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Currently every LWE-based cryptographic schemes analyze their security using lattice estimators and lattice estimators analyze the security of standard LWE even though the actual scheme is based on Ring-LWE or Module-LWE. As far as I know, there is no specific attack algorithm on Ring(or Module)-LWE exploiting the ring... |
I am going through Dan Boneh's video on PLONK - https://www.youtube.com/watch?v=LbpPCN-f_XA&t=952s
At around 19 minutes, he gets to the Prod Check Gadget.
Background:
$\omega \in F_p$ is the primitive $k$th root of unity (i.e. $\omega^{k} = 1$)
$\Omega = \{1, \omega, \omega^{2}, ..., \omega^{k-1}\}$
Then he sets $t \in... |
I am dealing with the bounding of compression and decompression functions in CRYSTALS-Kyber, see the lemma in this post or the original reference KYBER, section 2.2 topic "Compression and Decompression".
I have not yet found a formal proof of the assertion and have tried to construct my own proof at this point.
As for ... |
Binary extension and prime field-based elliptic curves are used in Elliptic curve cryptography (ECC). From the performance point of view, ECC using Binary field are faster and easy to compute on hardware platforms than the prime field. However, ECC using prime field is in use extensively and many standards and many new... |
This is a hypothetical question. Is it possible to use a stream cipher instead of a block cipher for an OCB type single pass AEAD?
The xor of the plaintext blocks for the authentication tag can't work because a change in the ciphertext doesn't change the plaintext enough so maybe the answer is no.
|
In the paper of BGV, I find an interesting sentence as below:
One may view our new scheme as a very powerful SWHE scheme in which this dependence on degree has been replaced with a similar dependence on depth. (Recall the degree of a circuit may be exponential in its depth.)"
The author says that BGV scheme relys on t... |
I want to get feedback on the security of a modified merkle tree data structure. Using the image above as a reference assume I have a random oracle function $H$. Assume $H$ outputs a value in $\mathbb{F}_p$, and all math is happening in this field too.
The standard approach to calculate $D$ is
$B = H(A, C)$
$F = H(E, ... |
Unfortunately, I don't have any references, but I remember people mentioning that some large integer libraries can be unsafe to use for writing cryptographic algorithms such as the RSA.
That made me curious if anyone knows of any examples of vulnerabilities that would be introduced by an unsuitable implementation of a ... |
I remember reading a previous stack exchange post (unfortunately was unable to find the link, if someone knows the link that would be great!) about a method to make password checking time for the server be on average less than that for an attacker. Essentially, when the password is first created a random number between... |
Can someone please point me to or give me stepwise example of VSH hash function. I couldn't find an example or a reference implementation. I tried to go through original publication but it seems way too cryptic to me.
|
In other words, what does ZKP brings on top of the practice of not reusing addresses?
From my research, ZCash is currently a state of the art example of ZKP application, but what extra benefits does it bring to the scenario where let's say a bitcoin holder created new addresses for each tx it was receiving and not reus... |
I am trying to implement a basic Diffie-Hellman key exchange using ECC and HECC of genus 2 and 3 and compare them. However, I am a bit confused about the concept of key size in HECC.
In ECC, from my understanding so far and considering I am new to the field, the private key size is basically the bit size of the prime t... |
My guess is:
Known attack algorithms only work on 2 primes factorization, they don't work on 3+ RSA primes.
More than 3 primes is cpu waste time, better is to increase key length.
So 3 primes will be the optimal number.
Example of my program (open source) generating a 30k bits RSA key.:
Enter rsa NUMBER of primes: 3... |
Say that I have a random oracle function $H$. This function outputs a value in $\mathbb{F}_{p}$ where $p \approx 2^{256}$. $H$ can accept either one or two inputs (outputting a single value in both cases).
I can hash two elements $x$ and $y$ using either
case 1: $H(x, y)$
case 2: $H(x) + H(y)$ (using modular addition)
... |
In Authenticated Encryption, we use an authentication tag to make sure the message is not tampered. The authentication tag can prevent any random bytes sent by the attacker being decrypted by the receiver.
