instruction stringlengths 32 27.2k |
|---|
I have two secret numbers $A$ and $B$. Both are uniformly-distributed 32-bit numbers.
I need a deterministic function $f(x)$ such that $f(A) = B$. $f(x)$ must not leak any information about $A$ or $B$.
Naively, what if $f(x) = x + C$, where $C = B - A$. What information is leaked, if any, in this case, and what would b... |
If I take a large truly random portion of data, I know that I can generate a 2048-bits key with it (assuming the random data has more entropy than the key). I read in this forum that Shake-256 has this ability.
I also read in Wikipedia this: "KangarooTwelve and MarsupilamiFourteen are Extendable-Output Functions, simil... |
If we possess the knowledge that the expression $d^e \equiv c \pmod{n}$ holds for an RSA key pair, what would be the implication or consequence of this? Here, $e$, $n$, and $d$ represent the public exponent, modulus, and private exponent, respectively.
|
I'm trying to analyze a stream of communication I captured from a game. I know the keys but I don't know how to apply them.
I've tried:
Various AES-256 modes, splitting the message at different offsets into (nonce, ciphertext, MAC)
RC4
Debug the client binary for hints
But to no avail. The modes with MAC tell me it's... |
Can anyone please provide an example of an identification protocol that
With a private key
Resistant to attack with a fake ATM
Not resistant to eavesdropping attacks
?
|
I'm developing a program that uses a hybrid Key Encapsulation Mechanism (KEM) scheme, employing Kyber and X25519, with each producing a 32-byte shared secret. What would be the best scheme to combine these two shared secrets and derive a key for encryption?
I have a few schemes in mind:
First scheme:
CONCATENATED_KEY... |
I've read many e-voting papers that use El-Gamal scheme which I recall is vulnerable to man-in-the-middle attack, yet I find no discussion or even mentioning of it in those papers.
-Does anyone knows why?
-Is it completely solved or dealt with?
-I only found this old paper about it
https://www.semanticscholar.org/paper... |
I am faced with a problem of selecting an appropriate message authentication code (MAC) for a particular application. These are the constraints:
I have two 64-bit integers $r_a$ and $r_s$ as input, where:
$r_a < 2^{52}$ and $r_s < 2^{52}$
$r_a$ is a multiple of 4, i.e. $r_a = 0 \pmod{4}$
$r_s$ is a multiple of 16, i.e... |
I'm currently working on a project where I want to map Curve25519 public keys to uniformly random noise. The main idea is that when these transformed public keys are sent over a network, an outsider wouldn't easily recognize them as typical public keys. I came across a solution using Elligator (elligator).
The current ... |
I am trying to understand some concepts such as DH problem and its variants. I have the following question from the book I read. (note that I translated the question from my language to english)
Assume that two parties are using DH to make key exchange, so they
need to use a group with an element x in it. Let's also a... |
I have a noisy one-way communication channel where data is sent as a series of words of width n bits.
Assume n is a constant roughly in the range of 16...48.
I don't want bit errors in one word to affect the other words.
To achieve confidentiality in such a scenario, one would use a stream cipher,
as that guarantees th... |
I am studying RSA cryptosystem and here is the question that came to my mind. Let's pick $p, q$ to be two primes and $n = p * q$. From that we calculate Euler's totient function:
$$
\phi(n) = (p - 1)(q - 1).
$$ Then we chose the public and private key pair as $e, d$ such that:
$$
e * d \equiv 1 \text{ mod } \phi(n).
$... |
Assume Bob is sender and Alice is future recipient.
In ideal situation Bob know Alice public key, and encrypt message with it.
But what if Bob don't know Alice public key (he only will know Alice public key when agreement met), I saw two solutions:
Bob encrypt message with Alice pub key after agreement met and pub key... |
Consider the elliptic curve E1:y2=x3+7 over F17 with the base point G=(15,13)
I am trying to compute point double of (15,13) i.e (15,13)+ (15,13)
Expected point is (2,10) , however I am not able to calcualate it.
