instruction stringlengths 15 30k |
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Do Safe and Sophie Germain primes maintain a relatively stable distribution as numbers get larger, or do they become rarified beyond a predictable value?
This is important in one area of triangular number comparison for some of my study.
What is the predicatable, stable distribution?
Is there a comparab... |
If i understand correctly, hashes run a defined set of operations iteratively until the original data is all hashed.
Can you take a hash value, run it backward through the last step (or once, for an approprately sized starting block), and get a pool of possible starting states?
If you run that pool of states thro... |
Is it possible to deduce the input of a hash by running in reverse? |
Yes, you could in principle do something like this, but
> how many steps becomes prohibitive (too expensive) to continue reconstructing a hash original data input?
will be a quite small number. I'll discuss the details for a particularly simple/common type of hash, with the caveat that there are many other types... |
Accidentally used ed25519 public key to create libsoidum_sealed_box. Is there any way to decrypt the data if the private key ed25519 is known? |
I'm exploring elliptic curve cryptography, specifically on the secp256k1 curve. I've come across the concept of point division by integers using scale multiplication which can be achieve my multiplying $P$ by $(n+1)//2$, particularly for powers of 2 (2, 4, 8, 16, 32, 64). However, I'm curious if it's possible to perfor... |
The basis for this question is a 1-dimensional [NTRU](https://en.wikipedia.org/wiki/NTRUEncrypt) cryptosystem.
After some literature inspection I have found out it can be also generalised into higher algebras: quaternions ([QTRU](https://eprint.iacr.org/2009/386.pdf)) and octonions ([OTRU](https://www.math.uci.edu/~... |
Are high-dimensional versions of NTRU cryptosystem more secure? |
Consider a floating point number $f$ in IEEE 754 format with sign, exponent and significand values as $f.s$, $f.e$, and $f.sig$. Given this floating point number $f$, I want to compute the shares of $f$, denoted as $f1$ and $f2$, such that $f = f1 {+_{fp}} f2$, where ${+_{fp}}$ denotes the usual floating point addition... |
I'm exploring elliptic curve cryptography, specifically on the secp256k1 curve. I've come across the concept of point division by integers using scale multiplication which can be achieve my multiplying $P$ by $(n+1)//2$ using the script in [this post](https://crypto.stackexchange.com/questions/108146/how-to-convert-rx1... |
Consider a floating point number $f$ in IEEE 754 format with sign, exponent and significand values as $f.s$, $f.e$, and $f.sig$. Given this floating point number $f$, I want to compute the shares of $f$, denoted as $f1$ and $f2$, such that $f=f_1{\underset{\mathsf{FP}}+}f_2$, where ${\underset{\mathsf{FP}}+}$ denotes t... |
> Is there a standard method or cryptographic approach to achieve point division on secp256k1 for these non-power-of-2 integers? If so, how would one go about it? If not, what are the constraints or considerations that make it impractical?
Here's what's happening: multiplying by $k^{-1}$ is the inverse of multiplyin... |
I'm exploring elliptic curve cryptography, specifically on the secp256k1 curve. I've come across the concept of point division by integers using scale multiplication, my question is how can I devide a point by $7$, i tried `mul((n+1)//7,77G)` which was supposed to result in $11G$ but it didn't work.
However, I'm curio... |
I'm exploring elliptic curve cryptography, specifically on the secp256k1 curve. I've come across the concept of point division by integers using scale multiplication, my question is how can I devide a point by $7$, Is there a standard method or cryptographic approach to achieve point division on secp256k1 for these non... |
let `F` be a finite field, `E(F)` an elliptic curve of order `n`, `r` a factor of n, `k(r)` for the embedding degree of `E(F)` with respect to `r`.
Then why the `full r-torsion group` contains `r^2` many elements and consists of `r+1` subgroups? |
- **Participating entity**: multiple data owners, computing clouds
- **Protocol**: The multiple data owners send their data to the computing clouds, which perform the computation of the data.
- **Privacy protection**: Using a public key based homomorphic encryption scheme, the multiple data owners encrypt their data ... |
I am working on an experiment to compare the efficiency of brute-force attacking block ciphers like AES and DES with reduced key sizes for different programming languages and library implementations. However, I am restricting it to using a ciphertext only attack, so I will generate 1 block of random plaintext, encrypt ... |
We have access to an encryption and decryption server with the following implementation. How can we get the secret key by interacting with this server?
```python
from Crypto.Cipher import AES
KEY = ?
def encrypt(plaintext):
if len(plaintext)%16 != 0:
return {"False"}
cipher = AES.new(KEY,... |
Two hints:
- How can you craft a chosen plaintext so that the encryption will tell you the value of $E_k(k)$?
