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I'm currently studying the different adversarial settings for digital signatures.
In Goldwasser, Micali and Rivests paper they propose three different chosen message attack settings, which are vastly different.
More specifically they specify:
Generic chosen message attacks
Directed chosen message attacks
Adaptive chos... |
I'm tired of going online looking for a simple explanation of how the Diffie-Hellman Key Exchange works. Many guides I've found attempt to explain it using anything from "paint" to massive holes in the explanation such as "g is usually 2" which infuriates me. If you can't explain it simply, you don't understand it well... |
Is there any way to derive the RSA private key from another RSA private key?
Let's say I have a base RSA key $(P, Q)$ (both prime), and then use some salt and an algorithm that creates a new primes, e.g. $(P', Q') = f(P, Q, \mathsf{salt})$.
Is there any security issue with my approach?
Does anyone have a better solutio... |
I have AES-GCM output with GMAC tag. The plaintext consists of some bitfields I know the structure of. When I generate input which should only affect timestamps and counters in very specific bytes, I see corresponding ciphertext changes only in those bytes for 2 subsequent calls to the encryption function.
Ignoring the... |
my question is as in the title.
For example, there are 2^256 different values that a SHA256 code can take.
But is it possible to shorten this number somehow?
|
One uses a Schnorr group both for Schnorr signature (or DSA), and for Diffie-Hellman Key Exchange. They target 128-bit security, and choose prime $q$ that's 256-bit, prime $p=q\,r+1$ that's 3072-bit, and $g$ of order $q$ (e.g. $g=2^r\bmod p$). In DHKE, a participant chooses an ephemeral secret $x\in[1,q)$ uniformly at ... |
The company Qrypt states that "Key distribution based on asymmetric algorithms is a weak link for cryptography" and claims to "enable encryption without distributing encryption keys" using its BLAST architecture. It gives non-technical explanations here and here and a technical explanation of the underlying math here. ... |
[Computer scientist here who is not totally familiar with the factoring literature -- please forgive my ignorance.]
It's well known that hard-to-factor integers, $n$, are typically semi-primes, such that their factors are roughly $O(\sqrt{n})$ in size. However, it's not clear to me that all such semi-primes are necessa... |
I have a question about the implementation of the functions
$$Compress_q(x,d) = \left\lfloor (2^d/q)\cdot x\right\rceil mod^{+}2^d$$
and
$$Decompress_q(x,d) = \left\lfloor (q/2^d)\cdot x\right\rceil$$
from Kyber.
I have copied two lines from the GitRepo, which contain the compression:
t[k] = ((((uint32_t)t[k] << 11) +... |
There seems to be a common trend among forums involving the topic of cryptography to shutdown any conversation very quickly, least in my experience.
From the stand point of a newcomer to the field making bold claims and selling snake oil I can understand the trepidation and warnings. But as someone who has been reading... |
Simple question, Given c=$b$$e$ mod $m$, we all know finding $e$ is equivalent to solving the discrete logarithm.
But what about finding $b$ from c ; $e$ and the semi‑prime $m$ ? Is it something harder than factoring $m$ too ?
If yes as this is different from the ʀꜱᴀ problem, how to compute $b$ when $e$ is more than 1... |
I am a new dev dabbling in ECC. I am currently building an Android app in Java/Kotlin and can't get a piece of content that was signed with a private key to be verified using the corresponding public key. I have been stuck for a few days so I thought I'd come here!
Here's my code for keypair generation:
fun generateKey... |
Is there a direct non-iterative formula for point multiplication by 3 in the secp256k1 elliptic curve just like point multiplication by 2 (point doubling)? If such a formula exists, could you explain how to achieve this? If not, could you clarify why it's not possible?
|
In a certificateless aggregate signature scheme, can a signature aggregator be a type 1 adversary (external attacker who can have access to secret value of a user)? I thought signature aggregator is always assumed to be trustworthy in a certificateless aggregate signature scheme.
|
I'd like to know if there's any cryptographic scheme that implements something similar to what I'm summarizing here below.
Thanks a lot for reading and for any hint or question.
Intro-Scenery:
There's a public encrypted ledger of accounts such that each contains a balance of funds.
