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Given that H is a collision-resistant hash function from 2n-bit strings to n-bit strings.
How do I prove that Hash is collision-resistant if:
$$\text{Hash}(X_1∥X_2∥X_3) := \text{H}(X_1∥H(X_2∥X_3))$$
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I'm currently reading the specification of Salsa20 (link). DJB on whether he chooses
"xor-a-rotated-sum" instead of "add-a-rotated-xor" states the following :
Should there be modifications other than xor-a-rotated-sum?
There are many plausible ways to modify each word in a column using other
words in the same column. ... |
I want to AES-GCM some user data that I‘m going to persist in a database. I‘m wondering if I should encrypt individual columns (all with an individual IV ofc) or JSON stringify the sensitive data and then encrypt the whole dataset.
Despite the problem that I need more database space for storing additional IVs, I feel l... |
How can I ensure that person X on website A is the same person who contacts me?
Here is my use case.
On website A I post message asking username X to contact me. Someone send me an email - how do I ensure it is the same person? Website A does not have a private messaging functionality and all posts are public and visib... |
Given $E/K$ defined over a finite field extension $K$, can I find another curve $E'/K'$ and a group isomorphism $\phi: E/K \to E'/K'$, where $K'$ has an extension degree lower than that of $K$?
If $K = K'$ then we speak of isogenies defined over $K$, but I am specifically looking for an isomorphism defined over finite ... |
I have two ETH transactions (both belonging to the same address) that both have the same r value in the transaction signature, is it possible to extract the private key from it?
Details of both transactions below:
address:
0xF55f348c48bd2811a34105899db5fF7C2EBD9934
transaction hash(1): 0x374180005946ef3b1906ee1677f85fa... |
I know that SSL Certificates use a private key on the server side and the public key for verifying it on the client side.
I am wondering, is it the same for Code Signing Certificates?
Or do they just use a single Certificate, signed by the CA, that you use to sign your code with. Or do you sign it with a private key, a... |
I have read that some integers are not appropriate to be chosen as the modulus in an RSA cryptosystem. Some of these numbers are those that, given a modulus $n=pq$, then $p-1$ or $q-1$ do not have large factors. This is due to the fact that there are factorization algorithms that allow this type of modulus to be factor... |
On first glance, the optional customization string for cSHAKE resembles the optional salt input to HKDF-Extract. Indeed, the Noise Protocol Framework initially uses a protocol identifier string as its HKDF salt value (chaining key in Noise), which looks very similar to examples of customization strings given for cSHAKE... |
The MD5 algorithm is no longer considered secure for most applications of a hash algorithm. However, is it safe to initialize a PRNG via a password?
If it is not, how could it be exploited?
|
I am looking for symmetric cryptography algorithms that can be implemented on chips with very few resources (about 256K RAM and 16MHz CPU).
An algorithm that works perfectly in this environment is RC4, however it has multiple vulnerabilities. Are there algorithms that can be implemented in this type of systems that do ... |
RFC 8784 introduces a straightforward mechanism to use a pre-shared key to make modified IKEv2 key agreement resistant to a quantum computer Shor algorithm attack- thus providing a "quantum-safe" information channel. One use of this information channel could be to share keys.
QKD authentication requires a PSK in order... |
This question is related to "Is it safe to initialize a random number generator with MD5?".
But in the context of steganography we don't know which pixels have been selected to hide information. In addition, the content could be encrypted, so we do not know if the hidden information that we extract (with a guessed pass... |
This is not for a production application, but just my exploration to help me understand cryptography.
At the simplest level, I want to design a key-value store for user secrets.
This is exposed over an HTTPS API with usual create-read-update-delete operations supported: send a post request with a body of a sercret, the... |
AES-GCM-SIV takes a 96 bit nonce, like the original GCM. The RFC states that "it is RECOMMENDED to use this scheme with randomly chosen nonces". It uses the random nonce to generate per-message encryption and MAC sub-keys using a PRF based on AES, and claims this construction offers beyond birthday bound security:
Th... |
Let $\mathcal R$ be the ring of integers of a power of two cyclotomic field.
That is, $\mathcal R = \mathbb Z[x] /\langle x^{2^k}+1\rangle $ for some integer $k$.
