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This is somewhat a basic question but the reason is not spelled out clearly anywhere.
Say we have 2 web applications running on https://one.abc.com and https://two.xyz.com.
I visit https://one.abc.com and a page is displayed which has a button on it and when clicked, submits to https://one.abc.com and responds with a r... |
To my understanding, whilst the definition of zero-knowledge (zk) is the same in the non-interactive context, how one shows a non-interactive scheme is zk is very different from interactive zk protocol. This is because a Simulator cannot simply produce a valid transcript (as it does in the interactive setting) as doing... |
Do we have something proven APPS for generate ssh key from some words?
I mean private key(without reason wich type rsa or eleptic curves) generated deterministic from seed
I found this fork of ssh-keygen - https://github.com/cornfeedhobo/ssh-keydgen
But I don't found information about this tool, can I use it to make my... |
I am trying to understand how exactly lattice reduction and LWE are linked.
The attacks on LWE I have seen all use lattice reduction in some way or another, dual attacks, uSVP type and so on.
Naively, if I just care about (a couple of) short vectors, it seems overkill to produce a full basis change.
So, what is the int... |
I am looking for an encryption algorithm that's secure and commutative. This means that if N parties encrypt their data in any order, it could be decrypted in any other order.
|
Okay, I have a ECDSA public key $P$. The curve is arbitrary and not necessarily secure.
The finite field of curve, $q$, is a $315$ bit prime. I know the following information regarding key:
The private key, $x$ is of the form $2^t \mod{n},$ $t \epsilon ]0, k[$, where $n$ is the order of subgroup (a 300 bit prime) and ... |
Recall Short Integer Solution:
$\textbf{SIS}_{n, q, \beta, m}$: Given $\textbf{A} \in \mathbb{Z}^{n\times m}_q$, $\vec{b} \in \mathbb{Z}^{n}$, find $\vec{z} \in \mathbb{Z}^{m}$ of norm $||z|| \le \beta$ s.t. $\textbf{A}\vec{z} = \vec{b}$.
We must take $\beta < q$ to avoid trivial solutions and $\beta \ge \sqrt{n \log q... |
We've all seen tables of characters useful in encoding or decoding a vigenere cypher. Could such a chart be implemented in a decoder ring?
I envision three rings in one. As the user turns the top ring to align a text-character with a key-character on the second ring, the third ring turns to align the cypher-character, ... |
Let me ask one question. Maybe, you know an answer. Thanks in advance for any response.
Let's fix an elliptic curve $E$ over the field $\mathbb{Q}$ of rationals without complex multiplication, i.e., its endomorphism ring is just the ring $\mathbb{Z}$ of integers. I want to generate an elliptic curve with the same $j$-i... |
I would like to come up with a MAC algorithm that is simple and provably secure.
The message and mac are OTP encrypted. For the purpose of this exercise lets say the entire plaintext is known to the adversary (they have predicted it), but the MAC for the authentic message is not known.
I'm not an expert, but it seems t... |
I read that SWIFFT is a linear hash function, but I don't understand what this means. The obvious interpretation is that if you have inputs $X1, X2$ each of which is an array of 16 64-dimensional binary vectors, then $H(X1) + H(X2) = H(X1 + X2)$. But then that leaves me confused about what $X1 + X2$ represents. Are eac... |
Is there a TLS cipher suite with perfect forward secrecy (PFS) but without authentication, i.e. anonymous key exchange?
I am not asking or wish to discuss the principle question whether an unauthenticated key exchange is something one should do and that it is prone to man-in-the-middle attacks. The question above is mo... |
I'm trying to prove that semantic security implies key-recovery security.
There is already a question that addresses this, but it doesn't explain the setup of the security reduction, which is what I'm interested in.
My idea is as follows:
Given an efficient key-recovery adversary $A$, I'm constructing an semantic secu... |
I have recently read about the BGW Multi-party Computation protocol, more specifically the multiplication gate by Gennaro et al (PDF here), however, some concepts raised questions.
Context: From what I understood, to multiply two secrets $a$ and $b$ each party $P_{i}$ is required to own two shares $f_{a}(i)$ and $f_{b}... |
Intro
When using cosign for keyless signing, the flow that happens is as such:
The user runs cosign sign to sign an artifact
Cosign redirects the user for a OpenID Connect flow to log in via a OIDC provider and bring a code
The user enters the code to cosign
Cosign retrieves a JWT from the OIDC provider.
