instruction stringlengths 32 27.2k |
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Edited: changing the notation according request by fgrieu.
I have prepared 4 transactions for 2 pubkeys with the same r1 and r2.
properties of secp256k1:
p = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 # order of curve
It is according to: ecdsa-revealing-the-private-key-from-four-signed-messa... |
What combination of public key cryptography (DH) and symmetric key cryptography is currently available that is (subjectively) as secure as possible over other ciphers (AES,curve448) when security is prioritized over efficiency?
translator user
|
As far as I understand, the biggest problem of requesting authentication in disk encryption is that the plaintext and ciphertext are not having the same size -because of tag-. The XTS mode is already designed with this issue in mind (length preserved). However, as far as I know, it is not possible to preserve the size ... |
I'll get straight to the point here.
There are two different programs I'm looking at. They both use secp256k1 to deterministically sign data (RFC6979) & provide the results online in-browser. However, both programs produce different DER-encoded signatures and I'm honestly baffled at this point as to why.
Program #1: ht... |
I have been recently studying LLL-reduction. I get from the size condition and Lovasz condition that the basis are guaranteed to be somewhat orthogonal. But I couldn't figure out how orthogonal the LLL-reduced basis has to be in the geometric or intuitionistic sense. For example,
How small can an angle be between two ... |
I am looking for some cryptographic algorithms suit to the below usage scenario.
$A$ has a set of data, e.g., $\{x_1,x_2,...,x_n\}$. $A$ publish those data in ciphertext (maybe that they are encrypted by different public key, I do not know).
Then participants $\{P_1,P_2,...,P_m\}$ come to pick the data belonging to the... |
I have seen multiple sources claim that the Merkle-Damgård transform is able to build a collision-resistant Hash-function $H$ for arbitrary-length inputs from a compression function $h : \{0,1\}^n \to \{0,1\}^\ell$ (with constant-length inputs). See, e.g., [1].
However, the construction relies on suitably padding the i... |
I am very interested in encryption algorithms, especially AES encryption algorithm in symmetric encryption. To this end, I have studied a lot of theoretical knowledge about AES encryption algorithm and the code samples I can obtain.
I wrote a 512-bit encryption algorithm after referring to AES-CBC-256 mode in detail.
I... |
For example, Threefish has a key length of 1024 and a very long number of rounds (80). but, I have not heard much about Threefish-1024 being particularly secure, so what symmetric key ciphers are there that are secure not because of their large number of rounds or long key length, but because of their intrinsic cryptog... |
Related to this question. I'm trying to find a way to use this fingerprint system without a second pre-image attack.
Assume I have a set of elements $V = [v_0, v_1, v_2]$ in $\mathbb{F}_p$. Assume the elements of $V$ are randomly distributed over the field.
I have two random values in the field, $R_0$ and $R_1$, both n... |
I'm working on a protocol that uses zero-knowledge proofs. I'm looking at systems of polynomial equations as cheap solutions for checksumming data. Note, I'm not looking for trapdoor functionality here; I don't care if an adversary can determine the pre-image from the output.
In a zk proof I can compute $m$ multivariat... |
Im creating a super increasing knapsack encryption scheme. Im supposed to ask the user to key in the size of the super-increasing knapsack. My question is - is there a minimum number of elements that the user need to key in?
Based on my research, because ASCII is using 7bit encoding, I need to have at least 8 elements.... |
I hope this is not offtopic.
Since NIST has rather recently announced the winners of its PQC competition I was wondering how significant this development is. Does that mean that CRYSTALS-Kyber will become the new standard for general encryption?
|
What's the difference between UOWHF and CRHF and why are UOWHF useful?
