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I am new to this encryption scheme, so I may not be exactly sure of its implementation. I have a list of (u, v) ciphertext pairs to decrypt, each of them are 1-bit. { "u": [ 1, 19, 3, 2, 24 ], "v": 16 }, { "u": [ 3, 20, 22, 26, 15 ], "v": 21 }, { "u": [ 7, 3, 24, 26, 22 ], "v": 13 }, ...
I'm having trouble testing a not-so-popular algorithm that I haven't found an implementation of, so I wrote it myself and now I'd like to test it with nist tests, but I have a suspicion that I'm doing something wrong. I got encrypted file with ~10,000,000 bits. I tested my algorithm in the following wayю. I set the inp...
I know I should calculate the multiple inverse of plaintext with ciphertext $\pmod {26}$. However, the problem I have is that the plaintext is a $3 \times 4$ matrix which is not square, so how would I get an inverse? Should I get the inverse of one side (left or right) of the plaintext or is there another way?
In simulation based proof of cryptographic scheme, if k parties are invovled in the scheme, then k simulators should be constructed for all the parties?
I started studying CSIDH a few weeks ago and, seeing these papers [1] [2], I was wondering: Given $[a]E$ and $E$, find $[a]^{-1}E$. I read that is easy to find $[a]^{-1}E_0$ knowing $[a]E_0$ by quadratic twisting, but I haven't found any resources explaining how to compute $[a]^{-1}E$. So, is it possible to compute $...
When I look up who developed SHA-2 family, the result I get is along the lines of SHA-2 was first published by the National Institute of Standards and Technology (NIST) as a U.S. federal standard. What I am really looking for is "Which individuals have developed SHA-2 family?". I understand, that most probably there ...
I have an algorithm that encrypts large text. I want to test this algorithm on statistical tests. The ciphertext contains ~10,000,000 bits. I decided to test the algorithm in two different ways, I took the ciphertext and passed it to the input of statistical tests: The first parameters were as follows: /assess 1000000...
I am writing to request information about the difficulty of finding z in Z/pZ (where p is a large prime) given z^l and l. I am working on a project that involves this problem, and I am interested in learning more about its complexity. Specifically, I would like to ask for your insights on the following: Is there any k...
I have a chat system where multiple clients communicate securely using Libsodium authenticated encryption. Every client have their own 32 byte key pair. If two clients want to communicate they first share their public key out of band and then use e.g. crypto_box_easy for encryption. I want to create a service that allo...
These days I'm generating some PGP keypairs, and I'm struggling to understand the correct terminology behind ECC keys. Moslty in the differences between ed25519/cv25519/ECDSA/EdDSA/ECDH. I tried to check RFC 6637 and this RFC draft without being sure of what I understood. Let's take a practical example, with RSA first....
secp256k1 is an elliptic curve $E$ over a prime field $\mathbb F_p$, of equation $y^2\equiv x^3+b\pmod p$, with prime order $n$. I noticed† that the different curve $E'$ over the prime field $\mathbb F_n$ with the same equation has order $p$. The roles of $p$ and $n$ are reversed in $E$ and $E'$. That also holds for se...
LWE Encryption Scheme by Regev is inefficient due to its public key sizes in $O(n^2)$. This led to the variant problem RLWE, defined in this paper : Let $n$ be a power of two, and q a prime satisfying $q = 1 \mod 2n$. We define $R_q = (\mathbb{Z}/q\mathbb{Z})[X] / (X^N+1)$, which is the polynomials with coefficients ...
Naively, when one applies rounding to a uniform random value one anticipates that the change is uniformly distributed. In lattice-based cryptography, is there a formal notion or proof of equivalence between learning with rounding and learning with uniform error schemes? Secondly has anyone proposed a dynamic version of...
I'm trying to implement impossible differential cryptanalysis on 3.5 round IDEA using Miss in the Middle Attack on IDEA and Khufu paper as a reference and I'm stuck on the first two steps of the attack: In the paper the authors say that I should choose a structure of $2^{32}$ plaintexts $X^1$ with identical $X^1_{2}$ ...