Could anyone point out where I am making mistake
s = 3 * (15*15) / 2 * 13 mod 17 = 375/26 mod 17 = 750 mod ... |
since the NTT is a variant of the DFT respectively FFT, it seems possible to implement a recursive algorithm for the NTT of Kyber with a divide-and-conquer concept. This is the reason for my question here, I would be interested in how to recursively realize the NTT from the current Kyber specification which is defined ... |
Ive been assigned research involving online gaming companies and their use of cryptographic algorithms to produce 'provably fair' results. The largest player in the industry uses a method involving a client provided seed, which is then combined with a server seed and an incremental nonce. The server seed is shown to ... |
There is a very popular method to represent a message $m$ (number) as a point on elliptic curve over a finite field:
Set $i = 0$
Check whether $m'=m\cdot K+i$ is on elliptic curve. If not, try again for $i+1$. If it is, compute such $y$ for $m'$ and you have point $(m', y)$
And it is very often said that chances of f... |
A company wants to poll employees about their view of the company (by using a web system, say). They would like to do it anonymously, but they don't want people filling out forms more than once. An intern in the company suggested the following.
Each employee has a certain identification number that only the employee h... |
Let's say we have Bob, Alice and third party.
Bob make message signature hash and upload to third party, then encrypt message with Alice pub key and send it to Alice
Alice receive message and decrypt it. She also ask third party for message hash and verify message.
However. What if Bob upload random signature hash to t... |
I was reading Limits on the provable consequences of one way permutations by Impagliazzo and Rudich when I got stuck on a sentence.
First of all, they define a polynomial relation that is any relation $ R $ verifiable in polynomial time in $ ||x|| + ||y|| $, i.e., $xRy$ iff we can decide in poly time if $y$ is a valid ... |
RFC 2313 has this specific callout:
1. An RSA private key logically consists of only the
modulus n and the private exponent d. The presence of the
values p, q, d mod (p-1), d mod (p-1), and q-1 mod p is
intended for efficiency, as Quisquater and Couvreur have
shown [QC82]. A pr... |
So I read parts of the following article:
https://blog.cr.yp.to/20231003-countcorrectly.html
But I quite dont understand it. NIST assumes Kyber 512 is just as hard as AES128 nowadays, in presence of quantum computers. The error they mention is that Kyber has the security level of 2^41 bits, instead of 2^80 bits, but do... |
The plain, normal-form, decisional LWE problem over $\mathbb{Z}/q\mathbb{Z}$ is: given a uniformly random $n\times n$ matrix $A$ and vector $b\in \mathbb{Z}/q\mathbb{Z}^n$, decide if $b=As+e$ for small $s$ and small $e$.
The decisional ring LWE problem is, in $R_q:=\mathbb{Z}[x]/(q,p(x))$, given uniformly random $a\in ... |
secp256k1 Generator:(G_X, G_Y, 0x1),
secp256k1 any public key using affine coordinates : B=(X, Y)
secp256k1 any Public key using jacobian coordinates:BB=(P_X, P_Y, P_Z)
(B's private key)==(BB's private key)
I consider projective Jacobian coordinates for secp256k1.
Given any public key B, if the z-coordinate after conve... |
I am currently exploring the workings of the Tor network, specifically how the Diffie-Hellman (DH) key exchange protocol is employed to establish shared secret keys between the client and each relay in the circuit.
In this lesson from Nick Mathewson (https://youtu.be/OgGTJIgNewE?si=ft3a0Y0Brgtuj5eF&t=2035) it is explai... |
I've read [DDLL13] paper and want to understand how the lemma 3.4 is changed for NTRU version of BLISS.
In the naive construction of BLISS, the commitment entropy is bounded in Lemma 3.4 as below:
$$ \text{Pr}[\mathbf{A}(y = t; \; y \leftarrow D_{\sigma}^m)] = \text{Pr}[y_1 = (t - \bar{\mathbf{A}}_{y_0}); \; y \leftarr... |
I am attempting to get a hardware implementation of RSA working but I am having trouble with encryption and decryption. First, I ran these commands to generate the keys:
openssl genrsa -out private-key.pem 2048
openssl rsa -in private-key.pem -pubout -out pubkey-key.pem
I then ran some of my own programs to generate ... |
So I've been learning about RSA for quite a while (mainly by playing around in CTF competitions) and I came across an interesting problem.
The other day I was looking to create a challenge in which I needed $\phi(n)$ to be a perfect square, but under the condition that $p \neq q$.