The question is: what sorts of attack (other than sending lots of meaningless random bytes) is the authentication ... |
After tinkering with cryptographic hash functions, I started wondering if they do have counterpart functions that would imitate their cryptographic properties but with a lower level of strength in terms of their time/space complexity.
For instance, if I were to test certain collision algorithms in a simplified version ... |
I saw a statement that the probability of finding a key $k'$ to simulate 3 keys $k_1$, $k_2$, $k_3$ is neglectable: $\mathrm{Enc}(k_3,\mathrm{Enc}(k_2,\mathrm{Enc}(k_1,x))) = \mathrm{Enc}(k′,x)$
When not considering MITM attack, the probability of brute forcing triple DES is $1/2^{168}$.
According to the statement, do... |
Let $(X, Y, Z)$ be a set of binary strings of length $n$. Let random $X$ be the private key for encoding (or decoding) message random $Y$ as $Z$. Let the encryption algorithm $m$ be a matching function, i.e., for $m(X, Y) = Z$, if $x_i = y_i$, $z_i = 1$, otherwise $z_i = 0$. Now, $m$ is clearly not a one-way function: ... |
I'm learning about AES. According to the book The Design of Rijndael refers to the design criteria S-box $S_{RD}$ as follows:
Design criteria for $S_{RD}$. We have applied the following design criteria for $S_{RD}$, appearing in order of importance:
Non-linearity.
a) Correlation. The maximum input-output correlation a... |
In many proposed lattice PKE schemes, the plaintext is encoded or modulated in a simple fashion, e.g. using Kyber-ish notation:
key gen: $pk=(A, t=As+e)$, $\quad sk=s\quad$ ($A$ random, $s$, $e$ small random)
encrypt: $u=A^tr+e_1$, $\quad v=\langle r,t\rangle +e_2+\tilde{m}\quad$ ($m$ message, $r$, $e_1$, $e_2$ small ... |
Let $\{(q, G_1, G_2, G_T, e: G_1 \times G_2\to G_T)_s\}$ be a family of bilinear groups parameterized by the security parameter $s$. We use $g_1$ (resp. $g_2$) to denote the generator of $G_1$ (resp. $G_2$).
The XDLIN problem is to guess bit $B$ ($B = 0$ or 1), given
$$P_B:= \{g_1^a, g_1^b, g_1^{ac}, g_1^{bd}, g_2^a, g... |
Bulletproof and dory reduce the witness size by a half during each interaction, until the witness is compressed to be only one element. But what about the witness is not precisely exponential size? Can we still use the two schemes by padding the witness?
|
Let's suppose I have a 8-bit substitution box composed of 256-bytes and invert it.
Does changing one byte in the substitution box will make the inverse result completely different than if I didn't change it?
Or will only the changed byte be different in the inverse S-box?
|
I am having a prime field of large size (assume it of the type GF(2**18)) and I need to find linear complexity of a sequence (of some specified length) defined on this field. I am using the inbuilt berlekamp_massey function to get the linear complexity (the degree of minimal polynomial) of the sequence.
Current Work:
f... |
We use DES in cipher feedback mode (CFB) to encrypt a plaintext $m = m_1\mathbin\|m_2\mathbin\|\ldots\mathbin\|m_{100}$ into a ciphertext $c_1\mathbin\|c_2\mathbin\|\ldots\mathbin\|c_{100}$, where each $m_i$ is 8-bit long. The ciphertext is sent to Bob. If $c_{15}$ and $c_{25}$ are missing and $c_8$ and $c_{88}$ are re... |
I need to encrypt some user's data. However to make it more apparent to the user what data is stored in each key, I was thinking to also store the length of the actual data along the cipher.
E.g.
user_1_secrets = [
{
"key": "mysecret"
"encrypted_data": b"abf4c2",
"length": "10",
},
{
"key": "myoth... |
Hi I am currently developing a research project, but it seems that my implementation of Pedersen commitment is not efficient. I wonder if there are any efficient implementation of Pedersen commitment in c++? Or if using things like ECC would boost the efficiency(seems number of bits could be smaller), or does anyone ... |
I have a cipher algorithm that doesn't seem to be one of the "well known" ones I could find. I expect someone has already come up with this and I just don't know the name. Hoping one of you can point me in the right direction.