I want to know if there's any algorithm to find the embedding degree of elliptic curve? for example SECP256K1 curve has embedding degree 19298681539552699237261830834781317975472927379845817397100860523586360249056. this number is so large that it can't be found using brute force. So there has to be an algorithm to fig...
I'm implementing a digital signature algorithm for academic purposes using elliptic curves. I am familiar with equations of the form $$y^2 = x^3 + ax + b$$, but the paper I am reading for implementing point addition and doubling uses the equation $$Y^2Z = X^3 +aXZ^2 +bZ^3$$. I guess the $Z$ comes from representing the ...
If we have a (possibly imperfect) cryptosystem that generates ciphertext $C$ from plaintext $P$ and key $K$, we have: $H(C, P, K) = H(C | P, K) + H(P, K)$ where $H$ is entropy. My question is why following is true: $H(C | P, K) = 0$ It seems because each key and plaintext uniquely define a ciphertext but I want to ...
I am studying about RP-algorithm from the book Algebraic Aspects of Cryptography by Neal Koblitz. The following example is given in the beginning which is the Probabilistic Primality Test. I understand the scheme of the algorithm but I am facing difficulty in understanding and deducing the probability that given the n...
I've been given that an attacker has a 2-Key Triple DES Cracker that is capable of performing 10$^{24}$ encryptions per second and have subsequently been asked how long it must take before the attacker successfully finds the correct key. This doesn't seem too hard however I'm caught between two different answers, here'...
A vigenere cipher is just a ceasar cipher (ROT13) based on a SECRET word from my understanding. Are there variations of a vigenere cipher that are similar? I want to create a new type of vigenere cipher where the SECRET is used 2-3 times. Once forward for encrypting it once, then a second time encrypting it twice with ...
Are ideal functions and leakage collections the terms of UC security? Why I often see them in a simulation-based proof under stand-alone model? Some papers use the definition in Lindell's How to simulate it? while defining ideal functions (sometimes with leakage collections), which really confuse me a lot!
Is there a non-deterministic encryption scheme that is vulnerable to a CPA? I got asked this in an interview and I answered with no but the interviewer said that my answer is wrong. Would somebody clarify if this is possible?
On 6 March, Yi Lee sent over the NIST mailing list an announcement of their submitted paper that found a flaw in the original security proof for Dilithium. In their manuscript, they fix the proof on paper, and they also verified whole proof using EasyCrypt. URL: http://ia.cr/2023/246 In Section 3.2, paragraph "The ‘Pro...
Given two numbers $x_1$, $x_2$ and their respective binding numbers, $b_1$ and $b_2$, let's take their Pedersen Commitment to be $C(x_n, b_n)$ $\forall n=1,2$. What is $C(x_1 * x_2, b_1 * b_2)$?
I want to encrypt Bluetooth Beacon data. I was wondering if having very little entropy in the clear text would make the key easier to guess? The maximum data length is 31 bytes An example of the data (packed struct): where sequence monotonically increases, all other measurements have small variations between readings (...
I would like to use JWT but one thing I'm still thinking is ¿what is the best length for the secret? If I'm using HS512 as a signing method the secret should have a length of 512 bits as far as I understand and I imagine that 512 bits are 64 characters (of 1 byte) because the secret is a string, as far as I understand....
Given two field elements as input of Arithmetic Circuit (consists of adding gates and multiplicating gates only), how could I output the bigger one? Or, how to place the gates in order to distinguish which one is bigger (using Arithmetic Circuit)? Could you please describe the method in picture? In Zero-knowledge Proof...
Several texts talk about malicious/dishonest verifiers in a zero-knowledge interactive proof but none of them properly detail how a dishonest verifier can gain extra knowledge over an honest verifier using some examples like "Quadratic Residue Interactive proof" or "graph 3 colouring Interactive proof". I went over the...