As far as I understand, Universal One-Way Hash Functions are an alternative to CRHF. While for CRHF it is hard, given randomly chosen hash function parameters, to find any collision of the hash function; for UOWHF it's hard to find a collision where... |
I read in an introduction to a paper that if $e$ is small enough and we were given secret key $d$ in RSA, then there is an efficient deterministic algorithm to factorize $n$. I've searched about that and I've found the probabilistic one: Algorithm to factorize $N$ given $N$, $e$, $d$
I guess, the fact that $e$ is small... |
Assuming there is a lattice basis $B=\{b_1,...,b_n\}$, we use $B^*=\{b_1^*,...,b_n^*\}$ to denote the Gram-Schmidt orthogonal basis, where $b_i^*=\pi_i(b_i)$ and $\pi_i(b_i)$ denotes the projection of $b_i$ on the orthogonal complement of the space $span(b_1,...,b_{i-1})$. We use $\|b_i^*\|$ to denote the Euclidean nor... |
I'm trying to understand the definition of a partially blind scheme that is described with Game A presented in
Abe and Okamoto paper
In line 5 is $msg_0$ correct or should it be replaced by $(info_0,msg_b,sig_b)$? similarly for $U_1$. I'm confused since if $msg_0$ is always on the private tape of $U_0$ then S can a... |
Hi I am trying to calculate the abs or a float number $x$, however, I want to apply this operation when $x$ is under fully homomorphic encryption (typically CKKS Scheme). So I come up with the idea that if we can use only addition and multiplication (some constant value like $2^k$ could be involved) to get abs, then we... |
I'm troubled by a system of equations presented in the paper "Provably Secure Partially Blind Signatures" Masayuki ABE and Tatsuaki OKAMOTO.
In lemma 1 the authors define $t_2=w_j-c_i$ however $c_i$ following the signature protocol creates a feed back loop as $t_2$ is defined and used as input in a secure hash fu... |
I currently have a DER-encoded X.509 ECC SECP256K1 public key, also known as SubjectPublicKeyInfo (SPKI) from AWS KMS. How do I convert it to a 66 hexadecimal compressed public key string?
|
Grover, a quantum algorithm, weakens AES and ChaCha20. Is it possible to use multiple symmetric keys to encrypt a message multiple times to achieve 256-bit security for quantum computers?
|
In "Memory Leakage-Resilient Encryption based on Physically Unclonable Functions" (ASIACRYPT2009), the authors use a construction based on a PUF and a Fuzzy Extractor and argue that this yields a Memory-leakage resilient encryption.
The definition of a Fuzzy Extractor is the following:
A $\left(m,n,\delta,\mu_{FE},\ep... |
I have a problem in combining encryption with a host software tool based on LibTomCrypt sources, then decryption with the hardware BEE (Bus Encryption Engine) of an i.MX RT1062 NXP processor. I am using AES 128 CTR with KEY = 0xdc5301d107837268e68ffc887df29528, IV (nonce) = 0x73793afe52944a1b61fae8bcaa6d3cf9, and for c... |
I have been trying to understand the method of recovering the MSD of the nonce proposed by Fan et al. (section 4.2), in their attack targeting wNAF implementation for scalar multiplication in the OpenSSL implementation of ECDSA. They assume that the value of $L_0$ is known. I can see that using Flush+Reload, one obtain... |
I am looking for a scheme for dynamic threshold public-key encryption, which includes dynamic distributed key generation.
Namely, the number of parties that participate in DKG is bounded, but unknown. The list of public keys of each party is known, but we don’t know who will participate and who won't. So the number can... |
Let's suppose that there is a filter generator which based on $n$-size LFSR.
Denote a feedback polynomial as $g(x_1, x_2, \dots, x_n)$ and nonlinear filter function as $f(x_1, x_2, \dots, x_n)$.
Let $a = a_1, a_2, \dots, a_k$ be filter generator output sequence.
Attacker knows $f$ and $a$.
What are boundaries for $k$ ... |
Is PoA persistent against quantum attacks? If not, How can we make it post quantum?
I mean the PoA used with blockchains that delivers comparatively fast transactions through a consensus mechanism based on identity as a stake. In a PoA based blockchain network, machines earn the right to generate new blocks by passing ... |
Please detail secp256k1 and its role in a public key cryptography. Please explain can we use it into a post-quantum cryptography and how can we do it?
|
When is it generally acceptable, if ever, to generate RSA keys without encrypting the PEM output with another encryption algorithm?