For very small bitlengths (such as $<=... |
I am looking for a protocol where each party generates a share such that $\sum_{i\in [n]} s_i =0$ where the shares should remain secret. The adversary may corrupt n-2 parties, and the parties can be malicious. However, it should be verifiable if the sum is not 0. Is there an efficient protocol that achieves this in a d... |
I am trying to argue about the hardness of LWE, but in a setting that is different from the standard one.
Consider the task of learning the LWE secret $s$ from noisy samples. The specifications of the problem are an $m \times n$ matrix $A$, a $n \times 1$ vector $s$, and a Gaussian noise vector $e$. By a noisy sample, ... |
Ok we know when we add a random IV in our "modified encrypted" MAC became useless and the IV can be forgery, then our encryption scheme becomes vulnerable to chosen plaintext attacks.
According those proves :
Finding IV for forgery of AES CBC-MAC with non-fixed IV
CBC-MAC insecure with random IV
But the addition at the... |
When designing the search LWE problem, how do you set the dimensions of the A matrix? Or under what circumstances can I use very few matrix dimensions to achieve 128-bit security? Up to noise level? Or some other way?
|
I'm working on a project where we have three different software systems—let's call them A, B, and C.
Systems A and B handle user data identified by phone numbers and want to send user actions to System C for tracking purposes. The goal is to achieve user tracking across systems while maintaining privacy through the use... |
I was told in passing that (key, plain) pairs could be chosen to produce a zero state in AES encrypt in some middle round (say 5). [The application here being to side-channel leakage assessment.] However, I can't find any reference. I assume such a thing could be constructed from various attacks on reduced-round AES... |
I am trying to understand the process of transitioning from a NIST standard to the attacks based on of the Unique Shortest Vector Problem (Unique-SVP). Specifically, I am working with Crystals Dilithium 2 and would like to understand how to obtain the lattice dimension associated to the uSVP.
For example in Crystals Di... |
If entropy is hashed with SHA-256 for example, and the input has exactly 256 entropy bits, how much entropy is reduced after hashing due to collision? Is there any reference that explains how to calculate this?
|
Dears,
In RFC 2409 "The Internet Key Exchange (IKE)", its mentioned there are four available authentication methods for IKE, there are different calculations for SKEYID for each method and hence we get HASH_I & HASH_R which seems it has one calculation way but the SKEYID gets engaged on its calculation.
Referring to t... |
Are all doubled points on an elliptic curve even, meaning if you compress the point, it will have '02' plus the $x$ coordinate? If not, what distinguishes a doubled point from a point resulting from point addition?
|
I'm trying to implement a simple 1-out-of-2 Oblivious Transfer with RSA. I was checking the code and tried to work it step by step. The 2 messages by Alice, let's say, are $m_0 = 7$ and $m_1 = 9$. Bob's decryption turns out to be -8. Can you please help me understand what I'm doing incorrectly? Am I missing $\bmod N$ s... |
Problem
I'm working on an AES implementation in C++, and I have been testing the performance of my code, and its functions. I've noticed a significant performance slowdown in my 'addRoundKey' function. The time it takes to complete the 'addRoundKey' function seems to scale linearly, i.e. if I give it 1mb it takes ~650m... |
BLAKE2 uses a message schedule I did not see before. It uses permutations of pieces of the message block.
The BLAKE2 book did not state the rationale for such a choice and how it contrasts with the message schedule of SHA2 for example.
If the BLAKE2 key schedule is sound why wasn't such an approach taken with SHA0/1/2?... |
I have a prime number, $p$, with $n$ bits. To generate a new prime number, $q$, I shift the bits of $p$ from left to right by a certain length. For example, if $p$ is represented as 1101110011 in base $2$ (which is $883$ in decimal) and it happens to be prime, I shift it one bit to the right, resulting in 1011100111 (w... |
It is not quite difficult to understand the idea of differential cryptanalysis applied to a standalone block cipher. The method investigates, how differences of plaintext evolve while going through rounds of the cipher.
But several sources mention the analysis of a block cipher in a mode of operation. But, for instance... |
Is generating Keccak-256 hashes with timestamp + nonce (ensured to be unique for each run), and taking its most significant 16 bytes sufficient to generate random V4 UUIDs?
Obviously the 13th hex character will be made 4, and 17th character will be made one of 8,9,a,b after the random generation. But I believe this is ... |
Recently, I read some security proofs about the secure multi-party computation (MPC) protocol, which includes statements about information leakage, such as the security proof below from the paper CWL+20$^{1}$, but I'm confused about the "security with information leakage".