I am making an implementation of Niels Ferguson's paper: Single Term Off-Line Coins in Python. In the Coin withdrawal protocol, in the last steps, Alice checks that the signatures she received are correct. She checks if she needs to adjust the signatures by making corrections. When I run the program I get most of the ...
I'm having troubles in interpreting the output of the SUPERCOP benchmarks of some digital signature schemes. Precisely, I don't understand how to read the number of cycles for the key generation. This should be found in the line of the SUPERCOP output file with the keyword "keypair_cycles". However, I find three such l...
I was reading this paper, where I came across the following statement: We consider the problem of unbounded MPC with security against semi-malicious adversaries in the dishonest majority setting. In our communication model, parties publish their first message through a broadcast channel which is immediately delivered ...
From section 4.4 of this book https://www.ic.unicamp.br/~rdahab/cursos/mo421-mc889/Welcome_files/Stinson-Paterson_CryptographyTheoryAndPractice-CRC%20Press%20%282019%29.pdf I'm confused on how the differential trail is formed given they don't know the round key. I would love if someone could give a clear example of how...
I was reading this paper, where I came across the following statement on Pg 4 under the Homomorphic Commitments: A witness encryption scheme, associated with a NP language, consists of an encryption and a decryption algorithm: Anyone can encrypt their message µ under an NP instance and the decryption algorithm can obt...
In SMhasher, it seems that data (keys) are read one by one sequentialy, and not splited and: MiB/sec: The average of the Bulk key speed test for alignments 0-7 with 262144-byte keys. The higher the better. /\ This is written in its README. The author said that are the output of hash functions that is measured. Take a ...
We have the RSA function: $c = m^e (mod n)$. I would like to know the proof that there is not an $m_1$ and an $m_2$ message that produce the same $c$. My thoughts: We know that $m \le n$, so $m_1 \ncong m_2 (mod n)$. We also know that if $a \cong b (mod n)$, then $a^k \cong b^k (mod n)$. So if $m_1 \ncong m_2 (mod n)$ ...
Let $\mathbb{F}_q$ be a finite field of odd characteristic. I know that a constant-time implementation of the square root extraction $\sqrt{\cdot} \in \mathbb{F}_q$ is used in the context of hashing to elliptic curves (see Appendix I of the draft). Are you aware of other cryptographic contexts in which a square root $\...
Bob has two detectors + and x. You can see it in the picture I sent. Alice sends a photon with vertical polarization and Bob uses the + detector and the detector is detecting Alice's photon. Bob's + detector detects when the polarization of the photon from Alice is either vertical or horizontal. (because it is + detect...
An adversary is able to insert a random string (which he does not control: he can only randomly generate it and insert it). The random string is parsed by the victim as an ECDSA public key. This public key is used to verify a signature (the adversary can insert whatever signature he chooses). Is this a vulnerability? E...
I'm implementing impossible differential cryptanalysis on AES and I've started with implementing it on mini-AES to fully understand the process using R.Phan's paper as a reference. But I don't understand the initial pairs preperation step: In the paper the author say to obtain $2^{13}$ plaintext $P$ and another $2^{13...
If understood right, CMAC is not quantum-safe because it relies on AES-128 (which isn't considered as quantum-safe), while HMAC is, because it relies on SHA3 (which is considered as quantum-safe). Did I understand this right?
I'm having trouble understanding how time complexity of trial division is exponential. If it takes $\sqrt n$ tries to factor $n$ in the worst case scenario then time complexity is $\mathcal{O}(\sqrt n)$, which I thought would mean that the number of operations grows slower than the increase in the number of inputs. So ...
In the AES proposal, the last sentence on page 30 it is said: To be resistant against LC, it is a necessary condition that there are no linear trails with a correlation coefficient higher than 2^(n/2) I know that the correlation coefficient can have values in the range [-1,1]. Moreover, In the same proposal, they men...