We denote $\mathcal R / q \mathcal R$ by $\mathcal R_q$. This is a well known setup for ring-LWE.
I think that for randomly chosen element $a \in \mathcal R_... |
I am looking for authenticated key exchange protocols (AKE) based on a generic key encapsulation mechanism (KEM) and providing full/perfect forward secrecy. Optionally, the protocols should offer external anonymity.
The idea is to plug into the protocol an existing post-quantum KEM such as CRYSTALS Kyber or SABER.
My r... |
I have seen a few answers here and elsewhere that say a salt doesn't need to be cryptographically secure randomness but rather just unique since they are stored in the open anyway. I am working on an implementation of PBKDF2 and AES-CBC and reading NIST SP 800-132 Recommendation for Password-Based Key Derivation from 2... |
From the Wikipedia page for DSA(Digital Signature Algorithm) we have the following private/public key generation:
Choose an integer x randomly from [1, q-1]
Compute y := g^x mod p
x is the private key, y is the public key
My question is: How are we sure that there does not exist z != x from [1, q-1], such that y = g^... |
For encryption, we want identical plain-text's to encrypt to unique ciphers, also called Semantic Security.
For Signatures, the plain-text (i.e. message hash) is not a secret. The plain-text, if you can call it that, is publicly known. We don't need Semantic Security. There is no “plain-text”, so to speak. We aren’t en... |
If I had a true random number generator that had a fault where 10-20% of the bits never change (these bits always produced the same value every time the TRNG was called), could I feed the result of the TRNG through a hash function (let's say SHA-256) to generate a unique and secure key?
|
The F5 steganography algorithm hides information in images using binary codes. But when hiding a bit, the affected DCT coefficient becomes zero, it is necessary to hide the same bit again. This is because the receiver ignores DCT coefficients with a value of zero, and otherwise would not be able to read that bit. As th... |
I am interested in a polynomial form of the lattice problem Closest Vector Problem (C.V.P), or in other words if C.V.P. can be ''transferred'' to Ring-LWE.
My idea about this question is that a polynomial form of C.V.P will look like the following:
Let $R = \mathbb{Z}[X]/\Phi_M(X)$ and its residue filed $R_q = \mathbb{... |
While reading A Graduate Course in Applied Cryptography by Dan Boneh and Victor Shoup. There was the next exercise (Ex. 4.2 (b)), let $F$ be a secure PRF over $(K,X,Y)$ where $Y := \{0,1\}^n$ and $|X|$ is super-poly. Define $F_1(k, (x,y)) := F(k,x) \oplus F(k,y)$, prove that $F_1$ is weakly secure even if we modify the... |
I'm having an issue with a key created by the manufacturer of an equipment. Checking the details of the key I've noticed that it's exponent is zero. Is this a valid exponent?
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Searches here indicate that D/H primes of 2048 bits are "safe"? How do we know that this is true? Using a pathetic retail laptop (Intel N5000 Silver) it's possible to find 60,000 bit primes and test them in about a week! Using a 60,000 bit prime in a custom D/H encryption program, and using the same pathetic retail ... |
I have implemented an authentication scheme using JWT with assymetric keys (RS256). The idea is that (assuming some microservice-based acrhitecture) the authentication service will sign all JWTs with a secret/private key (PRIVATE_KEY) and distribute the public key (PUBLIC_KEY) to all other microservices, so they can ve... |
I am working on problem 2.11 from the book: A Graduate Course in Applied Cryptography by Dan Boneh and Victor Shoup. The problem reads as follows:
Problem 2.11: Let $\mathcal{E} = (E, D)$ be a cipher defined over $(\mathcal{K}, \mathcal{M}, \mathcal{C})$. A key recovery attack is modeled by the following game between a... |
It might be a little dumb: I think it should be possible, if I encrypt a plaintext using the same public key twice, it should be possible to end up with two ciphertexts that for whom the statistical distance is non-negligible.
Specifically, I was exploring a paper which required that the statistical distance between ci... |
I'm new to the topic guys, but as there are literally too many encryption methods out there, too that I could even come up with many ideas of them, how to we actually test/calculate "how secure" an encryption algorithm is?
Do we a standard or a formula that we can use to test security level of encryption algorithm?