Cosign genera... |
I was wondering if I could use Wireguard's keys to sign messages, and prove authenticity of a node that runs Wireguard with its known public key from other nodes, so that I can use it in a system to prove something originated from a certain node and wasn't injected in some other way.
I came across Encrypt text message ... |
BKcrack and BK94 states that a minimum of 12 bytes plaintext is required to perform the attack but that was more than 20 years ago, even Michael Stay's improvement is not utilizing modern resources like RAM and so many threads or a proper tradeoff.
I do not know exactly where to pin this but the algorithm store somethi... |
$p$ - is the order of the finite field
$n$ - is the order of the group. Private keys can range from $1$ (the generator point $G$) to $n - 1$.
All the private keys ($Priv$) lie in certain ranges of 2.
$2^{a} < Priv < 2^{b}$
If we know the $a$ then after converting our private key to the public key ($Pub$), we can divide... |
Point doubling formula
Calculate the slope
$\lambda = (3\times Q_x^2) \times$ pow($2 \times Q_y$, -1, $p$) % $p$
Calculate the new point coordinates
$R_x = (λ^2 - 2 \times Q_x)$ % $p$
$R_y = (\lambda \times (Q_x - R_x) - Q_y)$ % $p$
Point addition formula
Calculate the slope
$\lambda = (Q_y - G_y) \times$ pow($Q_x - G_... |
Background
I have constructed a function $F':X × K → Y$, which has a characteristic that the quantity of $x\in X$ mapping to a single $y\in Y$ follows a binomial distribution $B(\frac{1}{2}, 2\frac{|X|}{|Y|})$.While a pseudorandom function $F: X × K → Y$, where the quantity of $x\in X$ mapping to a single $y\in Y$ foll... |
I always thought that part of the idea behind SSS was that there is only a single $t-1$ degree polynomial through $t$ unique points; that this holds when the polynomial coefficients are over the reals and also in particular for SSS when the elements are chosen from a finite field. However I'm running into (what I think... |
Is the result of 4G the same when calculated as 3G + 1G or 2G + 2G in projective coordinates? Considering a curve like (y^2 = x^3 + 10x^2 + x (mod 83)) with a Generator point G = (3, 28) in affine coordinates, or (3:28:1) in projective coordinates, the calculations indicate that 2G = (64:Y-coordinate:65) and 3G = (25:Y... |
Some projects (e.g., https://zkpass.org/) are claiming that interactive ZKPs can be more efficient than non-interactive ZKPs. What is the rationale behind this?
|
I'm currently tasked to implement this cryptographic scheme. But currently struggle to understand these hash functions of the scheme. Can anyone explain and suggest a way or some kind of tool to build these hashes?
Two groups G1 and G2 of the same order p and a bilinear pairing e: G1 × G1 → G2.
Hash functions H1, H2: ... |
In target app users are equivalent to adversaries. They are allowed to pick chosen keys.
If we use standard AES (in ECB mode)
$$c = AES(m,k) $$
Every user $u$ gets a cipher $c_u$. Two users $u_1, u_2$ have the goal to find a suitable key $k_u$ which leads to a common message $m$ (any 128-bit number) with
$$m = AES^{-1... |
My knowledge of cryptography nothing beyond basic so I am by no means an expert, but I do know a bit of undergraduate mathematics including number theory.
I know that stream ciphers like ChaCha20 is inspired by the one-time pad, but is there a way to use ChaCha20 or modify it to guarantee the same information-theoretic... |
This question is with reference to the python file model_BKZ.py provided in the GitHub repository https://github.com/pq-crystals/security-estimates/blob/master/model_BKZ.py
In this file, there is function called construct_BKZ_shape. I am not able to understand what it is doing. I have read BKZ algorithm from this paper... |
I am writing an ECC based zkp circuit and need to express the constraints:
a + b + c = d
a, b, c, d >= 0
a, b, c, d will be represented by points on the curve so addition can wrap around the curve module. (Imagine d is total amount, and a, b, c are partial payments that total d)
is easy, it's just a + b + c = d
is m... |
Hello im got stuck at ctf crypto challenge, so at the challenge is given 3 file which is
flag.enc pub.key priv.key
,
so i tried to decrypt using openssl here is my command
openssl pkeyutl -decrypt -in flag.enc -inkey priv.key
.
But it get an error with this message
`
Public Key operation error 40870E30C87F0000:err... |
I took a look at the implementation of Kyber, which can be found in this GitRepo. I made a small discovery in the indcpa.c in the function indcpa_keypair, starting at line 205, which I can't quite interpret. The line is given below.