Suppose the correctness requirement of private-key encryption scheme is now relaxed to require only that $$ \Pr[Dec_k(Enc_k(m)) = m] \ge \frac{1}{2} + \epsilon. $$ Prove of disprove that if an encryption scheme satisfies the perfect secrecy and the relaxed correctness, then $|M| \le 2|K|$, where $M, K$ are the message ...
I was recently trying to perform a AES-128 CTR Encryption and Decryption. I had a observation that if a AES-CTR encrypted value is encrypted again (with same key and Iv) it results in the plain text that was in encrypted in first place. Just want to the reason behind this and does any other AES scheme support this simi...
I am using Montgomery ladder with Montgomery curve $by^2=x^3+ax^2+x$ using XZ coordinates and I recovered the $X$ value using $X3=X1/Z1$, but I don't know how to recover the $Y$ coordinates. for Double and add ladder I am using this: A = X2+Z2 AA = A2 B = X2-Z2 BB = B2 E = AA-BB C = ...
As detailed in the paper Statistical test suite for random and pseudorandom number generators for cryptographic applications by NIST, the first test is given as a basic significance test, it uses a bit sum and calculates the p-value and test statistic. But I do not have the clearest understanding of why $S_{obs}$ is de...
Is it insecure to sign the plaintext 0 with ElGamal signature algorithm? Can this leak the private key, give the possibility to forge other signatures or does provide any other attack vector?
One experienced user of this forum said: "The key is the input of the hash function to build up a fast internal hash table. The key is hashed again to perform the lookup.". If I hash a data such as a 262144-bytes seed (as SMhasher does) is passed through a hash function to build up a fast internal hash table, can the s...
When I try to generate decimal numbers in the range 0-18446744073709551616 using a hash function I always get big numbers like this: $ A=$(date | b2sum -l 64 | awk '{ print $1 }'); echo $(calc 0x$A) 16324260068905187599 $ A=$(date | b2sum -l 64 | awk '{ print $1 }'); echo $(calc 0x$A) 5500525113920202581 $ A=$(date | b...
In Crystal Kyber specification, page no10, there are 3 algorithms namely KYBER.CCAKEM for making the CPA-secure Kyber into CCA-secure one. Q1: How is the shared key K being generated in KYBER.CCAKEM.Enc & KYBER.CCAKEM.Enc related to the CPA-secure algorithms ? Q2: Is the shared key K used as input parameter of sorts, f...
Due to protocol limitations, I can put in 24 bytes of data only for tx (excluding headers), if I use AES_GCM for encrypting my data, I understand I don't need to worry about padding. For instance, if my data is 22 bytes, I would be getting a 22 bytes encrypted output. So, I had zero-ed in on AES-GCM or AES-CTR. However...
In TCS, functions need to be converted into boolean circuits. So is this Boolean circuit a combinational logic, i.e. a directed acyclic graph, satisfying the topological order? I would appreciate your answer. Thanks!
In the encryption process, the ciphertexts c1 and c2 are added to errors e1 and e2 each to get noisy ciphertexts u and v. c1 = A * r c2 = b * r + m * (q/2) u = c1 + e1 v = c2 + e1 However, choosing a random value for e1 and e2 would cause u and v to not match to its message m. Wikipedia and several research papers su...
I am working with hardware that can only encrypt with AES. The problem with this is that the message must be publicly verifiable, without the encoding key being exposed. This is the textbook use-case for asymmetrical keys, yet the hardware does not support this. I cant come up with a method myself where a message is en...
I recently read a paper that proposed a matrix-DDH which is a matrix variant of DDH assumption. The brief definition is follows: Let $G$ be a group of prime order $q$. Then, the matrix-DDH says that it is hard to distinguish between two distributions: $\{[A], [A\cdot w] \} \approx \{[A], [u], u\leftarrow \text{random} ...