I am working on a CI/CD process and want to leverage asymmetric encryption, but not entirely sure whether or not it is safe to generate the RSA keys without encrypting the output. At the m... |
I'm learning about the padding oracle and had a question about a modified padding oracle. Essentially the only difference is the length of the original message is prepended to the message as a 4 byte string. It is then padded and encrypted as normal. How would the approach to this scheme be different from the standard ... |
Recently, I began researching fully homomorphic encryption. I'm reading the "Efficient Fully Homomorphic Encryption from (Standard) LWE" paper by Brakerski and Vaikuntanathan and came across this piece where they are multiplying two symbolic functions together where the function is defined as:
$$
f_{a,b}(x) = b-\langl... |
So there’s LadderLeak.
RFC6979 produces uniformly random nonce $k$.
There are other techniques, such as hash-to-curve standard (draft-irtf-cfrg-hash-to-curve-16 section 5), which allows to produce uniformly random scalars. They mention it’s OK to use 128 additional bits of entropy, e.g 48-byte hash to produce 32-byte p... |
I keep hearing CBC with fixed IV mode is bad because it has similar issues to the codebook breakdown of ECB mode. However, people seem quite willing to recommend AES-GCM-SIV for deterministic encryption. Why is GCM-SIV superior to claim CBC with fixed IV?
|
The final SP800-186 outlines mappings between Twisted Edwards and Montgomery curves, and between Montgomery and Weierstrass curves.
These mappings are defined in Appendix B. Relationships Between Curve Models.
There are two types of mappings outlined:
Standard maps between curves on these different models (both in B.1... |
I'm reading through the EDHOC draft spec and they talk about passing just the X portion of the (ephemeral) public key across in message 1. I've only ever heard of EC public keys (in this case the curve is P-256, if it matters) having both an X and a Y. The implication is, I guess, that you can derive the Y from the X? ... |
I want to use TweetNaCl.js for encrypting user data that is stored in LocalStorage. Therefore, I want to prompt the user to provide a PIN/password that shall be used to derive a key that is then used as a secret key for TweetNaCl's secretbox.
Looking for a modern scrypt implementation in JavaScript, I couldn't find any... |
Many cryptographic protocols are parameterized by a uniformly random reference string (e.g. the commitment key for Pedersen commitments).
Our goal is to publicly generate the random values of this string (in a finite field), and to do so using the simplest and fastest seed-expansion process (measured I supposed in `byt... |
I was going through some text related to designated verifier signature (DVS). I came to know that DVS can be thought of as the two party ring signature. Can we extend this concept and say that ring signature is nothing but multi user DVS.
|
I am studying Lybashevsky's ID-scheme from the article Fiat-Shamir With Aborts: Applications to Lattice and Factoring-Based Signatures(https://www.iacr.org/archive/asiacrypt2009/59120596/59120596.pdf) by Vadim Lybashevsky.
I am trying to work trough the soundness and completness of the ID-scheme through the four steps ... |
I know that there are previous questions on the subject e.g. here, however I would like to ask it for my particular (simple) case.
I have an application firmware that is downloaded to a microprocessor through a bootloader firmware that is taking care of decryption and signature verification.
The signature is implemente... |
I was going through this simulation tutorial.
For example, let x and y be lists of data elements, and
let f be a functionality that outputs an independent random sample of x ∪ y of some predetermined
size to each party. Now, consider a protocol that securely outputs the same random sample to
both parties (and where ea... |
I am learning about Elliptic curve and I reached to Montgomery curve with XZ coordinates with this equation: b*y2=x3+a*x2+x and regarding the information from this link: XZ coordinates add and doubling
and I made this small code in matlab to understand the concepts:
% Define the elliptic curve parameters
a = 1;
b = 1;
... |
I have been reading Vitalik's series on STARKs recently (Part 1, 2 and 3). It is a nice and very understandable read for a layman like me.