// matrix-vector multiplication
for(i=0;i<KYBER_K;i++) {
polyvec_basemul_acc_mo... |
I am an undergraduate (grade three). I am confused about the cryptanalysis. Because a lot people say that the modern ciphers are complete and they can't be cracked. Maybe the prospects for cryptanalysis are bleak?
|
Can someone explain the logic behind the claim that the second equality is because we condition on the event that $M$ is equal to $m$ in the proof of Lemma 2.4 from "Introduction to Modern Cryptography"? I have added the relevant fragment below.
LEMMA 2.4 An encryption scheme (Gen, Enc,Dec) with message space
$\mathca... |
The usual hybrid argument tells us that if two efficiently sampled ensembles are computationally indistinguishable based on a single sample, then, computational indistinguishability holds even for polynomially-many independent samples.
My question is based on the fact of a quantum state induces a probability distributi... |
It is well-known that a One-Way Function is hard to invert on uniformly random inputs. As per Wikipedia,
for [sic] all randomized algorithms $F$, all positive integers $c$ and all sufficiently large $n = \mathsf{length}(x)$, $$\Pr[f(F(f(x))) = f(x)]\leq\mathsf{negl}(n)$$ where the probability is over the choice of $x$... |
When i know the value "c", How do I find factored numbers "a" and "b" : (a*b) == c (mod N) where, N is bitcoin order.
For example,
0x2eb4110dd5ca04a63de5b4ba2654ad2012ece01827e92af6734553150fae332a * 0x251469c4e7202526c1571ba2e9a9d90ad46f52172b9d63e779a2165ee7201f66 == 0x5a1b9916812f186ef2c26f314fccd20af8222b022b0154e6... |
Is it possible to construct a PRF that is secure under non-adaptive queries but not secure under adaptive queries?
|
In vitalik's post here the below is mentioned,
This is the pairing. Mathematicians also sometimes call it a bilinear map; the word “bilinear” here basically means that it satisfies the constraints:
$e(P, Q + R) = e(P, Q) * e(P, R)$
$e(P + S, Q) = e(P, Q) * e(S, Q)$
Whereas the textbook definition of linearity (as m... |
Suppose I want to commit to the following information:
I have an integer $i\in\mathbb Z$ and I want to commit to $i$ and that $i\gneq 0$, without revealing $i$.
I have an element of a prime field $x\in\mathbb F_p$. I want to commit to $x$ and that it's nonzero, without revealing $x$.
Can anyone advise on the curre... |
I'm referencing Jason A. Donenfeld's Random number generator enhancements for Linux 5.17 and 5.18 available here. In summary:-
significant outward-facing change is that /dev/random and /dev/urandom are now exactly the same thing, with no differences between them at all...
So entropy is collected at boot, ChaCha's sta... |
I am exploring a modification to ECDSA to produce shorter signatures, even though it compromises security (in a controllable way). My rationale behind this change is in this discussion. In my application, the main focus is on keeping the signature short, while storage isn't as crucial.
Here is my new ECDSA method: (the... |
If I was to use AES-NI as a high performance 128-bit permutation/PRF would AESDEC offer faster/better diffusion than AESENC? The reason I ask is because both instructions have the same cost, but the inverse MixColums step of AES has a more complicated matrix, so it appears to me as if there are more operations being pe... |
There is a algorithm listed in D.1.6, Algorithm 3, it seems that it is used to solve the quadratic equation when $m$ is even in $F(2^m)$. However, I can not find any reference about this algorithm, as well as the definition about half-trace when $m$ is even. Can anyone introduce some basic ideas or reference about this... |
Given public key $pk$, message $M$ and its signature $\sigma$, is it possible to get another $pk'\not =pk$, $M'$ with the totally same signature $\sigma$? In other word, the following ones are both satisfied: verifySig$(pk,M,\sigma)=1$ and verifySig$(pk',M',\sigma)=1$.