(Section 4.4 Security Proof from CWL+20) Theo... |
Given a generator $g$ of a cyclic group, I am trying to look for a case where I use pairing over an element that has an exponent which is a one-way function, e.g., $g^{x^2\mod n}$ (here $x$ in the exponent is hard to compute by the quadratic residue assumption), where $n=pq$, for primes $p$ and $q$. For instance, to ch... |
I'm currently working in a constrained environment and need to derive a symmetric key (that will be used for AES-256 in GCM mode later) based on a low-entropy shared secret obtained via X25519.
To derive a symmetric key RFC 7748 states: Alice and Bob can then use a key-derivation function that includes K, K_A, and K_B ... |
It looks like the IETF draft specification of Classic McEliece has penciled in separate variants of the algorithm for so-called "pc" and "non-pc" variants (as well as the familiar "f" and non-"f" variants); presumably they're going to be assigned separate OIDs for X.509/CMS/PKCS#8/related AlgorithmIdentifier use.
These... |
I am trying to create an AES Sbox masking based on this paper. In the paper, they tried to mask the sbox described in this other paper. The inversion is been done in GF(4). I know that it is mostly implemented in hardware, while the software implementation requires use of EEA or sbox table. However, I am implementing i... |
There are some very large safe primes listed here: https://en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes
Would using any of them result in a secure DH construction? Generator is 2.
The exponent would be of the same magnitude as the prime.
Performance impact of using such large numbers is irrelevant to the questi... |
The notation of a strongly universal function was introduced by Wegman and Carter here and it states, that such a function has to be pairwise independently and uniformly distributed. I would like to know if a PRF also has this property and how the relation looks like. I would argue, that a random function has those pro... |
When RSA is strictly used to exchange random shared secrets, is the padding scheme important for security or can it be omitted entirely?
The party in possession of an RSA public key will generate entropy for a symmetric key, encrypt it with the RSA public key and send it off. After that point any failure will only be k... |
Let's say I had an arbitrary number that was large, say 512 bits or bigger, but wasn't necessarily a semiprime. What is a computation that I could do on this number that would give me a unique solution that is guaranteed to be very inefficient to compute, but very quick to verify? I am looking for something in number t... |
We know that OPRF is a two-party protocol, where Alice inputs $X = {x_1, ..., x_n}$, Bob has no input, and after executing the OPRF protocol, Alice gets $F_k(x_i)$, and Bob receives a pseudorandom key $K$.
I wonder if it is possible to construct a permutation(shuffle) OPRF, where Alice inputs $X$, Bob inputs a random p... |
I have two signatures $(r,s)$ and $(r,s')$. So the same $k$ is being used for generating the $r$ value.
I know that this exposes a vulnerability such that I can recover the secret $x$.
The first step I did was recovering the value $k$, but when I perform the following calculation, which should recover $k$, I get a floa... |
In the Wikipedia page for WPA3 enterprise mode, it states that WPA3 has an "...equivalent 192-bit cryptographic strength in WPA3-Enterprise mode..." yet it also says that it uses AES-256-GCM with SHA-384 HMAC. How does the combination of these two yield 192 bit cryptographic strength? Shouldn't it be 256 bit strength?
... |
We assume a standard secure RSA public key $(n,e)$, e.g. 3072-bit $n$ and $e=65537$.
The Meet-in-the-Middle attack (not to be confused with Man-in-the-Middle attack) on textbook RSA recovers $m$ from $c=m^e\bmod n$ for a sizable fraction of small $m$ and $\mathcal O(\sqrt m)$ modular operations modulo $n$. It does not ... |
A HMAC is usually said to be H(sk || msg) for some secret key sk and message msg.
My first question is, can we compute it as H(msg || sk) instead ? Is there any drawbacks doing it ?
If the answer is yes, consider H as vulnerable to length extension attacks, would such a MAC be vulnerable to length extension attacks ? I... |
Can you take a curve equation from https://safecurves.cr.yp.to and a large safe prime from existing DH parameters (for example openssl dhparam 9000), combine them, and result in a secure ECDH curve?
Are there some special considerations when pairing a curve equation with a prime?