I don't think this falls foul of Should we allow questions about amateur ciphers? - but happy... |
In Openssl, is there a way to systematically generate a private key such that every time you perform this key derivation, you produce the same private key?
It seems like every openssl command that generates private keys does so randomly. So, if you lose your private key file for whatever reason, there's no practical me... |
I designed 8 bit lfsr in vhdl. According to mathematical theory, I xor processed the outputs of registers 1, 4, 5, 6 and 8 and connected them to the input of register 1. theory says that if I give the inputs the polynomial "10111000", I get the repetition of (2^8)-1.
I tried some more. And I tried the circuit without c... |
I am going over the paper https://verifiable-timed-signatures.github.io/web/assets/paper.pdf and on page 5, it says the following:
Suppose I have a t-out-of-n threshold sharing scheme for the secret $\sigma=H(m)^\alpha$. The first $t-1$ shares are defined as $\sigma_i = H(m)^{\alpha_i}$, where $\alpha_i$ are sampled ra... |
I noticed that it seems the original Plonk paper introduced that there were two extensions with state width = 3 or 4 (as described in https://github.com/matter-labs/proof_system_info_v1.0/blob/master/README.md). I recently reviewed some code and they set the state width = 5 and set the verification key as follows.
uint... |
I came across the following enterprise encryption scheme. I laughed when I first saw it, but I'm not a specialist and I'd like to know how bad it really is.
3DES-CBC
k1=k2=k3 for 3DES
IV for CBC is repeated every 256 messages. Every communication party has a different set of 256 IVs but they are all predictable and si... |
I'm trying to find a way to have multi party hash computation, more specifically for SHA256. I want for two people to be able to compute a hash so that none of them knows the pre-image but when they get together they can reconstruct the pre-image.
Is there any known way to do it in general or any hack that can be used ... |
Certain number-theoretic cryptographic hash functions, such as $x^2\bmod N$, are known to be broken by a quantum computer. For example, one could use Shor's algorithm to factor $N$ into its product of two primes $(p_1,p_2)$, and use these primes to find collisions at-will. It's also been a long-open problem to find a... |
on the wiki page of Rustdesk, it states "the connection is unecrypted, please do not send us issue about this." for local direct IP.
BUT, Rustdesk is intended "Virtual / remote desktop infrastructure for everyone! ", (so not localdesktop)
While Rustdesk claims Rustdesk is encrypted between client and server, which seem... |
If we do not encrypt a message, we can use a checksum to check data integrity. For authenticated encryption, we no longer need the checksum because we use the authentication tag to verify data integrity.
The above is about error-checking. Now, for error correcting (like Hamming code), is there an encryption scheme that... |
Let us consider a hypothetical situation.
What would be the implications if there is a method by which one can calculate the public keys for incremental private keys, with the help of only the public key?
For instance, one is given a public key only. (that public key has the private key as 1001) and he is asked to calc... |
Is SHA-3 normally used with a LUT or hash table?
|
I'm relatively new to the field of security.
I'm working on an IoT system with WiFi-connected nodes (Bio-sensing devices) communicating with a server for centralized monitoring.
I need to authenticate each device when connecting to the server.
So, each device has a unique certificate with a signature (ECDSA).
However, ... |
Hypothetically,
IF we were to create a SSL/TLS or QUIC ciphersuite from a single (unkeyed) permutation operating in sponge mode to provide hashing and duplex mode to provide AEAD cipher,
AND IF the permutation is wide enough, and the capacity in both modes are large enough,
THEN, to what extent can capacity make-up ... |
Consider following simple RBG where SHA-256 of random noise (more than 200Bytes of 4 bits entropy per byte) is computed to produce 256 output bits
$\text{output} = \operatorname{SHA-256}(\text{randomNoise})$
Is security strength of collision resistance or pre-image resistance applicable to it i.e it provides 128 or 256... |
Let me start by saying that I have a mathematical background, and have very little experience with cryptography. I only know the very basics.