And... |
Is it possible to introduce a new signed attribute in the CMS Advanced Signature format (RFC 5126) for a custom data type? I want to include location data from GPS or Galileo and extend CAdES for my thesis.
I would appreciate it if you can provide me with some directions if it makes sense.
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I'm new to crypto!
The situation is,
Aes-256-cbc encrypted message(including not encrypted iv & salt) is revealed.
We also know pbkdf2 function uses 10000 rounds with sha256.
All we need to decrypt the message is just put all the possible passwords in pbkdf2 function with 10000 rounds & sha256,
and then decrypt encryp... |
I want to distinguish different concepts: Bootstrapping, Modular Switching, and Key Switching. I am also sometimes confused about Evaluation & Relinearization.
My understanding of these concepts are:
Bootstrapping is a method to shrink errors in ciphertext.
Modular switching is just an arithmetic technique to transfe... |
TLDR/End goal
I want to encrypt a tree of data/files so that anyone with the master key K can decrypt everything, key K-1 can encrypt and decrypt anything encrypted with K-1-*, and so on. However, K-2* must not be able to decrypt any of K-1*.
First ideas/initial research
To be quite frank the only way I can think of ac... |
A probable attack for RSA (factorization): how to improve it?
$N=8*G+3$ can be factored if there is a non-trivial negative $k$ such that
$\frac{(N*(9+24*k)-3)}{8}=-6*m^2 $
[to exclude the two trivial solutions $m=\frac{(N+1)}{4}-N*t$ and $m=N-\frac{(N+1)}{4}-N*t $]
given the system
$
\frac{[[8*[\frac{(N*(9+24*k)-3)}{8}... |
Let us say that we have 3 entities: an Issuer I , a user/prover P and a verifier V.
V trusts I but does not trust u
u wants to show that he respects some kind of property (eg. being over 18yo) to V without revealing their whole birth day
V possesses the data that u needs to convince V, eg. using a ZK-proof, but V woul... |
I am struggling to solve this proof.
The goal is to prove that $H \circ G$, which is a composite function $H(G(s))$ can be a pseudo-random generator under some conditions on $H$, given that $G$ is also a pseudo-random generator. Note that $H$ is length-preserving.
However, I can't find a way to prove (using the definit... |
As an amateur, my first encounter with commitments has been in the form of an hash of the committed value, then I have learnt about seeding the hash as blinding technique. Going on I have discovered how useful is the structure induced by Pedersen or El-Gamal commitments and the binding/hiding flavours. All of this to e... |
I have a my own PBKDF2 automated implementation that automatically salts the hash. The output looks like this:
xxxxxxxxxxxxxxxxxxxxxxxx.xxxxxx.xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
\-- 24 byte salt ------/ \data/ \-- 48 byte output hash --------------/
Salt is a random byte array
Interations are stored in data
Outp... |
Although many different lattice-based signature schemes exist, Hash and Sign signatures schemes, like [GPV08], are prevalent. On the other hand, it is well known that collision-resistant hash functions may be built out of lattice problems [SWIFFT08]. However, I've never seen a scheme that combines both; why? Such compo... |
I am implementing BLS signature verification on smart contracts and I have a question regarding the way that Ethereum verifies the signature. Recall that bls signature works as
$e(P_2,H(m)_1)_T=e(G_2, S_1)_T$ where $_2$ and $_1$ denote points of $G_2$ and $G_1$, and $_T$ for $G_T$.
Off-chain, you take your secret $x$ ... |
Is it possible to get the x, y of the compressed public key?
I have decompress it and naturally it gives the xy of the decompress public key.
I need the xy coordinates of my compressed public key . How do I get it? Is there a python script I can get my hands on?
Update: I have tried it via
#! /usr/bin/env python3
im... |
Assume a standard ECC curve in a prime field $\mathbb F_p$ with $p\equiv3\pmod 4$, such as secp256k1; and code turning a bytestring for a compressed ECC public key into an Elliptic Curve point, that does as specified except in the following two emphasized spots:
2.1. Parse $M=Y\mathbin\|X$ as a single octet $Y$ follow... |
Here's a modification of the textbook RSA scheme, in an attempt to achieve semantic security.
Key generation: chooses public key $pk = (N,e)$ and secret key $sk = d$ as in any RSA-based encryption scheme.
