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In the paper
"Hybrid Key Encapsulation Mechanisms and Authenticated Key Exchange"
by Bindel et al., I looked at the IND-CCA security experiment (figure 3).
In the first line of the game, we have $H \leftarrow \mathcal{H}_{\mathcal{K}}$
However, I cannot find the definition of $\mathcal{H}_{\mathcal{K}}$ in the paper.... |
Let us take example of secp256k1 curve. The current known public key with most leading zero (in x cordinate) is:
pubKey = (0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63,
0x3f3979bf72ae8202983dc989aec7f2ff2ed91bdd69ce02fc0700ca100e59ddf3)
private = 0x7fffffffffffffffffffffffffffffff5d576e7... |
Do Safe and Sophie Germain primes maintain a relatively stable distribution as numbers get larger, or do they become rarified beyond a predictable value?
This is important in one area of triangular number comparison for some of my study.
What is the predicatable, stable distribution?
Is there a comparable density, like... |
I saw posts tangentially related to this, but not this one specifically.
I'm building a content-addressable storage layer where I'd like to store the contents encrypted. The question is what is a safe 'content address'/lookup identifier that would not weaken the encryption.
In an unencrypted store, I would have some da... |
If i understand correctly, hashes run a defined set of operations iteratively until the original data is all hashed.
Can you take a hash value, run it backward through the last step (or once, for an approprately sized starting block), and get a pool of possible starting states?
If you run that pool of states through th... |
Accidentally used ed25519 public key to create libsoidum_sealed_box. Is there any way to decrypt the data if the private key ed25519 is known?
|
I'm exploring elliptic curve cryptography, specifically on the secp256k1 curve. I've come across the concept of point division by integers using scale multiplication, my question is how can I devide a point by $7$, Is there a standard method or cryptographic approach to achieve point division on secp256k1 for these non... |
The basis for this question is a 1-dimensional NTRU cryptosystem.
After some literature inspection I have found out it can be also generalised into higher algebras: quaternions (QTRU) and octonions (OTRU) while keeping the same logic of operations in a modular quotient ring. One may therefore encrypt multiple messages ... |
Consider a floating point number $f$ in IEEE 754 format with sign, exponent and significand values as $f.s$, $f.e$, and $f.sig$. Given this floating point number $f$, I want to compute the shares of $f$, denoted as $f1$ and $f2$, such that $f=f_1{\underset{\mathsf{FP}}+}f_2$, where ${\underset{\mathsf{FP}}+}$ denotes t... |
I want to find the minimum distance of an $[8,4]$ Near MDS code over a finite field F_4 (NMDS Code is a type of linear code). I want to know which programming language has a built-in function that will return the minimum distance (or the minimum weight) of this code.
|
let $F$ be a finite field, $E(F)$ an elliptic curve of order $n$, $r$ a factor of $n$, $k(r)$ for the embedding degree of $E(F)$ with respect to $r$.
Then why the full $r$-torsion group contains $r^2$ many elements and consists of $r+1$ subgroups?
|
Participating entity: multiple data owners, computing clouds
Protocol: The multiple data owners send their data to the computing clouds, which perform the computation of the data.
Privacy protection: Using a public key based homomorphic encryption scheme, the multiple data owners encrypt their data before transmissi... |
I am working on an experiment to compare the efficiency of brute-force attacking block ciphers like AES and DES with reduced key sizes for different programming languages and library implementations. However, I am restricting it to using a ciphertext only attack, so I will generate 1 block of random plaintext, encrypt ... |
We have access to an encryption and decryption server with the following implementation. How can we get the secret key by interacting with this server?
from Crypto.Cipher import AES
KEY = ?
def encrypt(plaintext):
if len(plaintext)%16 != 0:
return {"False"}
cipher = AES.new(KEY, AES.MODE_CBC, KEY)
... |
I am trying to implement the algorithm suggested in Section 5 of the Black & Rogaway paper titled "Ciphers with Arbitrary Finite Domains" in C++. It is a Feistel cipher that tries to encipher to a target "unusual" domain size $k$, using cycle-walking when necessary. This excerpt describes an example:
In order to spec... |
Consider a matrix $H \in GF(2)^{a \times b}$ where $b > a$. This defines two linear codes. First, we have the code for which $H$ is the parity check matrix:
$$
C = \{ \mathbf{x} \in GF(2)^b | H \mathbf{x} = \mathbf{0} \}.
$$
Secondly, we have the dual code, for which $H$ is the generator matrix:
$$
C^\perp = \{ \mathbf... |
I'm implementing Argon2id from the RFC 9106 and I'm at the part where each thread computes J_1 and J_2 in order to generate indices [l] and [z].
I'm confused as to which TYPE (y = 0, 1 or 2) of Argon2 to use when computing J_1 and J_2, because the RFC basically says:
"If you're doing Argon2id, compute J_1 and J_2 as de... |
Research paper: "Extended-Chacha20 Stream Cipher With
Enhanced Quarter Round Function"
The initial matrix is 6x6, but what are the exact inputs for each index, in other words, how will you fill the two additional columns that are added to the matrix?
Is it possible to change the constant values? and is it based on a s... |
I am researching ASCON. I can find cryptanalytic attacks ASCON authenticated encryption and ASCON HASH, But I am not finding anything ASCON MAC. Anyone knows of any attacks, any research on this?
|
I know that DES has 56 independent key bits, and that 3DES has 168 independent key bits by using 3 separate 56-bit DES keys. 3DES also has a block size of 64 bits.
If I use 3DES as the underlying block cipher to construct a Davies-Meyer compression function, what would be the input/output size of this compression funct... |
Normally, the chinese theorem looks like this:$$
x = a_1 \bmod n_1\\
x = a_2 \bmod n_2\\
x = a_3 \bmod n_3$$
but what to do if in my situation it looks like this:$$
c_1 = x^e \bmod n_1\\
c_2 = x^e \bmod n_2\\
c_3 = x^e \bmod n_3$$
I know $c_1$, $c_2$, $c_3$, $e$, $n_1$, $n_2$ and $n_3$. So how do I find $x$?
|
In GRR3,we make the first row of the Garbled table to be zero by choosing a special value of $C_1$.
Why don't we make the second row also zero by choosing a special value of $C_0$?
|
Suppose $\Pi=(Gen,Sign,Vrfy)$ is a secure signature scheme, is the following signature scheme $\Pi'$ secure?
$Gen'$: The same as $Gen$, output public-private key pair $pk,sk$ on input $1^n$
$Sign'$: On input a private key $sk$ and message $m\in\{0,1\}^n$, choose uniform $r\gets \{0,1\}^n$. Output $\sigma=(r,\sigma_0,\... |
Montgomery Reduction requires that $gcd(R,N) = 1$, where N is the original modulus and R is the selected modulus which is like $2^k,k\in\mathbb{N}$, because the computer adopts binary coding.
When N is odd, R and N must be prime, but when N is even, we cannot find the R in form $2^k,k\in\mathbb{N}$.
The paper “Montgome... |
Many blockchain users have wallets that hold a private key, which can interact with a website. For example, the website can request the wallet to sign a specific message.
'Do only sign this message if you trust the frontend and you want to give it access to your private key used for XYZ.'
From the deterministic signatu... |
Is it possible to change the constant values of ChaCha20?
and how it will affect the security of the cipher.
|
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?
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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... |
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