Brutal summary of my current understanding
Vitalik outlines the following technique to prove the correctness of some arbitrary computation:
Encode the computation trace in the valu... |
Recently, I was reading the paper One Hot Garbling published on CCS 2021. I noticed a sentence in it:
In this work, we forgo the standard GC notation of garbled labels in
favor of garbled sharings of cleartext values held by G and E. This
will be convenient for handling vectors and matrices of bits.
I don't understan... |
According to a Reddit post I am participating in, SpiderOak “repented” of its incorrect usage of the term “zero knowledge” in 2017, as shown here:
https://medium.com/@SpiderOak/why-we-will-no-longer-use-the-phrase-zero-knowledge-to-describe-our-software-ddef2593a489
NordPass has yet to walk back its claim to a zero kno... |
For Monero, the scheme for stealth addresses is pretty straightforward. (For example: https://monero.stackexchange.com/questions/1500/what-is-a-stealth-address) However, I haven't found any details on how the same functionality is done in Zcash, can someone provide more information on this?
|
I know, that PBKDF2 uses HMAC with SHA2 function as PRF. But.. can I use many iterations of HMAC with SHA2 directly? Is this effective and securely? P.S I need the best function, but I can’t use bcrypt, argon, pbkdf2.
|
I've been reading about Crystal kyber, and i read that the in the key generation process, the public key pk is computed using secret key s in such a way that the error e is added to inner product of random matrix A & secret key s.
It is said that an attacker trying to crack secret key from public key needs to solve Mod... |
On July 5, 2022, NIST chooses one KEM (Key Encapsulation Mechanism) as a PQC standard and 4 KEMs as four-round candidates. Why aren't there any key exchanges?
Similarly, KEMs are usually studied in literature. The post-quantum key exchanges in literature are very rare. Moreover, in those key exchanges, the message to b... |
Does it exist an upper bound for the advantage of solving the Gap Diffie-Hellman problem (possibly expressed in terms of the order of the group, number of queries to the oracle, time, etc.)?
|
How can I create a "reverse" GHASH algorithm for GCM that allows me to compute an input value that generates a specific chosen output, given that I know the authentication key H? If this is possible, what is the process for achieving this?
|
I am running into the Goldreich Levin Theorem.
According to what I know a predicate $h: \{ 0,1 \}^* \to \{ 0,1 \} $ is a hardcore predicate for a function $f: \{ 0,1 \}^* \to \{ 0,1 \}^* $ if:
$h$ is deterministic and efficiently computable
It's hard to find $h(x)$ given $f(x)$ for any probabilistic time adversary
Th... |
I know that it sounds like a very stupid question but if Shor's algorithm has a complexity of roughly $n^3$ why cant we just increase the bit size until the time for the algorithm to run is unfeasible on a quantum computer or would it just take too much memory and too much computation for RSA/ECC to be worth it?
|
Would a replay attack be possible in any of these scenarios? My understanding is that in only images 3 & 4 it is possible.
|
From Ronald de Wolf's The potential impact of quantum computers on society:
The first is so-called post-quantum cryptography. This is classical cryptography, based on computational problems that are easy to compute in one direction but hard to compute in the other direction even by quantum computers. Factoring does no... |
Scenario:
There are 3 people: PERSON1, PERSON2, and PERSON3
PERSON1 and PERSON2 each have a 2-dimensional polygon on an x,y
plane
It is PERSON3's job to assess whether the polygons overlap
However, PERSON1 and PERSON2 must encode their polygons in such a
way that PERSON3 cannot identify the location of their polygons,... |
We know that in the black-box sense, we cannot use one-way functions to construct Collision Resistant Hash Functions.I feel that in my impression, I have never seen CRHF based on integer factorization problem or RSA assumption
|
I have some rudimentary cryptography knowledge but am by no means an expert.