With that said, I recently read about Homomorphic Encryption (HE), and thought that it was a very interesting concept. What one really cares about, though, is Fully Homomorphic E... |
As stated in RFC8032 and FIPS 186-5, Ed25519 signatures uses the following encoding method:
A curve point (x,y), with coordinates in the range 0 <= x,y < p, is
coded as follows. First, encode the y-coordinate as a little-endian
string of 32 octets. The most significant bit of the final octet is
always zero. To form... |
Suppose $N$ many messages has been sent from $A$ to $B$ in this format:
$\operatorname{HMAC}(K, C(i)) \mathbin\| C(i)$.
Where
$C(i)$ is some cipher-text encrypted with some secure algorithm using some key
$K(i) \ne K$ for any $i$ in range $[0, N-1]$.
There is no implication whether $K(i) = K(j)$ for any $i \ne j$.
... |
I have a question about the decryption in Kyber [1]. I will first give important statements of the paper and then ask my actual question with an example.
In the paper it is stated:
... decrypt to a 1 if $v-s^Tu$ is closer to $\lceil \frac{q}{2} \rfloor$ then to 0, and decrypt to a 0 otherwise.
On the other hand, whe... |
Hi everyone I am trying to implement the Basic skeleton of the PQC Kyber Algorithm. Until now I have obtained t=As+e and s after performing point-wise multiplication (Frequency to Time domain). Now I got stuck at encode12 algorithm which is required to obtain pk(12xnxk/8+32 bytes) and secret key(12xnxk/8 bytes). Can yo... |
In adversarial context of MPC, the corruption behavior
refers to the assumptions about the corrupted parties’ deviation level from the protocol
specification. Three main types of corruption behaviors are: semi-honest, malicious, and
covert.
In practice, dealing with semi-honest corruption behavior is considered more fe... |
How long time does quantum computers take per operation when search the key of Kyber? Grover's algorithm weakens 256-bit AES to 128-bit security, quantum computers at most take 2^128 operations to find AES key, but it must take some time per operation; as mentioned https://www.ambit.inc/pdf/KyberDrive.pdf : Kyber-1024 ... |
What is there to say about using a power basis or a tensor basis or some combination of them for the RSIS problem in lattice cryptography?
Restricting to dimension 3 for illustration, usually the basis is $(1,x,y)$ for uniform $x,y\in R$.
I'm instead wondering about power basis $(1,x,x^2)$, and tensor basis $(1,x,x^2)\... |
I wonder if there is any scheme or algorithm to generate HMACs that verify with multiple keys.
Suppose I have the secret keys K1, K2 and K3 and I have a message M1. Is the following possible?
Generate an HMAC1 with M1 that can be verified with K1 and K2 but not with K3
Generate a HMAC2 with M1 that can be verified wi... |
In federated learning using homomorphic encryption, all participants in most schemes share the same pair of keys, which can easily cause key leaks and lead to data privacy leaks.
After research, I found that someone proposed to use a multi-key homomorphic encryption algorithm to solve the above problems. But I wonder w... |
I have been thinking about this question: if I directly replace the hash function with the message in the BLS signature, does the security of the BLS degenerate from existential unforgeability(EUF) to selective unforgeability(SUF) under the known message attack(KMA)?
The modified BLS signature scheme is defined as bel... |
Experts suggested 3DES when AES wasn't developed yet, since meet-in-the-middle attack, they suggested triple DES. Grover's algorithm, a quantum algorithm, weakens symmetric encryptions, how about triple ChaCha20? Does triple ChaCha20 have 256-bit security against quantum computers?
|
I am using some ark libraries, such as ark_ff and ark_bls12_381, to implement some cryptographic algorithms. In these algorithms, random oracles are needed, which gets some group elements in G1,G2,Gt in bls curve, will output a scalar number(ark_bls12_381::Fr). How to do these steps? To be specific, I need to hash grou... |
According to
https://www.reddit.com/r/cryptography/comments/v0sw2r/enigma_ring_settings_question/
While the rotor is in the machine, the ring+notch+rotor all rotate in
sync. While the rotor is pulled out, the ring+notch can be detached
and rotated to a different offset compared to some canonical
orientation of the ins... |
Walkthrough the textbook content, understand that we need to compute the slope of 2 points before can compute the new point as the result of addition.