Encrypting message $m \in \mathbb{Z}^*_N$ using $pk$: Choose $x\gets \mathbb{Z}^*_N$, output $\mathsf{ct}_1 = x^e ... |
Hi I'm trying to understand the logic behind a CTF challenge basically we are given a program which encrypt some data, we have the following options:
Select encryption mode (EBC, CBC, CTR, OFB, CFB)
Encrypt the flag and see the resulting ciphertext
Encrypt a choosen plaintext and see the resulting ciphertext
Now I th... |
I'm curious to hear of algorithms that use this new standard (there is a new IRTF CFRG Draft for it, for instance). It's useful for verifiably deterministic signatures on elliptic curves, but what else?
|
I am wondering does AES-GCM which uses Authenticated Encryption provide us with all 3 properties (Authenticity, Confidentiality, and Integrity), or does it not provide integrity?
|
Suppose the highest level is $L$. There are 2 ciphertexts from 2 different messages under the same secret key but in different level, one is in level $\ell$: $\mathsf{ct}(\pmb{m})\in\mathcal{R}_{Q_{\ell}}^{2}$, one is in level $k$: $\mathsf{ct'}(\pmb{m}')\in\mathcal{R}_{Q_{k}}^{2}$, and $k<l-1$.
We want to calculate ho... |
I want to encrypt a private key $sk$ (it's actually an RSA private key in PKCS#8 format) with another person's (and/or my) public key $pk_A$ for secure storage. With JWE, it is possible to use hybrid encryption: we generate a random symmetric key $k$ to encrypt $sk$ and then encrypt $k$ with $pk_A$.
I would use AESGCM+... |
A lot of writeups, books & webpages say that to get 112 bit security (i.e $2^{112}$ steps), you need to use RSA or DH with 2048 key size or ECDH with 224 key size. In reality, I think what is meant in most of these cases is modulus size or group size rather than key size, but for some reason it's always referred to as ... |
I noticed that when using AES-256-CBC with a 128-bit IV, the ciphertext is always at least 16 bytes long (size of IV).
I also noticed that when using AES-256-GCM with a 96-bit IV, the ciphertext size can be smaller than the IV.
Normal? Why?
|
I'm working in a context where it is cheaper to calculate pow(a,b) via modular exponentiation (modexp(a,b,m)) than to do exponentiation directly. For this I need the minimum modulus value such that the function returns only the exponentiation part of the function call.
Is there an efficient algorithm that exists to cal... |
I was wondering out of the functions (MD5, SHA-1, SHA-256, and SHA-512), do all provide 128-bit pre-image resistance and 128-bit second-image resistance?
Also, out of these hash functions, do only SHA-256 and SHA-512 provide 128-bit collision resistance? (Due to $l/2$ bits of security)
|
Let we have $G_1 \times G_2 \to G_t$
let $g_1 \gets G_1, \\g_{2.1} \gets G_2, \\g_{2.2} \gets G_2$
$$e(g_1^a,g_{2.1}^b) = e(g_1, g_{2.1})^{ab}$$
$$e(g_1^a,g_{2.2}^b) = e(g_1, g_{2.2})^{ab}$$
Is it working?
|
I have two linkable ring signatures, each signed with the same key pair. Therefore, the signer's public key will appear in each of the rings. However, the set of other public keys appearing in each ring are different.
Is it possible to tell that the same person signed both rings, or can this only be known if each ring ... |
Imagine a scenario whereby Alice and Bob have a symmetrical messaging system for talking with each other. It's effectively two polystyrene cups joined by a piece of string. Crucially, there is no central server, and nobody logs into nothing. They do though both have the same messaging application. Also imagine that the... |
I'm wondered about what arithmetic operations are supported from FHE.
I want to know for 2nd Gen(BGV,BFV), 3rd GEN(GSW,CGGI), 4th GEN(CKKS)!
Is 3rd can support more than and/or/not? I heard it is for a bit.