I generally understand stream ciphers, such as such as ChaCha20-Poly1305, to be symmetric. I am wondering how age (https://github.com/FiloSottile/age) uses public and private keys to encrypt data with ChaCha20-Poly1305. Is it similar to how in... |
Hi I have started studying on crystal kyber recently. Gained some knowledge regarding its algorithm and how it works. My doubt is why it is tough for attacker to extract secret vector from pk itself by predicting error vector since from pk we know mat_A,t. (B=As+e)
How can the attacker predict error from Gaussian distr... |
I've read the documentation of Crystal Kyber, but nowhere it is mentioned about good basis and bad basis.
Please explain how and where is the good basis and bad basis is used in crystal kyber.
|
In the process of learning zk-SNARKs, I'm faced with this problem:
I understand why if the prover sends a polynomial $P$ that can be divided by $T$, the target polynomial, the prover knows a valid assignment. But I don't understand how the verifier makes sure that the prover actually sent a polynomial $P$ which matches... |
I am trying to understand what the Hybrid Argument is in cryptography and why is it useful.
By the definition of the Hybrid Argument we know that to prove that if two distributions $D = D_1, D_2, ..., D_k = D'$ can be distinguished, then $\exists D_i, D_{i+1} $ that can be distinguished.
Let:
$\alpha, \beta, \gamma ... |
I would like to know the security of using key size that is larger than the message digest (output) of a HMAC in one time pad encryption.
One time pads for the message and the key of HMAC are different, scenario:
A single message will be sent from A to B on insecure medium but is not known WHEN, in advance.
Both A and... |
This is sort-of a reply to the top answer given to this question, which states that whereas RSA-PSS, defined in terms of $H(r \ || \ M)$, only relies on target collision resistance and is secure even if MD5 is used (or at least was at the time of writing that answer), RSASSA-PSS, defined in terms of $H(r \ || \ H(m))$ ... |
How to give an example for collision in modified Mekle-Damgard construction that does not include input length, with two message that ARE multiple of the block length? (Assume the resulting hash function is only defined for inputs whose length is an integer multiple of the block length.)
It is easy to consider a count... |
Im following these slides from "An Introduction to the Theory of Elliptic Curves" http://www.math.brown.edu/johsilve/Presentations/WyomingEllipticCurve.pdf,
but I'm having some difficulty understanding how the ECDLP can be solved in anomalous curves.
On the slides it says: "If #E(Fp) = p, then there is a “p-adic logari... |
LMS is specially used for applications, such as code-signing (https://csrc.nist.gov/CSRC/media/Publications/white-paper/2018/01/26/security-considerations-for-code-signing/final/documents/security-considerations-for-code-signing.pdf). Given the parameter list in table 3, found here https://datatracker.ietf.org/doc/html... |
As several intermediate values are used as sentive data for side channel analysis (DPA), I don't understand why sbox input ^ sbox output is also wide-used and effective.
This value does not applied in AES algorithm.
|
Goldreich justifies why we work with the term negligible by saying among other things "events that occur with negligible (in n) probability remain negligible even if the experiment is repeated for polynomially (in n) many times.".
Now I want to proof this statement. So I assume we have a problem with a verifiable solut... |
I was studying about the Microsoft exchange server data breach attack of 2021 as part of assignment case study. One of the tasks of the assignment it to find its relevance with IND-CPA, IND-CCA1, IND-CCA2 standards.
From my understanding the attack is seemed to be caused due to some logical bugs in the code base of cer... |
Assume $\phi(N) = (p - 1) (q - 1)$ as in the original paper. Suppose that we are using the same modulus $N$ for public and private key pairs $(e_1, d_1)$ and $(e_2, d_2)$. How can we get a multiple of $\phi(N)$ from these two pairs?
|
Let's say I have three messages: A B C
And I run each of these through two different Hashing algorithms: MD5 and SHA1 for this example
MD5(A) = X
MD5(B) = Y
MD5(C) = Y
SHA1(A) = N
SHA1(B) = N
SHA1(C) = M
Notice the MD5 hash of B and C collide. And the SHA hash of A and B collide.
If I simply concatenate the digest... |
Based on Differentia-addition on P I can understand (Xp,Zp) which is the base point, (Xq,Zq) which comes from Doubling, but I don't know what is the equation used to get P-Q to get X-,Z-.