Whoever owns the private keys to one ... |
I understand that AES-CBC uses the following scheme for encrypting data (diagram from Wikipedia):
And, I understand that we don't want initialization vectors to be predictable or constant, and also that you don't want it to just be a plain counter.
But, what if the Initialization vector is computed with some number of... |
Given the ring $R_2=\mathbb{Z}_{2}[x]/(x^8+1)$, initiate a public key encryption based on RLWE $(A,b=As+e)$ where all the parameters are selected as polynomials over the given ring. Under the assumption of brute force attack only and if the vector $s$ is 248-byte long, I have the following questions:
is this secure i... |
In systems where computations are performed in remote or potentially untrusted environments(e.g. Ethereum NaaS providers such as Infura), how can we gain confidence in the accuracy of the results? Zero-knowledge proofs (ZKPs) provide an intriguing solution for verifying specific aspects of computation.
My focus:
Proo... |
I was reading LAC (https://eprint.iacr.org/2018/1009.pdf). They mention about high-hamming weight attacks on the Centered Binomial Distribution (CBD). To counter this, they propose CBD with fixed hamming weight.
To prevent high hamming weigh attacks, we switch to n-ary centered
binomial distribution with fixed Hamming... |
I am working on generating pseudo random numbers from a chaotic oscillator's signal. In literature I have read about the Nist 800-22 test used for checking randomness. I friend gave me a software "random number analyzer to use for this test. Has any one ever used this software before? Is it reliable?
If not, what recom... |
I know that the normal construction for Ajtai hash functions is as follows:
Pick $n, m, q \in \mathbb{Z}^+$ such that $n \log q < m < \frac{q}{2n^4}$ and $q = O(n^c)$ for some $c>0$, and some random matrix $A \in {\mathbb{Z}_q}^{n \times m}$. Then the Ajtai hash function $f_A: \{ 0,1 \}^m \to \mathbb{Z}_q^n$ is defined... |
I'm trying to decrypt a message that has been encrypted using a one-time pad with a repeated key. The encryption technique involves using the same key twice. We know the message was encrypted with $k = k_0 \ ||\ k_0$ and that the length of the subkey $k_0$ is half the length of the complete key. We also know that the e... |
in the Montgomery Curve using Affine coordinates, we have points that lie on either the (0,0) coordinate or have a y-coordinate of 0. The question here is: Can we use these points as the Generator Point (Base Point)? Because if we did, then the denominator of the slope in the point doubling process would be zero, and w... |
Although the conjecture regarding the existence of one-way functions remained open, there are numerous NP-based methods for constructing diverse one-way functions, including DL, lattice, and subset sum problems.
Recently, I have been endeavoring to employ multivariable polynomials in the construction of a one-way funct... |
I'm trying to hash (as secure as resonably possible) a password inside my db.
Per user I have their email, username and password and a uuid4 to identify them.
And for the password I though of using python's hashlib library with the pbkdf2_hmac function.
It takes:
a hash function I went with sha512
the password itself ... |
I just saw this article and many like them before where they use a video of some random movement and a hashing function to make a cryptographic random number generator
but I'm always curious why this is as "unpredictable" as they claim. These random generators, they're supposed to help with random number generation wit... |
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... |
The protocol would look like this:
User creates account and provides username, static public key
User logs in by sending username
Server responds by sending an ephemeral public key
For the duration of the user's session, all requests must be accompanied by the ECDH shared secret between user-static and server-ephemera... |
In university, I'm currently learning how to use Scyther to model security protocols. Currently I am trying to understand what is happening in an example protocol given to me which is:
# Key Establishment Protocol
#
usertype SessionKey;
protocol ke11(I,R,S)
{
role I
{
var Kir: SessionKey;
sen... |
I was trying to come up with simple padding functions for the RSA, then trying to break them just to have a better understanding of why we need all the pieces used in the RSA OAEP... So, I am considering the following.
Let $N = p\cdot q$, $pk = e$ and $sk = d$ be the RSA parameters and keys, as usual.
Now, let $n = \lc... |
I rent a room in a building. There are also 9 others who rent other rooms in this building. Just like everyone else who rents a room I only have one key of this building.
