfuscate his secret, i.e. $K(x_i) = o_i$, using the notion of $d-$privacy defined in the following.
We assume that we have a numeric function $d(x,x^{\prime})$, giving the distinguishabil... |
Context
I've used OpenSSL to encrypt some socket communications.
I am however using some functionality from the windows API that prevents me from using OpenSSL's opaque builtin sockets, so I am buffering through their BIO_s_mem interfaces - that requires 4 extra copies for all data passing through (socket->read buffer-... |
I'm a beginner in cryptography, currently focusing on AES GCM, specifically the GF(2^128) multiplier which employs the irreducible polynomial x^128 + x^7 + x^2 + x + 1. I try to explore the transformation of GF(2^128) into composite fields, like GF((2^64)^2) or GF(((2^32)^2)^2), through isomorphic matrices.
However, I'... |
Greetings from a newbie and crypto ignaramus. I hope that this is an appropriate forum for this question - please advise if not, or feel free to move it to another SE section.
First heard of chaffing years ago when government agencies were trying to ban PGP etc. from civilian use, especially internationally. With compu... |
Unconditional zero-sharing was presented in the following paper
Practical Multi-party Private Set Intersection from Symmetric-Key Techniques, by Vladimir Kolesnikov, Naor Matania, Benny Pinkas, Mike Rosulek, Ni Trieu
Unconditional zero-sharing allows all parties to obtain a share corresponding to each element in the... |
What's actually the difference between a (noisy) CVP and LWE? It seems to me that both are the same.
With the definition of LWE:
$$A * s + e = b$$
solving for secret vector s is the same than solving for the coefficients of the CVP, or do i understand something completely wrong?
|
I am currently working on a project involving RSA-PSS (Probabilistic Signature Scheme) for digital signatures. While researching potential vulnerabilities, I came across the well-known Bleichenbacher attack, which primarily targets PKCS1 v1.5 padding.
My understanding is that the Bleichenbacher attack is not applicable... |
I am a professional developer with a mathematics background, but know next to nothing related to cryptography. I would like to know if the following scenario is even possible.
Let's say Alice and Bob each have a bitstring of length n. Alice sends her (encrypted) bitstring to a (maybe vulnerable) server where it is stor... |
I'm studying generalized sumcheck in RZ21 P.10 and have come across a modular equivalence that I'm trying to understand. The specific step that's unclear to me is the following equivalence:
$$
\left(\sum_{\mathsf{h} \in \mathbb{H}} P(\mathsf{h}) \lambda_\mathsf{h}(X)\right)\left(\sum_{s \in \mathcal{S}} \lambda_s(v)^{... |
There is a two-party computation protocol based on 2-out-of-2 additive secret sharing in Figure 1. Party $P_0$ holds secret shares $[a]_0, [b]_0$, and party $P_1$ holds secret shares $[a]_1, [b]_1$ where $[a]_0 + [a]_1 = a$ and $[b]_0 + [b]_1 = b$. We assume that $P_0$ and $P_1$ have obtained Beaver's triples $([u]_i, ... |
Imagine a simple auction made with Pedersen commitments rather than sealed envelopes.
Participant 1 commits their bid, $b_1$, choosing a blinding factor $x_1$ and using publicly known G and H generators. As they do so, the commitment value $C_1$ appears on a public website.
Participant 2 does the same. Again, as they c... |
Suppose that $(\mathrm{Gen},\mathrm{Enc},\mathrm{Dec})$ is a secure encryption scheme. Encryption scheme is secure if for any two sequences $\{a_{n}\}_{n\in\mathbb{N}},\{b_{n}\}_{n\in\mathbb{N}}$ of messages such that $|a_{n}|=|b_{n}| = p(n)$ $\mathrm{Enc}(k,a_{n})$ and $\mathrm{Enc}(k,b_{n})$ are computationally indis... |
I am a beginner in cryptography (on my way to retirement) and have programmed the Trivium algorithm in C++ for practice. To check if the bitstream generated by my program is correct, I am looking for some bitstreams with given key ind IV. I think 200 bit length should be enough as a comparison.
Unfortunately I couldn't... |
Let $G$ be a secure PRG and let $s$ be a private key. We can define $\mathrm{Enc}(s,m) = G(s)\oplus m$. As long as we know only one encrypted message this scheme is secure, since $G(s)\oplus m \sim r\oplus m \sim r$, where $r$ is a random string. I have several questions:
If we know two encrypted messages $G(s)\oplus ... |
I'm trying to write a C++ program to solve the shortest vector problem. The program is given a basis of a vector space V and needs to find the shortest non-zero vector in V.
Right now I'm using the Ajtai-Kumar-Sivakumar (AKS) algorithm described here on slides 12 and 34. The problem is the time/memory complexity: for a... |
in this paper https://eprint.iacr.org/2015/399.pdf
how to make the lattice?
|
Consider the definition of the dual lattice for a lattice $\mathcal{L}(\mathbf{B}_{m\times n})\in\mathbb{R}^{m}$ where $\mathbf{B}\in\mathbb{R}^{m\times n}$ and $n\leq m$ [sp2 Seminar, Luxembourg 2019, DualitySlides, page 5]:
$$ \mathcal{L}^{\vee}=\{\vec{v}\in span_{\mathbb{R}}(\mathcal{L}(\mathbf{B})): \langle\vec{v},... |
I'm currently testing the randomness of using SHA-256 in Hash_DRBG mechanism based on this research. The parameters used in the testing are the default parameters, except for when the PRNG fails a certain test, the p-sample is doubled in a subsequent test. The result is as follows.
Test
n-tuple
p-samples
p-value
As... |
Suppose that $(\mathrm{Gen},\mathrm{Dec},\mathrm{Enc})$ is a semantically secure public-key encryption scheme. I define $E' = (E(e,m)\oplus m)\parallel (E(e,m)\oplus e)$. Clearly, this is now not secure, since knowing $e$ allows to know $E(e,m)$ (applying XOR with $e$ to the second half) and, consequently, leaks $m$. N... |
There is an algorithm called EIG (Extra Information Gathering) protocol for Byzantine agreement of a bit over $n$ parties. The protocol has $t+1$ rounds. Can anyone help me understand how the time complexity of the algorithm is $\mathcal{O}(n^{t+1})$?
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I'm working on an idea for a backend data store that stores encrypted data that is zero knowledge/trust, however is shareable to a number of parties. I don't want the backend service to know anything about the data or manage keys, so if the data was ever compromised then it would be meaningless to an attacker. Theref... |
I want to concretely understand how exactly choice of error distribution effect the security of KEM in the context of Lattice Based Cryptography.
For example, I would like to know the concrete analysis of CBD used in Kyber. How Kyber justiify the use of CBD from the security point of view.
Could someone please suggest... |
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