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In its application of Shamir secret sharing, the FROST paper in Figure 1 Round 2 Step 1 requires each participant $P_i$ to securely send to each other participant $P_\ell$ a secret share $(\ell, f_i(\ell))$.
I wonder what securely means in this context. I assume at least the Security Assumptions from §4 (Message Valida... |
In AES-CTR, a key, a nonce and a counter are all encrypted to produce a value that is then XORed with a plaintext to produce the ciphertext.
Let's say we were to make a hash out of the key, the nonce and the counter instead of using the AES algorithm, and then XOR our plaintext with the hash to make a ciphertext.
Would... |
I had asked one question before One-More Computational Diffie-Hellman in asymmetric pairing groups and have not received answer. I am posing a supplementary question now that I just realized I don't have even idea what to call the building block problem.
That is in an asymmetric pairing groups $e:G_1 \times G_2 \to G_T... |
Recently a friend of mine showed me a "puzzle" he created with curve ed25519
It is based on adding and multiplying points on the curve
You supply three arguments to the program
The 'public key'
The 'private key'
additional data
He considers the puzzle as solved if the following 'equation' applies:
static-point = cdaaf... |
Sorry for asking another question but is BN254 specification standardized? I am using two different implementations one python another solidity and the prime field $F_p,F_{p^2}$ and the the group order $q$ are defined differently in those two versions.
Solidity version:
$p = 21888242871839275222246405745257275088696311... |
Let $(\mathsf{Gen}, E, D)$ be a CCA-secure public key encryption system with a message space $\{0,1\}^{128}$. Is the following derived cipher $(\mathsf{Gen}, E', D')$ also CCA-secure?
Justify your answer.
$$\begin{array}{l}
E’(\operatorname{pk}, m)&=&E(\operatorname{pk}, m + 1^{128})&\text{and}\\
D’(\operatorname{sk}, ... |
Let's say that i know that the output of an LFSR with length 4 is 1,1,1,0,0,1,1. Constructing the 3 equations modulo 2:
$$s_{4} = \sum\limits_{i=1}^{4}c_{i}s_{4-i} \Leftrightarrow c_{2}+c_{3}+c_{4}=0$$
$$s_{5} = \sum\limits_{i=1}^{4}c_{i}s_{5-i} \Leftrightarrow c_{3}+c_{4}=1$$
$$s_{6} = \sum\limits_{i=1}^{4}c_{i}s_{6-i... |
About the Naccache-Stern cryptosystem, I have found two different encryption algorithms:
In the original paper from Naccache and Stern, the encryption step is performed by calculating $c = g^m \hspace{2mm} (mod \hspace{2mm} n)$, with $m$ being the plaintext, with $\sigma$ being optionally kept private. Then decryption... |
Is there an official database with curve parameters for common curves? Asking for generator point, order, prime, a, b
I found one for secp256k1 in the mbedtls library.
static const mbedtls_mpi_uint secp256k1_p[] = {
MBEDTLS_BYTES_TO_T_UINT_8(0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF),
MBEDTLS_BYTES_TO_T_UI... |
I am building an application in which I need to sign a message without revealing my entire identity.
To do so, I just compute a zk proof with the following purpose:
prove I own the secret key sk associated with a public key pk (that matches some properties, e.g. $pk \in Authorized\_keys$)
sign a message with $sig = H(... |
As part of Spontaneous Anonymous Group (SAG) signatures of say 16 participants, the prover generates fake random responses for 15 elements and a real response at some secret index. I want to hijack this scheme and instead of putting random data in the 15 elements, I want to fill it up with data encrypted with some secr... |
In DGK encryption, one of the parameters of public key is value u where it is a small prime with minimum length l+2. It is not obvious for me what is the security compromise if u is not prime. Any help and idea appreciated.
|
I know that in Active Directory environments passwords are stored in the form of hashes depending on encryption types used in the environment.
I understand also that when using AES as a symmetric encryption type, the user password goes through PKDF2 first which generates a key derived from the password, salt included.