Multiplicative inverse is part of the operation in a process to find the slope, where we know Extended Euclidean Algorithm is one of the best method to be used.
However,... |
I'm working on an open source iOS-native (both UX- and implementation-wise) 2FA app. Two of primary goals for the project are ensuring security and simple backups. Addressing these two areas is the last blocker before the release.
I'd like to ask you for your opinion and advice regarding the scheme I devised for the a... |
I wanna do an experiment. I wanna see if it's possible to sign in to an outdated website that still uses MD5 to store passwords (there are surprisingly still a lot) with two different passwords.
For example "Password123" must have another string that produces the same hash value. I've found a few examples online of two... |
I have private keys that are close to 2kb big.
Now I want to password encrypt them in the following manner.
Generate the private key of an asymmetric encryption algorithm (public key can be derived from private key later) with a random number (I'm using a system PRNG).
Generate a random salt of length 48 bytes (also f... |
I want to derive session keys for many clients from a Master Key. Suppose I derive a key for the client $n$ in the following way:
master_key = HKDF-extract(salt, IKM)
key_client_n = HKDF-expand(master_key, info_client_n, L)
Then, I generate session keys for the client $n$:
key_client_n_session_0 = HKDF-expand(key_clien... |
This recent paper shows that discrete logarithms are solvable if you have an oracle for the Diffie–Hellman problem. However, to me, it seems there is a much simpler reduction and I wonder where I am wrong:
Core idea: A DH oracle allows us to exploit the multiplicative structure of a curve's scalar field, whereas normal... |
May I ask if I use top-K to compress the gradient, can the attacker recover the original information of the data from the compressed gradient?
|
Such as integer factorization problem and discrete logarithm problem. Assuming a large polynomial is obtained by multiplying two generated polynomials, is it NP hard to decompose it into these two generated polynomials ? And Assuming that A is the generator of the Galois field and B is a random number, is it NP hard to... |
In RSA encryption, the larger the size of the prime numbers utilized for the creation of the public key, the more computational power is required in order to "Brute force" decryption.
Does a similar concept apply when considering lattice-based encryption?
Naturally, I would assume so, but how much more safe would a 3d... |
As XMSS is post-quantum we can use it to secure blockchain. One of the main disadvantage of XMSS is its signature size. If we can reduce the size of the signature then we can use XMSS in the blockchain. XMSS signature contains the Sign on message+ index of OTS + Authentication path. If we can store the OTS index and Au... |
I know that if using Grover's algorithm to break a cipher, one would need to perform (2^[key space])^0.5 queries (the square root of the number of all possible keys).
A simple transposition cipher COULD have their security of (transpositions)! (factorial of the number of transpositions), but how would it be in a post-q... |
Say that $\mathbb{G}_1,\mathbb{G}_2,\mathbb{G}_T$ are cyclic groups of prime order $r$ over which the pairing $e : \mathbb{G}_1 \times \mathbb{G}_2 \to \mathbb{G}_T$ is defined. It is well known that $\mathbb{G}_1 \subseteq E(\mathbb{F}_p)$ and $\mathbb{G}_2 \subseteq E(\mathbb{F}_{p^k})$ where $p$ is a prime number an... |
Assume a given pseudo-random function $H:\{0,1\}^a\mapsto\{0,1\}^b$ with $b\in[104,256]$ and $b/2<a<b$. We want to exhibit a collision if there is one, which has probability $>63\%$.