I am uncertain whether all signature schemes posse... |
I was reading this paper, and there, they use the ring $\mathbb{Z}_{\large p}[\alpha]/(\alpha^{\large n}+1)$ for all their operations. And that looks like a construction of finite field $\mathbb{F}_{\large p^{\Large n}}$ as the quotient ring of the polynomial ring $\mathbb{Z}_{\large p}[\alpha]$ modulo the ideal genera... |
I read the paper "Provable Security Evaluation of Structures against Impossible Differential and Zero Correlation Linear Cryptanalysis" - author: Bing Sun. In this paper proof of theorem 2 mentioned that from 1 difference in input state spreads to all other differences in other state after R_1(P) round, where R_1(P) is... |
Alice and Bob have a shared symmetric key k ∈ {0, 1}^256, which Alice
uses to identify herself to Bob, who holds a database of usernames and
shared keys. The identification protocol they use begins when Alice
sends her username, Bob responds with a challenge c ∈ {0, 1}^256, and
Alice chooses a response r ∈ {0, 1}^∗ and... |
In a cryptography exercise, I have to factor $N$ only knowing $e$ and $d_p+d_q$ (not $d_p$ and $d_q$ separately).
I came up with the following equations:
$$e*(d_p+d_q) = 2+K_p(p-1)+K_q(q-1)$$
$$e*d_p \equiv 1 \pmod{p-1} \implies 1 +K_p(p-1)\bmod e = 0 $$
$$e*d_q \equiv 1 \pmod{q-1} \implies 1 +K_q(q-1)\bmod e = 0 $$
Pr... |
I would like to know how many combinations per second we are able to brute-force today with a powerful server farm. Can someone give me some info on that? Also what would be the rental costs? TIA
|
Suppose we have $N = p*q$ and $C1 = (2*p + 3*q)^{e1} mod N$ and $C2 = (5*p + 7*q)^{e2} mod N$. We know N, e1, e2, C1 and C2, but the problem is that these numbers are really large. We want to find p and q with a python code. In my example N is 600 digits long.
I think that it should be solved as follows:
$N\ =\ p q$
$c... |
RFC8446 states that:
the full encoded TLSInnerPlaintext MUST NOT exceed 2^14 + 1 octets
It also states:
length: The length (in bytes) of the following TLSCiphertext.encrypted_record, which is the sum of the lengths of the content and the padding, plus one for the inner content type, plus any expansion added by the A... |
The Halo2 is the zero-knowledge proof scheme which is the improvement of HALO. However, it is not clear for me what is the time complexity of this scheme，including generating and verifying the proof. Thank you!
|
I’ve a signature scheme for 1024‒bit RSA with a 65537 exponent. The signed message is constructed as follows:
760‒Bits fully_user_controlled_message_content+8 Bits incremental nonce+sha256(fully_user_controlled_message_content+Nonce)
Verification then consists of:
the nonce in the remainder must be ++prev_nonce
sha2... |
How do I find decryption algorithm and key using a encrypted version of a file and a decrypted version of a file? I have 4 files, 2 encrypted and 2 decrypted, I think the contents are the same if the encrypted one would be decrypted, I'm a noob at this and don't know what to do, so can someone do this for me or help me... |
In the book IMC by Katz and Lindell, definition 3.8 says that "if for all PPT adversaries A, there is a negligible function negl such that for all n ......".
I am confused about why it holds not for "sufficiently large n's" but for "all n".
|
I'm no mathematician but when thinking about block ciphers such as AES I find it much easier to think of them as a mathematical function $f$ (rather than an 'algorithm') such that $c=f(m,k)$ with $c$ the cyphertext, $m$ the plaintext and $k$ the key.
When I think about breaking such a cipher the first thing I think abo... |
When directly invoking the ntt and invntt function in Dilithium's code with any polynomial $a \in R_q$, I get a unexpected running result: $NTT(a) \neq iNTT(NTT(a))$.
And in the test code of Dilithium(\test\test_mul.c), if want get an correct running, we need multiple the coefficients with -114592 before invoking the p... |
I am currently enrolled in a computer algebra class for engineers, and while I have some background in discrete algebra from a previous course, it's quite limited. I'm seeking assistance with understanding the application of the trace operation in the context of polynomials defined over the field $X = \mathbb{F}_p[x]/(... |
I’m interested in the tradeoffs of signing individual files vs. signing a manifest of cryptographic hashes and file names.
Let’s say I do some work that results in a handful of files (10s to hundreds), and then I send all that work out for someone else to look at and maybe pass on to others. Later, I may wish to verify... |
I'm a beginner still learning how ecc works... And i think I understand that in secp256k1 public keys there is something called addictive and negative inverse for example private key:- 0000000000000000000000000000000000000000000000000000000000000001 is additive inverse and it's public key is 0279be667ef9dcbbac55a06295c... |
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