Cant you look at the algorithm used to encrypt and find the private key from the public key that way? As an example, here's a simple python algorithm that encrypts an input: rnd.seed(int(pasc)) return [(tran_ltn[content[i]] + rnd.randint(400, 1400)) for i in range(len(content))] This is obviously symmetric. However, i...
I'm a novice reader of Introduction to Modern Cryptography, where it states: Let $G$ be a pseudorandom generator with expansion factor $\ell(n) > 2n$. In each of the following cases, say whether $G′$ is necessarily a pseudorandom generator. If yes, give a proof; if not, show a counterexample. (a) Define $G'(s) = G(s_1...
I am attending the video lectures from Prof Dan Boneh. He gives the following example. Let $G:\mathcal K\longrightarrow \Bbb Z_2^n$ be a PRG with the property that from the last $\frac{n}{2}$ digits of $G(k)$ we can easily compute the first $\frac{n}{2}$ digits of $G(k)$. We want to show that $G$ is predictable for som...
I am working on using the Hadamard transform as a way to map randomly generated values and then apply statistical tests as defined by Nist or other institutions. One resource online I found particularly helpful, yet I do not seem to have the mathematical intuition to understand some parts. The python code and the text ...
I'm using AES-256-CBC to encrypt password for a set of users, and for each user in the database we gotta generate and store the password in the database. The database has constraint that the name of the user must be unique, so I was wondering if using the name of the person as the initialization vector was okay, becau...
My question might be a duplicate but I wasn't able to find a similar question. I recently developed a wallet-like app and I am trying to implement some MPC features. I searched a little and even asked ChatGPT about how I can achieve that. I know how ECdsa and how Shamir’s secret sharing work but I can't find a way to c...
I am following this paper Encryption from Learning with Errors for the generation of errors e1 and e2 to retrieve the ciphertext u and v as described below. u = Ar + e1 v = br + m (q/2) + e2 For this text: We require for this algorithm to work that the χ distribution has a mean of zero and, with overwhelming probabil...
In ECDSA, when parsing the public key a test is made to ensure the public key really lies on the curve. What vulnerabilities appear if one does not do this?
Consider the following paper based OTP Plaintext has 11 possible symbols 0-10. $C_i = M_i + K_i\ mod\ 11$. $K_i$ comes from a pre-shared key material which is never reused. How to introduce data integrity/ MAC in it which can be calculated using pen & paper.
Because of the need of the project, I want to develop a simple public key cryptography algorithm, but I have doubts when generating the key pair. I have learned about the key generation process of RSA. It is to prepare two coprime numbers (p, q), multiply them to obtain N, and then calculate L (that is, L=lcm (p-1, q-1...
I'm trying to find a MD5 hash collision between 2 numbers such that one is prime and the other is composite (at most 1024-bit). I'm using fastcoll with random prefixes for each iteration. For this I wrote this script: import subprocess from Crypto.Util.number import bytes_to_long, isPrime import string import random w...
Consider the following two verifiable encryption schemes for Discrete Logarithm. FS01: “One Round Threshold Discrete-Log Key Generation without Private Channels” by Pierre-Alain Fouque and Jacques Stern, Section 3.2, "A Proof of Fairness". CS03: “Practical Verifiable Encryption and Decryption of Discrete Logarithms” by...
Consider a single hash table containing digests from about 10 different 256 bits cryptographic hashing functions, like SHA256, SHA3, KECCACK256, BLAKE2, BLAKE3, etc... Is such table still considered collision resistant? I am inclined to think so, but I might be missing something.
I'm looking for a general comparison of encryption algorithms in regard to Confusion and Diffusion (as defined by Claude Shannon), and if possible, specifically for their SAC and BIC quality. For example, xor-streaming ciphers have no (0, zero, zilch) diffusion - you switch 1 bit in the ciphertext, you know which singl...
For context, I'm making a non-production grade reference implementation of the balloon hash function using the Web Crypto API. In order to make it less susceptible to certain attacks on common memory hard KDFs, the number of memory blocks should be reduced, meaning their size should increase. I am however restricted in...