We are ready to perform $2^{b/2+1}$ evaluations of $H$ or slightly more, distributed among several search units. But we don't have $2^{b/... |
I am working with the securit yof CRYSTAL's Dilithium signature in the QROM. I am working with Kiltz et al.'s approach through lossy ID-schemes and looking at the proof of minimal entropy for the $DFS[ID, H, PRF]$ derived Dilithium-QROM signature. Unfortunately, I am not able to see how the proof of the lemma flows, no... |
When utilizing the closest vector problem for decrypting data, does lattice size matter. For example, is a 1000x1000 grid necessarily more safe than a 100x100 grid? And if so, why would these affect the computations of quantum computers? Also is there a "safest way" of choosing a lattice point that guarantees higher su... |
The following statements seems to be a consensus in cryptography community.
Oblivious tranfer is a complete primitive for secure multiparty computation (SMC).
But I cannot find any explicit construction. What I want is a general method to construct SMC from OT with as few assumptions as possible, especially without t... |
What is the specific process of recovering the original secret of secret sharing? Is the parties with secret shares communicating with each other and exchanging secret shares, and if the number of secret shares greater than or equal to the threshold is collected, the secret will be recovered, or a third party will coll... |
I have two elementary questions related to the special distribution $|x'-x \text{ mod}^{\pm} \, q| \leq B_q := \left\lceil \frac{q}{2^{d+1}} \right\rfloor$ in Kyber. The first question is about the paper and the second question is about a section in the specification. I am asking this as one question because I think it... |
I understand that domain separation in hashing is important, but I'd like to understand more clearly why and what are the risks involved.
What is the theoretical justification for requiring domain separation?
What are examples of schemes/protocols that can be broken if domain separation is not used?
How can one evalua... |
Let $H(h,k)$ be the expected entropy of some random oracle $X:\left\{0,1\right\}^h \to \left\{0,1\right\}^k$, where $h$ does not necessarily equal $k$.
Then, is it true that $\lim\limits_{h\to\infty}H(h,k) = k$ ? (for constant $k$)
If so, is the above still true if $h = 2k$? In other words, does $\lim\limits_{h\to\inf... |
Bilinear Pairings are widely used in many new schemes like Group Signature and Aggregate Signature. The problem is whether it is post-quantum secure. In other words, does Bilinear Diffie-Hellman intractability assumption stand against a quantum computer?
With a quantum computer, Shor's Algorithm solves Prime Factorizat... |
We have 2 ciphertexts, one encrypted using Paillier and another encrypted under Elgamal encryption schemes. Is there a way to design ZK-proof to prove equality of the underlying plaintexts of these 2 ciphertexts.
|
Some time ago I had a question here about WinRAR security and probably the most common recommendation I came across was to use Veracrypt.
Veracrypt uses XTS, but according to others, XTS encryption is unnecessarily complicated and does not provide such protection to be considered secure enough. (see Thomas Ptacek; Erin... |
Under which conditions is it secure to publish an encryption of the secret key $s$ under itself in terms of an $RLWE_s(s)$ ciphertext? Because for some schemes this is (repeatedly) used in bootstrapping or key switching, it seems to be secure (or at least it is assumed to be so).
On the other hand, if multiple encrypti... |
I want to prove that the DSA signature scheme is EUF-CMA secure in the random oracle model, if the discrete logarithm problem is hard. I know it can be proved by the following two parts:
Discrete logarithm problem is hard $\Rightarrow$ DSA identification scheme is UI-PA security
DSA identification scheme is UI-PA sec... |
I'm thinking about storing packed integers $(x_1,x_2,...,x_k)$ into a single ciphertext slot using the Chinese Remainder Theorem (CRT). However, in order for the CRT to work, the plaintext modulus would have to be a product of prime values (the same prime values used in the CRT). So I ask, does the plaintext modulus ha... |
Considering that I am writing a circuit that will take age as input and return true or false.
For this ZKP system, I guess I don't need a separate prover circuit and verifier circuit.
Consider that I am writing a circuit that will take age as input and generate a proof. Now I will write another circuit for a verifier t... |
The shape of the edwards curve is equal to $a x^2 + b y^2 = d x^2 y^2 + 1$ in $\mathbb{Z}_p$. Is there a way to know $p$ when we know the five points on the edwards curve without knowing $a, b, d, p,$ and generator $G$?