Thanks
|
In modern cryptography, IND-CPA is the lowest security we want. We want at least IND-CCAx security from encryption mode. Their relation can be found in
2007 Authenticated Encryption: Relations among notions
and analysis of the generic composition paradigm, Mihir Bellare & Chanathip Namprempre
All classical block ciph... |
I have two private-key encryption ($Π$ and $Θ$) and their concatenation $Π\#Θ$. For example:
$$
Enc_{Π\#Θ}( \ ⟨k_Π, k_Θ⟩, \ ⟨m_Π, m_Θ⟩ \ ) = ⟨ \ Enc_Π(k_Π, m_Π),\ Enc_Θ(k_Θ, m_Θ) \ ⟩;
$$
(Same for Gen and Dec)
I need to prove that if $Π\#Θ$ is secure against passive adversaries, then both $Π$ and $Θ$ are.
Actually I... |
ECDSA works by computing the hash of a message and then computing the signature for it. ECDSA uses the signature:
$$s = k^{-1}(h + rp_{pr})\,\textrm{mod } n,$$
where $n$ is the order of the group, $k$ is a randomly sampled nonce, $r$ is the projection onto the $x$ axis of $kg$, where $g$ is a group generator.
If you ar... |
The Argon2 specs claim that Argon2 can be used both for password hashing and key derivation.
I want to generate from a single password both a hash for authentication and a secret key to use for encryption. (It would be nice if this could be generalized to any (reasonable) number of hashes and keys.)
From the specs, it... |
I'm a bit confused regarding the bilinear pairing operation. Let's say I have a Public key of a receiver $P_r = P^x$ and I want to create a symmetric key using KEM with a pairing operation. If I chose $R = rP$ and compute $V = (Pr, P)^r $which results into $V = (P^x, P)^r = (P^x, rP) = (P^x, R)$. Here, I am confused ab... |
I was taking a look at the PRESENT lightweight cipher presented here. You can see an implementation of it in Python here. It is basically a Substitution-Permutation (SP) cipher with ultra-lightweight encryption and lightweight decryption.
The algorithm for encryption is the following :
generateRoundKeys()
for i = 1 to ... |
I have short (8-byte) messages which are effectively true random numbers, and I want to encrypt these messages with a (pre-shared) key....
I'm using AES-CTR for this purpose -- but with the SAME IV each time (which is seemingly contrary to best practice).... but since EVERY message that I'll encrypt with this key is un... |
I'm new to cryptography and having a hard time understanding PRGs and PRFs.
Question: $G'(x)$ and $G''(x)$ are two different secure pseudorandom generators, and $G(x)=G'(x) \mathbin\Vert G''(x)$.
Is $G(x)$ still a secure
I thought $G(x)$ is secure at first, since $G'(x)$ and $G''(x)$ are secure, their outputs are unifo... |
Basically, I need to find the probability that DES(p, k1) = DES(p, k2) = c
My guess is that probability = 1 / 2^64 since that's the total number of possible outputs, but honestly I have no clue about crypto. Thanks in advance for any help!
|
The $(t,n)$ Shamir’s polynomial based secret sharing scheme is $(+,+)$-homomorphic in which the addition of two polynomials secrets equals the Lagrange’s interpolation of the sum-of-shares for the same subset of shares.
My question is: Does the two polynomials need to have the same degree to satisfy the SSS $(+,+)$-hom... |
Context
I am trying to build a simple protocol for key derivation. I want to use SHA-3 family hash functions, which (as far as I understand) should not be combined with HMAC because their security properties make HMAC redundant. Thus, HKDF — which uses HMAC — would also be unsuitable for key derivation using SHA-3 fami... |
I'm trying to understand the security proof of Shamir's Secret Sharing method, as I want to adapt the polynomial creation a bit, and I've found the proofs I had available to be surprisingly vague or holey.
Some nomenclature
Given a secret $S$ in the finite field $\mathbb{F}_p$ for a $(k,n)$ threshold scheme the Shamir'... |
Despite working with AES-GCM and other AEAD algos for a few years, I've struggled with the concept of 'authenticated' in the term 'AEAD'. In my own experience (of Unix, PKI and blockchain) authentication means being able to attribute actions towards a particular entity (eg, a user account). In the simplest case, say au... |
I am familiar with any algorithm that is based on the number of bits in a key (n-bit) and how to restore a key, such as the Discrete Logarithm Problem or Factorization.