I haven't seen Threefish widely used. For example, I've seen Twofish used in file encryption software, even though it was not standardized, but I've never seen Threefish. Are there security issues?
I'm currently going through the book "Guide to Elliptic Curve Cryptography" by Darrel Hankerson, Scott Vanstone, and Alfred Menezes. In the book, the authors state that […] there is no mathematical proof that the ECDLP is intractable. That is, no one has proven that there does not exist an efficient algorithm for solv...
Lets say entity A sends a secret "token" to anybody that they trust. The token itself is the proof and its sent equally to everybody and it has or needs to be derived from application specific data. Entities B, C and D get the same token and want to publish a timestamped event for proof, but they don't trust anybody, e...
The padding fix by Albertini et al. for AEAD key commitment (pp. 3292 and 3301-3302) involves prepending a block or two of zeros to the plaintext before encrypting. After decryption, these bytes are checked to be zero to verify that the same key was used for decryption. The Counter-then-Xor (CX) construction by Bellare...
I am beginning my journey into Cryptography, having studied a theory-heavy master's degree module, and I have also read The Code Book by Simon Singh, among many other online resources. What puzzle books would the community recommend, just so I can get into the mindset of code-breaking? I noticed that certain newspapers...
On some lecture slides regarding to RSA-Encryption, the formula for calculation of the private key is given as $d = e^{-1} \equiv e^{\phi(N)-1} \mod \phi(N)$. The second equation is justified by the fact that $gcd(e,\phi(N))=1$. My questions: 1.How does the second equality come about? I know, that Eulers Theorem shows,...
I am reading this paper, which in the introduction, tells about two main types of key recovery SCAs : Reaction_type SCAs, which uses a decryption failure oracle Message-recovery-type SCAs, which uses a plaintext-checking oracle I don't understand the difference between these two oracles. In this presentation, the aut...
In Guillou and Quisquater's 1988 paper "A 'Paradoxical' Indentity-Based Signature Scheme Resulting from Zero-Knowledge", they say that an RSA identity has a shadow and go on to state that this property is being standardized: Let us mention that ISO is standardizing a “digital signature scheme with shadow (see ISO-DP 9...
I was reading up on the Triple Diffie-Hellman (3-DH) key exchange and noticed that the wikipedia description [1] is different from the the original protocol definition [2] and the modified definition [3] they reference. Two users have two key pairs each; $a, A$ and $x, X$ for one user and $b, B$ and $y, Y$ for the othe...
I am trying to solve a problem where private key exponent d, ciphertext c, and public key exponent e (65537) are known. How can I calculate φ(n) or n itself? An extended version of the problem would be : If we can get many d and ciphers for the same plaintext, where e is always 65537, is there a way to decrypt the ciph...
I'm looking for a protocol in which a Prover transforms a RSA signature $\sigma$ on a message $m$ that verifies under a public key $vk$ into a NIZK proof of knowledge, $\pi$ of that signature. A verifier should then be able to verify that the prover saw a signature for that message and that the signature would have ver...
I am asking this since I can't find definite answer. Is it secure if I use textbook RSA provided all my data is 2048 bits ( or any N <=2048 for 2048 bit key ) and it is random ( using Secure Random in Java for example) ? Or should I figure out maximal key length under padding scheme and use padding anyway ?
Is it possible to solve this: If you have the following information about an RSA ecrypted plaintext $m$: $e = 65537$ $d$, $c$ some very large numbers $p$ and $q$ are both random 128-bit long prime numbers $m$ is a string build with 16 random characters of both ascii letters and digits If $N$ would be known $m \equiv ...
I am reading a paper Round5. This public key encryption scheme is based on Ring-LWR but I found it is a little bit different from typical LWR-based PKE scheme. In the key generation algorithm of Round5 (Algorithm 1, Line 3 in the paper), they compute $$ b= \left< \Bigl \lfloor \frac{p}{q}\left(\left< as \right>_{\Phi_{...