I tried to find p by using the five points given to me by concatenating the relationship $a x^2 ... |
I want to hash my signature of JWT using public & private key, since we are using ES-256 algorithm in JWT. But the problem is that I have both the keys in JSON & .PEM format, so how can I do it in one openssl command? below is the shell script code which I am using to hash the signature:
SIGNATURE=$(echo -n "$DATA" | o... |
Can you explain the mathematical details of Grover's algorithm for children?
|
I am building the Threshold Signature Scheme (TSS) based wallet. I would like to run the each party's node separately with different host. And these nodes should be able to send the messages through the secured and authenticated channel to the other partie's nodes. So what channel protocol is prefered to used. Can i us... |
Is there a known feasible method for determining an unknown public key from a Diffie Helman shared secret and the other public/private key pair?
This would be rarely useful, but I am curious if the DH operation is 'invertible' given the derived secret and private/public key of one party.
So if the shared secret (which ... |
This question is about adding new data with different proportions to a dataset with equal proportions for each type of data, and determining at what point the added data can be distinguished.
For example, in a hospital with doctors, nurses, cleaners, and security personnel, with proportions of [0.5, 0.2, 0.2, 0.1], the... |
I am currently studying the Double Ratchet Algorithm from Signal (link to the documentation). I stepped over a security issue which I was not able to find that it was mentioned anywhere.
I assume that an attacker is able to delay messages at the public channel. Let's say Alice and Bob are having a conversation via doub... |
If we know the value of G*n, the value of n, and the value of p in Zp, is there a way to find out G?
I tried the code below on sage but the value was different from the original G.
# we know nG = (x, y)
Gx = inverse_mod(n, p)*nG[0] % p
Gy = inverse_mod(n, p)*nG[1] % p
G = (Gx, Gy)
|
I am learning Elliptic Curve cryptography, I have been working on an example from a book:
I don't fully understand the line where the slope is calculated, specifically how 2^(-1) * 9= 13 mod 17? I saw a post here that says to get the inverse with the Extended Euclidean algorithm.
I just don't see what 2^(-1) is the i... |
sbverify needs a certificate to verify digital signatures. I wonder why it's needed, since the signer certificate is already included in the digital signature itself ?
|
I have a program in Python to do the ECDH with the NIST P-256 curve. The program is seemingly working, ie I get the same private key pair at the end. But I want to make sure it's not a coincidence in my code, and that my double-and-add algorithm is working correctly.
TLDR: Is there a strong curve that gives all the det... |
I understand the only multilinear maps used in cryptography are bilinear maps, and higher arity multilinear maps are not "known."
Why does the composition of bilinear maps not yield usable higher-arity maps?
I thought the primary feature of multilinear maps in cryptography is simply their multilinearity along with non-... |
I implemented below algorithm in hardware and it works fine with first point addition.
However, when I continue to perform back-to-back addition, I got the wrong result.
The part that I'm not sure here is,
The original calculated X3 and Y3 are still in Jacobian coordinate and I do not want to convert them back to aff... |
When trying to implement ElGamal Public Key Encryption using Hyperelliptic Curves, one needs to map the message that will be encrypted to a valid Divisor (in my case in the Mumford representation, which is the most common).
I have not found any specific methods similar to Koblitz encodings in ECC. Are there any methods... |
What would be the method of choice to compute the private key from the public key on a baby analog of secp256k1, say with $p$ and $n$ 144-bit?
What would be the pros and cons of Pollard's rho and Pollard's kangaroo ?
How can the special properties of a Koblitz curve be put to use?
|
Our device comes with a device certificate which was signed with our private registration authority (CA). The private key (type ECC) was generated on the device itself - to be more specific directly on the on-board TPM. The public key is included inside the device certificate.
Now we have a use-case where we want to en... |
For a KEM mechanism like RSA, Kyber, etc. is there it usually worth doing key trapping/key encapsulation both directions in a key exchange? By this I mean: Alice wraps a symmetric key and sends it to Bob. Bob wraps a different symmetric key and sends it to Alice. They both then run the concatenation of these two keys i... |
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