When I use any algorithm for encrypting and decrypting images, such as RSA, how can I estimate this algorithm's security and work efficiently with ima... |
For example, if you have say, 3 distinct paragraphs of clear text a, b, c and you only know hash(a), hash(b) and hash(c), and then you have a clear text d, which claims to be the concatenation of a, b, and c, is there any way to use hash(a, b, c) to demonstrate that d either is or isn't a+b+c?
Not beng a math person, I... |
In Privacy-preserving machine learning, GC is usually used for privacy operation such as ReLU(x) where sign(x) needs to know. However, binary secret sharing also supports such computation via comparators($[x]_{encryted}$ > 0)(this paper).
While compare the performance, binary secret sharing is usually way faster than g... |
Suppose I have a set $S$ containing $n$ bit strings, where $n$ is on the order of about 10. Consider
$$\mathfrak{S} = \{ R : R \subseteq S, |R| \geq 2 \},$$
the collection of subsets of $S$ with two or more elements.
Does there exist a hashing function which outputs the same hash for any member of $\mathfrak{S}$?
A po... |
For communication between the client and the website, use password (P) as the key using AES-128. If P is less than 128 bits, it is padded with 0 to create a 128 bits key. is there any problem with such an approach if the average password length is 6?
|
Assuming evaluation in the online phase (no beaver triple/offline method used), each AND gate in GMW must be evaluated using a 1-out-of-4 OT. I've seen some sources (here, and here) say this can be implemented using 3 1-out-of-2 OTs over 1 bit strings. Can it also be implemented from 2 1-out-of-2 OTs over 1 bit strings... |
Is it feasible to efficiently calculate a homomorphic absolute value function over ciphertext given a pair of numbers $a$ and $b$, i.e., |a-b|? Although there are approximate methods that use addition and multiplication, their runtime in my project is intolerable. Is there any homomorphic absolute value function that i... |
I am using micro-services to interact between various cryptographic technologies like HSMs, keystores, vaults, etc., that are written in different languages. Usually, each technology, or even vendor, is using different names of the cryptographic algorithms, and in some cases they are also case-sensitive.
For example, J... |
$x$ is challenging string, $y$ is proof string. $\operatorname{H}$ is the proof-of-work (pow) function, to find a $y$ such that $H(x,y)<2^{256}/D$
$x ,y = \{ 0, 1 \}^{512}$
$\operatorname{H}(x,y) = \operatorname{SHA-256}(x \oplus y)$
find a $y$ such that $\operatorname{H}(x,y)<2^{256}/D$
the question is to prove:
If ... |
I totally have no idea about this Rabin decrypt problem.
source code:
https://github.com/shanzhuer/myctf/blob/main/crypto/rabin.py
Inside there were $2^{21}$ times of encryption and decryption of Rabin-cryptosystem, with 126 bytes plaintext, 1024-bit public key $N$(unknown 512-bit $p$ and $q$ when $p*q=N$)
the output l... |
I am trying to write a function that, given an EIP712 ECDSA signature, verifies the signature was signed by a particular person, and then (somehow) retrieves the information that is encoded in the signature.
Is it even possible to retrieve the unhashed data from an EIP712 ECDSA signature, or is it only possible to veri... |
this is my first post so I apologise if the formatting of my post isn't perfect.
I should start off by saying that this post is not for any malicious intent, rather for curiosity and understanding AES encryption/decryption.
I have been doing research about AES encryption and everywhere says that ECB mode should never b... |
It is known that there are two popular applications of lattices: dense sphere packings and lattice-based cryptography. I didn't find any information on the Internet about possible interaction of these domains. Let's forget for the moment that most dense lattices are quite theoretic constructions, hence they don't have ... |
Given p = 7 and q = 13, one can obtain n = 91, d = 29, e = 5. However, for plaintext with values less than the modulus both the public and private keys (n, d) and (n, e) are reversible, i.e. encrypting a plaintext value with either key and then using the same key a second time returns the original value.
What is the re... |
This is a slight variation of the shared nonce problem. We do have a lot more shared information between two nonces.
Given a random $k$:
$$
k_1 = ka,
k_2 = kb
$$
I am now signing two messages, which gives me $s_1,r_1,s_2,r_2$
Based on my understanding of the base equation for signatures in ECDSA
(with given generator $... |
I don't understand which DES key is used in the next round of Feistel construction.