With my key I can open the front door of the building. Just like everyone else who rents a room can with their key. However, only I can open the door... |
Suppose that Alice has an X25519 key pair $\{S_A,P_A\}$ (secret and public key, respectively). Using randomly selected X25519 public keys $\{P_*\}$ (such that $P_A\notin \{P_*\}$), Alice calculates several values $X_* = \operatorname{X25519}(S_*,P_*)$.
She then repeatedly flips a (fair) coin. Each time, if the result i... |
From here - Batch Opening of KZG PCS
One can prove multiple evaluations $(\phi(e_i) = y_i)_{i\in I}$,for arbitrary points $e_i$ using a constant-sized KZG batch proof, $\pi_I = g^{q_I(\tau)}$, where
\begin{align}
\label{eq:batch-proof-rel}
q_I(X) &=\frac{\phi(X)-R_I(X)}{A_I(X)}\\
A_I(X) &=\prod_{i\in I} (X - e_i)\\
... |
In this question, we restrict to RSA public keys $(n,e)$ such that
$n$ and $e$ are odd, $3\le e<e_\max$, $e<n$
Note: For some old Windows API, $e_\max=2^{32}$. In FIPS 186-4, $e_\max=2^{256}$. Other requirements are from PKCS#1.
For all $m\in[0,n)$, it holds $m^e\bmod n=m$. That is, textbook RSA encryption is the ide... |
How should I generate the remaining keys when performing subkey generation in AES encryption? I generated keys 0 and 1 first, but the other keys I generated later were wrongly generated, so what steps should I do to generate the rest?
I know the steps of shifting rows and mixing columns but I don't know what to use whe... |
Let $G:\{0,1\}^n \leftarrow \{0,1\}^{2n}$ be a PRG. Establish whether the following PRG candidates $$G^{'},G^{''}:\{0,1\}^n \leftarrow \{0,1\}^{3n}$$ are secure or not:
$G^{'}(s)=(x⊕y,u,v)$ where $(x,y)=G(s)$ and $(u,v)=G(y)$;
$G^{''}(s)=(x,y ⊕ u,v)$ where $(x,y)=G(s)$ and $(u,v)=G(y)$;
This was in my exam today and ... |
The iOS version of Signal application (not the protocol) includes a form of key wrap that I've never seen elsewhere: SHA256-HMAC-SIV.
It's used to encrypt your master key with your pwHash(PIN) before sending it to signal.org's Key Backup Service.
So far as I can tell, it does the following:
SHA256-HMAC-SIV(kek, raw)
ke... |
I wonder if it's possible to do public key authentication (preferably not vulnerable to replay attacks) before modern computers became a thing (e.g. in a medieval setting).
Specifically:
Authentication can be done in a reasonable time by hand.
Brute force by hand requires unreasonable time. (But it may be possible wit... |
I have a question regarding the paper:
Andreeva, E. et al, Securely Release Unverified Plaintext in Authenticated Encryption , 2014
(DOI: 10.1007/978-3-662-45611-8_6)
AE schemes such as GCM [28] and CCM [40] reduce to CTR mode in the RUP setting. This is because the adversary does not need to forge a ciphertext in ord... |
In a WPA2 (802.1X) scenario, there are 3 entities -> Supplicant (client), Authenticator (router) and Authentication server (Radius server). Radius server performs the authentication process and, as far as I understand, in the authentication process, the router works only as a proxy.
If an attacker is able to sniff the ... |
Does there exist a lattice in $\mathbb{R}^n$, with an independent generative family $(b_1, \dots, b_{n+1})$ of $(n+1)$ vectors (without any loss of generality I suppose $(b_1, \dots, b_{n})$ is a $\mathbb{R}$-basis), for no generative family of size $n$.
I know:
If these vectors are in $\mathbb{Q}^n$, then the answer... |
It's well known that two parties, Alice and Bob, can flip a fair coin using commitments.
Alice picks a random number $a \in \mathbb{Z}_q$ and computes $c_a = Com(a, r_a)$ where $r_a \xleftarrow{R} \mathbb{Z}_q$. She then sends to Bob $c_a$.
Bob does the same, pick a number $b \in \mathbb{Z}_q$, and compute $c_b$ and s... |
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