... |
In SafeCurves: choosing safe curves for elliptic-curve cryptography, Daniel J. Bernstein and Tanja Lange characterize Brainpool curves of the twisted variety (e.g. brainpoolP256t1) as not "Safe", specifically failing the "ladder", "twist", "complete" and "ind" criteria.
Which of these critics apply to the corresponding... |
I am new to cryptography and encountered the discrete log problem. Given generator $g$, a prime $p$ and an integer $b$ calculate $x$ such that:
$g^x \equiv b\mod{p}$
I have read that such a problem has been solved for a $240$ digit prime. So I am thinking how much time would be required to solve the following problem:
... |
Is the following a correct formulation for the assumed worst-case hardness of $SIVP_\gamma$?
For every PPT algorithm $A$
for every $n\in\mathbb{N}$ there exists a basis $B_{n,A}=\{v_1,\dots,v_n\} \in \mathbb{Z}^n$ such that
Pr[A produces an answer for $SIVP_\gamma$ on $B_{n,A}$]$\to 0$
faster than any 1/poly(n).
Spec... |
The Index Calculus algorithm solves the Discrete Logarithm Problem of finding $x$ with $g^x\bmod p=b$ given $g$, $b$, and prime $p$. Assume $g$ is a generator, so that $x$ is uniquely defined in $[1,p)$.
Can Index Calculus take advantage of $x$ much smaller than $p$?
If so, how low must $x$ be, and what's the saving? I... |
I am designing a pseudo random bit generator (PRBG) and I am using the NIST SP 800-22 suite to analyze the random characteristics of my PRBG. It turns out that my PRBG passes 14 out of 15 tests, and fails the Discrete Fourier transform (Spectral) test as can be seen in the Table below. I have already tested different ... |
I am trying to solve the following problem:
Alice generates a RSA key $(n, \phi)$, she shares with Bob the value $n$, and $y = g^{2^{t}}\;\text{mod}\; n$ for $g$ a generator of the group $\left(\mathbb Z/n\mathbb Z\right)^{*}$ and $t$ a very large number for example $2^{512}$. She then asks Bob for an input $z$ ($\neq... |
The Golang implementation of edwards25519 (https://tip.golang.org/src/crypto/internal/edwards25519/field/fe.go) uses radix-251 representation. The description in section 3.2 in https://dl.acm.org/doi/pdf/10.1145/2660267.2660370, as well as the description in https://www.cosic.esat.kuleuven.be/ecc2013/files/peter_schwab... |
I have trouble in understanding the security proof of this paper(Ciphertext-Policy Attribute-Based Encryption)
why are these two hybrids equivalent to the modified game above? It is obvious that $M_0e(g, g)^{\alpha s}$ and $e(g, g)^{\alpha s}$ are not euqal.
|
I am trying to understand illustrative example of Pollard's Rho method to solve ECDLP from the book "Guide to Elliptic Curve Cryptography"
I am referring to Algorithm 4.3 and Example 4.4
There is this table on Pg. 160
Could anyone explain me how right side of this table , c'' , d'' and x'' is computed.
I am simply not... |
I noticed that, when deriving a Classic McEliece public key from a private key, randomness is required, and also that this randomness is normally provided at once, during key pair generation.
I'm guessing it's not usual to ever generate additional public keys "after the fact".
I'm further guessing that if you did so, a... |
I'm attempting to build a blockchain network of IoT devices that would allow public access such that any person around the world could push data to it and there would be an immutable record of all data pledged to the network. The validity of the data or the trust of the client isn't important, but keeping a permanent l... |
There are three entities: the user (prover), the verifier, and the auditor. The user sends a message to the verifier encrypted using the public key of the auditor. The goal of the user is to convince the verifier that the message is encrypted using the public key of the auditor using zero knowledge proof. Can you expla... |
I am a graduate student and have encountered some problems in my research. When I generate a signature on the data block of the file, and the signature is composed of the user's private key, the data block, and the block index. Is there any signature algorithm that can modify the block index value after the original si... |
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 ... |
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