The generator point would be SHAKE(some... |
In the implementation of HEAAN, they have implemented the conjugate function. It computes conjugate of a polynomial. Effectively they have reverted the positions of the coefficients and negated their values. Can anyone please explain me how does it work (mathematically).
|
Let's say I have x bytes of data that needs to be encrypted with Stream Ciphers such as AES256-CTR, ChaCha20, Salsa20, XChaCha20, XSalsa20.
I would like to ask, since these ciphers typically requires MAC to ensure their integrity. Will current Poly1305 that comes along with ChaCha20,XChaCha20,Salsa20,XSalsa20 & GCM tha... |
Can we define one finite set of input strings for a SHA-3 hash (or SHAKE XOF) function so that the collision probability is arguably lower than for a random oracle, with a definition of the set making no reference to the function? If so, what's an example with the ratio of function's to oracle's collision probabilities... |
I'm new here and have a basic question about encryption. I plan to securely store sensitive data on a company computer. Being one of hundreds little branches of a bigger company, it is not possible to turn off the computer after business hours (back ups, updates, data exchange).
I started storing documents in Veracrypt... |
I am reading a book about blockchain. It said the asymmetric cryptography was invented by Whitefield Dime and Martin Herman in 1976. But I cannot find these two guys. Furthermore, what I know was RSA who invented asymmetric cryptography in 1978?
|
My question is about the verifiable encryption (Camenisch-Shoup).
in the Paillier cryptosystem, a message $m$ is encrypted using a public key (composed of $N$ and $g$) and a random number $r$, resulting in a ciphertext $C = g^m \cdot r^N \pmod{N^2}$.
Alice after applying Paillier Encryption has three values in her hand... |
We know that secure multi-party computation (MPC) does not have to be implemented based solely on public-key cryptographic primitives (aka asymmetric-key primitives). Many MPC protocols rely on symmetric-key primitives, such as secret sharing-based schemes (e.g., replicated secret sharing and Shamir‘s secret sharing). ... |
Does the security of RSA rest entirely on the modulus having at least 2 large random primes?
Suppose you were to generate 2 random 1,000,000-bit numbers and just use the product of those as the modulus.
What are the odds that all the prime factors of the modulus be much smaller than 1,000,000 bits? And would that be su... |
A common way to mask an integer $x$ in a range is to add a uniformly random integer $r$ from a much larger range. More formally, if $x$ lies in $[0,...,2^k)$ and $r$ in $[0,...,2^{k + l})$, then
$$\Delta(X+R,R) < 2^{-l}.$$
Edit: I mean multiplication in $\mathbb{Z}$. If more specifically we're modelling a range $[-2^k,... |
Does using a portion of a master seed, such as the last 12 bytes of a 128-byte random master seed, as a salt provide any additional security to the HKDF when deriving child seeds? Alternatively, is it better not to use a salt in this case?
|
pqRSA is MP-RSA with 4096-bit primes to build up a modulus of up to 1TB.
If the objective is to make processing the modulus as expensive as possible for the quantum computer why not use just two 4096-bit primes with the rest being 1024-bit primes? Would that offer comparable security?
|
I want to find the plain text from two cyphertexts of RSA, encrypted with two diffrent public keys. I know that: for E((n,e),m) = c0 and E((n,f),m) = c1 , c0^x . c1^y mod n = m mod n = m (ex + fy=1) But for some examples x (or y) is negative.
I am trying to find the m for E((493,3),m) = 293 and E((493,5),m) = 421 I fou... |
We consider the Discrete Logarithm Problem of finding integer $x$ random in $[0,n)$ where $n$ is the group order, given $Y=G^x$ (or $Y=xG$) computed in the group noted multiplicatively (or additively), group generator $G$, and the prime order $n$.
I ask how the cost of solving $k$ such problems with shared group and $G... |
(1) What's the meaning of the assumption of "honest majority" in a mpc protocol?
(2) How to prove the security when (not) an honest majority assumption?
|
Reading about Blum-Blum-Shub, I have found that everyone has stressed the importance of $gcd(p-1, q-1)$ being a small number, as this leads to a large period.
I found it really difficult to find a formula for the period of Blum-Blum-Shub. I understand that if $x_i = (x_0^{2^i} \mod n) \mod 2$, $n =pq$, then finding the... |
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... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.