Below is a description of a "cube" Diffie-Hellman, based on commuting matrix actions on tensor products. Some questions: References for something similar? Obvious flaws, is this a terrible idea? Any other comments? Definitions Let $S$ be a finite ring, $n$, $k$, positive integers, and $R=M_k(S)^n$ the $n$-fold produ...
According to the documentation of HighwayHash, for finding a collision are expected $m \over 2$ guesses, being $m$ the message. By contrast, 'strong' hashes such as SipHash or HighwayHash require infeasible attacker effort to find a hash collision (an expected $2^{32}$ guesses of $m$ per the birthday paradox) or recov...
If I hash a 256-bit message and generate an output digest of the same size with a cryptographic hash function then the number of guesses to find a collision is expected to be 2^128. Does increasing the message size also increase the expected number of guesses to find a collision? If yes, can the hash function internal ...
Not all the cryptographic hash functions have the counter parameter for making messages be different for each counter value. But many accept a key parameter. Is reasonable to use the key parameter as a counter? Is it safe?
In the paper "Efficient Pseudorandom Correlation Generators: Silent OT Extension and More (https://doi.org/10.1007/978-3-030-26954-8)" Boyle et. al. proposed subfield vole. For standard vector oblivious linear evaluation correlation one has, $\vec{v}+\vec{w}=\vec{u}*x$ ($v_i, w_i, u_i, x \in \mathbb{F}_p$). And for sub...
Is there a zero-knowledge proof that proves that two Pedersen commitments commit the same value?
This is not a technical question, but rather it seeks advice on what to do if cryptanalytical research goes wrong. I've discovered a new attack that works great in theory, but in practice, it fails. I don't know why. Haven't figured it out yet. Tried really hard. I work on this thing alone. Not sure If I could do this ...
If we should consider that in an MPC protocol, the confidential messages communicated between two parties can be eavesdropped on by adversaries? If so, should we build a secure channel for that?
I would like to implement domain separation in encryption/decryption along with MAC. The encryption algorithms consists of XChaCha20,XSalsa20,SM4 From China and MAC algorithms consist of HMAC-SHA512 and Poly1305. Some proposed the following for domain separation encryption and decryption. Have 2 variables, EKey and MK...
Is it possible to decipher a ciphertext, in RSA with small primes (two 128-bit factors) when we only have ciphertext $c$, private exponent $d$ and public exponent $e=65537$ to crack it? I try hard on this question but I couldn't find $N$. First try, I write the code to find factors of $ed-1$ and find it on factordb and...
Suppose one has a password manager, based on symmetric cryptography, that requires a master passphrase to be unlocked. Argon2 is used for deriving a secret key from the master passphrase. I need several secret keys to encrypt different components, so I'm faced with a choice: Output more material using Argon2. For exam...
I'm new to cryptography, so please don't bash me. I'm trying to learn to recover a RSA private key. As you can see from my profile I'm a cybersecurity professional, which is only now trying to learn some cryptography.. Let's assume we have 5 message and public keys derived from the same string message. It is short (the...
The rainbow signature was not seen in round 4 of the NIST PQC standardization process. Was Rainbow not shortlisted?
I want to understand how the hardness of Learning With Errors problem varies as size of the error term changes. For example, assuming that the other parameters are the same, LWE with errors sampled from centered binomial distribution of $\{-1, 0, 1\}$ LWE with errors sampled from centered binomial distribution of $\{-...
Let's suppose I encrypt a plaintext with one key and a nonce in CTR block cipher mode of operation. Can I reuse the nonce with another key in another plaintext if I start the block counting with different counters than those used in the first plaintext? I mean (for example), encrypt the first plaintext stopping at the ...
Since all evaluation in BGV scheme is on polynomials it seems that it does not really matter if the coefficients of the polynomials are within $q$ range or not. All must be okay for the congruent values. I have the following questions: If there are no specific optimizations (e.g. RNS) for BGV, can we work in modulo $K...