So for example if I have P1(8,3,1) so it means (X⊖,Z⊖) = (8,1) and the value of (Xq,Zq) is from doubling? what about (Xp,Zp)?
|
If we consider LMS with (SHA256 and LMS-OTS as the OTS scheme) as defined in sections 5 and 4 here:
https://datatracker.ietf.org/doc/html/rfc8554#section-5, they provide the following formulas for LMS-OTS (section 4.4):
In general, the LM-OTS signature is 4+n*(p+1) bytes long,
and public key generation will take p*(2^w... |
I'm currently working on implementing digital signatures on the curve secp256k1 (for learning purposes only), and I'm having some trouble implementing ECDSA on curve secp256k1. As I understand it, this curve is a koblitz curve, which means it can't be written in the Montgomery form. Due to this limitation, I'm unable t... |
We have a classic web application, and when a user sign in, we return a session token (UUIDv4). The user can choose if the session should expire when the browser/app is closed or if he prefer to always be connected (1 year at least).
If an attacker get the session token, I want a way to mitigate the possibility to uses... |
Assume a message protocol whereby one time pad messages are authenticated with a Carter Wegman type hash on the ciphertext, or some similar construct utilizing a unique authentication key per message.
Since this is a OTP system, there is a store of key material at both the sender's and receiver's ends. Some material is... |
FALCON is a cryptographic algorithm for digital signature, but is it slower than actuals algorithms (ECDSA)?
|
In the MixColumns step of AES, one multiplies each of the columns of the $4\times 4$ box of bytes by the polynomial $a(x)=\{03\}x^3+\{01\}x^2+\{01\}x+\{02\}$ (modulo $x^4+1$). But in this polynomial, the coefficient $\{01\}=1$ is repeated twice. Why is it acceptable for the MixColumns step of AES to have a repeated coe... |
I'm experimenting with the parameters for argon2, using argon2_cffi.
Whereas the iteration count or time_cost, and the memory_cost have obvious bearings on the speed and security of the result. I've not seen any guidance on a maximum for the parallelism parameter, other than enough for all the threads you have.
I have ... |
Here, an user says about using a seed to generate a key that is larger than the digest size:
"Do not use hash chaining: that's a bad way of constructing a key derivation function from a hash. If the output is H(S) || H(S||H(S)) || H(S||H(S||H(S))) || …, then it's possible to reconstruct the whole output from the first ... |
It's difficult to implement AES securely and efficiently if the adversary can observe the timing and (approximate) location of memory accesses, unless you have dedicated hardware. The naive implementation uses lookup tables, which are vulnerable to attacks based on caches or on memory bus contention. Timing-invariant i... |
I'm a computer programmer and I'm working on a truly unbreakable cypher and I keep going back to a book cypher (each letter of the message is referenced by a page,row,and column number in a random book where both the sender and receiver have identical copies.)
In my update we use data files and auto lookup. here is my ... |
I know that if the input size in a pseurandom-function is larger than its output, many different inputs will generate the same output by the Pigeonhole principle (I also read an article related to that).
AES with 256-bits key size in CTR mode will generate many equal outputs per IV across all the possible keys of such ... |
I'm curious if there's an encryption scheme where content may be encrypted to a public key where the associated private key can generate new decryption keys for the same content. The goal is to publish data that is encrypted with a server's public key and allow the server to produce new decryption keys as needed.
|
This is from Alan Rosen's video on Interactive proofs - https://youtu.be/6uGimDYZPMw?t=1754
Here the proof is that
the Verifier gets a random bit $b$ .
If $b = 0$, then Verifier gets a random $y \in Z^*_n$ & sends $z = y^2$ to the Prover.
if $b=1$, then the Verifier sends $z = xy^2$ to the Prover.
Now if $z$ is a ... |
I have the book "Handbook of applied cryptography". In there we have example for random tests.