As you can see below, we use our original key that has been inserted in permuted choice 1, where we got 56 bits, divided into two halves, $C_{i-1}$ and $D_{i-1}$. We will apply the left shift rule on that key and therefore obtain 16 dif... |
I understand that $\text{gcd}(m,n)$ needs to be $1$ so we can apply the Euler's theorem, and if it's not $1$, the result is one of the prime factors of $n$. But Why the result it is always $p$ or $q$? Couldn't it be any other number?
|
I understand that if the $\gcd(x, n)\neq=1$ then the $\gcd$ is one of the $n$ prime factors, $q$ or $q$. But how is the fact that $x \not\in Z^*_n$ related to $\gcd(x, n)\neq 1$?
|
Does anybody know or can point me to a source about SHA2 vs SHA3 usage statistics.
SHA3 is newer and is claimed to be more secure but ... is it more widely used in real life deployments?
|
I'm trying to understand how lattice-based schemes with the Reed-Solomon proximity testing work and why the scheme in Bootle's et. al. Fig 3 has no aborts at all (nor big number of repetitions).
TLDR: How do PCPs and Reed-Solomon allow to avoid aborts and multiple repeats in Bootle's et. al. exact proof? I see no abor... |
In NTRUEncrypt, we choose polynomials $\mathbf f,\mathbf g$ (with suitably small coefficients) such that $\mathbf f$ admits inverses $\mathbf f_p, \mathbf f_q$ with respect to the moduli $p,q$. The relationship between the public $\mathbf h=\mathbf f_q\mathbf g\text{ mod q}$ and the private key $(\mathbf f, \mathbf f_p... |
Suppose I had a new public-key or key exchange protocol. How do I objectively evaluate it so as to determine if it is worth sharing with the broader community? Whenever developing a cryptosystem, it is important to ask "who cares?", to see if it addresses any challenges that current systems face, but it is unclear ex... |
One party (master) wants to send data to another party (slave) over an insecure channel using public-key encryption and signature schemes such that:
master is authenticated,
data is confidential,
data cannot be replayed.
The minimal assumptions are:
master has slave's public encryption key,
slave has master's public... |
When using BLS, let's say Alice signs each of the 5 messages ($m_1, m_2, m_3, m_4, m_5$), aggregates the signatures and sends the aggregated signature to Bob. Bob can verify it.
Here's the goal:
However, Bob would also like to send the aggregated signature by Alice to Charlie but hide the values of $m_2$ and $m_4$ mess... |
I'm working on a Chinese Remainder Theorem Garner's Formula problem in my Cryptography module and was hoping for some help.
Question:
Given the data below use Garner’s formula to find T,U and s
$$ N = pq = 6815731 $$
$$ s \% p = 1 $$
$$ s \% q = 62537 $$
$ s = a \% p $
$ s = b \% q $
$ T = p-1 mod q $
$ U = (b-a)T mod... |
When a tag8 compressed data packet does not contain compressed data i've seen some products simply handle the packet as a tag11 literal data packet, yet i find nothing in the 4880 spec old/new suggesting this is an acceptable behavior. what am i missing here?
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What the state of the art for producing quickly verifiable proofs of correct computation when your proof is allowed to leak knowledge?
For context, I am inspired by Miden VM's promises:
For any program executed on Miden VM, a STARK-based proof of execution is automatically generated. This proof can then be used by any... |
The sever holds the N encrypted elements, each element is associated with an index (unencrypted). The receiver wants to retrieve only k-out-N elements using k-out-N OT.
The motivation for using OT is to retrieve only k elements, not all N elements, retrieving N elements results in storage overhead on the device (receiv... |
While I was reading the documentation for the cryptocode $\LaTeX$ package I stumbled across the "primitive" called puncturing in subsection 2.12. This was the first time I read about this "primitive". Additionally, I am no native speaker, which is why I have no intuition about what it could mean. Can someone explain it... |
I am confused about stream ciphers a little so I just wanted to clarify. We have a key that's lets say 2 bits. I have a message that's 8 bits. I used a pseudorandom generator that would add 6 bits to my key. Those 6 bits are deterministic and public. Hence why it's called pseudorandom, it looks random but because the 6... |
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