I have bits sequence [11100 01100 01000 10100 11101 11100 10010 01001]*4 length on this sequence n = 160. And I need test this sequence in order to understand this sequence is random or not. And problem with understanding thi... |
I've been trying to use AES from OpenSSL and got to know that I need to use the EVP-based implementations rather than the AES_*.
I need to use AES-128 implementation to generate bitstreams, essentially passing various keys, and plaintexts to analyze the ciphertext generated for cryptanalysis of the algorithm. I went th... |
I have come across two supposedly identical definitions of lattices in the lattice crypto literature. There are mainly these two definitions of lattices, the first considers lattices as discrete additive subgroup and the second is the common vector space definition.
Definition 1: Discrete additive subgroup
$$\forall x ... |
Would it be technically possible to use hundreds of computer processors together to work on an algorithm like the Shor's algorithm and break RSA?
I've been reading about the crazy amount of qubits required to break RSA but what if hundreds of 64 bit processors work together towards the same goal? I would assume, if pos... |
If I have 256 bits of handwavium "perfectly random data" and I hash these 256 bits of data with a secure hash function (possibly SHA-256).
Could the resulting hash be considered "perfectly random data" as well? I am assuming the answer is "no", but don't know why.
What information / keywords would I use to find out mor... |
I am given a set of $(u, v)$ values, matrix $A$, primary key vector, private key vector, error vector and prime $q$. I wanted to recover the binary value of each $(u, v)$ pairs using LWE decryption.
The formula I used to get that was: $\mbox{result} = v - s u$, where $s$ is the private key. I then compared the result w... |
Some famous cryptographical protocols rely on the construction of graphs $G_i= (V_i, E_i)$ for $i=0,1$ that are not isomorphic. For the safety of this protocol, it is central that one can not easily verify that $G_0\not\cong G_1$. So, for instance, one could easily establish that $G_0\not\cong G_1$ if $|V_0| \neq |V_1|... |
Is there an implementation of Shamir's Secret Sharing that can be regarded as a "canonical" (or "reference" or "standard") implementation, so that I can test other implementations to be "standard compliant"?
The above question is pretty vague. I have more details in mind, but some of them might be misleading or based o... |
Given a cryptographic prime $p$ and a generator $g$ of $\mathbb{F}_p$, the Decisional Diffie Hellman problem asks us to distinguish
$(g^a, g^b, g^{ab})$ from $(g^a, g^b, g^z)$ for random $a, b, z$. This is an easy problem, because the generator has Legendre symbol -1, which allows us to differentiate between such tripl... |
I was reading about some way to imagine the signature of a message using the RSA problem :
Let $N$ be the product of two prime numbers $p$ and $q$. Let $s$ be
the signature of a message $s$ (provided that such $s$ exists) defined
as $s^x = x \bmod N$.
Later on the following requirement is made on $x$ : $x$ is prime w... |
Im trying to learn more about cryptography and ran into a post, Is AES-128 quantum safe?, which asks if AES-128 is safe. From the articles and replies it seems that AES-128 (symmetric key) is safe even with the advent of quantum computers (for now). However, it seems that asymmetric keys are not safe?
So, assuming you ... |
I am generating large prime numbers to create a cyclic group for ElGamal encryption, I can specify the bit-length n but want to limit the size because this will ultimately allow me to limit the amount of data passed through external channels.
Also the data being protected has an extremely short time-value vector meanin... |
I am reading a paper named Verifiable Random Function, written by Micali, Rabin, Vadhan in 1998. In Residual Pseudo randomness propoerty of a VRF, it is written that If T runs for at most s(k) steps, it succeeds in the experiment with probability 1/2 + 1/s(k).
I do not understand the exact meaning of s(k). If it is pol... |
Previous:
https://web.archive.org/web/20160102181336/developers.yubico.com/U2F/Protocol_details/Key_generation.html
https://www.yubico.com/blog/yubicos-u2f-key-wrapping/
$$
PrivateKey = \operatorname{HMAC-SHA256}(AppID+nonce, DeviceKey)\\
KeyHandle = nonce + \operatorname{HMAC-SHA256}(AppID, PrivateKey)
$$
Now:
https:... |
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