- Given the value of $E_k(k)$, how can you craft a chosen ciphertext so that the decryption will tell you the value of $k$? How can you make sure that the padding is valid (so that you don't get a decryp... |
I am trying to implement the algorithm suggested in Section 5 of the [Black & Rogaway paper titled "Ciphers with Arbitrary Finite Domains"](https://www.cs.ucdavis.edu/~rogaway/papers/subset.pdf) in C++. It is a Feistel cipher that tries to encipher to a target "unusual" domain size $k$, using cycle-walking when necessa... |
Consider a matrix $H \in GF(2)^{a \times b}$ where $b > a$. This defines two linear codes. First, we have the code for which $H$ is the parity check matrix:
$$
C = \\{ \mathbf{x} \in GF(2)^b | H \mathbf{x} = \mathbf{0} \\}.
$$
Secondly, we have the dual code, for which $H$ is the generator matrix:
$$
C^\perp = \\... |
Efficient decoding a code dual to a Goppa code? |
Consider a matrix $H \in GF(2)^{a \times b}$ where $b > a$. This defines two linear codes. First, we have the code for which $H$ is the parity check matrix:
$$
C = \{ \mathbf{x} \in GF(2)^b | H \mathbf{x} = \mathbf{0} \}.
$$
Secondly, we have the dual code, for which $H$ is the generator matrix:
$$
C^\perp = \{ \... |
I'm implementing Argon2id from the RFC 9106 and I'm at the part where each thread computes J_1 and J_2 in order to generate indices [l] and [z].
I'm confused as to which TYPE (y = 0, 1 or 2) of Argon2 to use when computing J_1 and J_2, because the RFC basically says:
"If you're doing Argon2id, compute J_1 and J_2... |
Research paper (Extended-Chacha20 Stream Cipher With
Enhanced Quarter Round Function): "https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjtrdD3l-uCAxX-RKQEHcs4CCsQFnoECBMQAQ&url=https%3A%2F%2Fbth.diva-portal.org%2Fsmash%2Fget%2Fdiva2%3A1810206%2FFULLTEXT01.pdf&usg=AOvVaw0ZLNqbPx... |
Research paper: " [Extended-Chacha20 Stream Cipher With
Enhanced Quarter Round Function][1]"
1. The initial matrix is 6x6, but what are the exact inputs for each index, in other words, how will you fill the two additional columns that are added to the matrix?
2. Is it possible to change the constant values? and is... |
Consider a floating point number $f$ in IEEE 754 format with sign, exponent and significand values as $f.s$, $f.e$, and $f.sig$. Given this floating point number $f$, I want to compute the shares of $f$, denoted as $f1$ and $f2$, such that $f=f_1{\underset{\mathsf{FP}}+}f_2$, where ${\underset{\mathsf{FP}}+}$ denotes t... |
I am trying to implement the algorithm suggested in Section 5 of the [Black & Rogaway paper titled "Ciphers with Arbitrary Finite Domains"](https://www.cs.ucdavis.edu/~rogaway/papers/subset.pdf) in C++. It is a Feistel cipher that tries to encipher to a target "unusual" domain size $k$, using cycle-walking when necessa... |
I am trying to implement the algorithm suggested in Section 5 of the [Black & Rogaway paper titled "Ciphers with Arbitrary Finite Domains"](https://www.cs.ucdavis.edu/~rogaway/papers/subset.pdf) in C++. It is a Feistel cipher that tries to encipher to a target "unusual" domain size $k$, using cycle-walking when necessa... |
I am trying to implement the algorithm suggested in Section 5 of the [Black & Rogaway paper titled "Ciphers with Arbitrary Finite Domains"](https://www.cs.ucdavis.edu/~rogaway/papers/subset.pdf) in C++. It is a Feistel cipher that tries to encipher to a target "unusual" domain size $k$, using cycle-walking when necessa... |
I am trying to implement the algorithm suggested in Section 5 of the [Black & Rogaway paper titled "Ciphers with Arbitrary Finite Domains"](https://www.cs.ucdavis.edu/~rogaway/papers/subset.pdf) in C++. It is a Feistel cipher that tries to encipher to a target "unusual" domain size $k$, using cycle-walking when necessa... |
I am trying to implement the algorithm suggested in Section 5 of the [Black & Rogaway paper titled "Ciphers with Arbitrary Finite Domains"](https://www.cs.ucdavis.edu/~rogaway/papers/subset.pdf) in C++. It is a Feistel cipher that tries to encipher to a target "unusual" domain size $k$, using cycle-walking when necessa... |
My project is to build a true random number generator that relies on the avalanche effect in a Zener diode. This for a messaging device that uses one-time-pad encryption. Reading about similar projects, I assume to get fairly high entropy right from the raw stream. Next stage is to condition the bit stream in software ... |
As noted in the answer to [Why do we use 1024 / 160 bit primes in DSA?][1], the security of DSA needs to worry about two attacks (neither of which should be described as factorisation).
There is the general number field sieve (GNFS) index calculus attack that depends on $L$. Calculating the difficulty of an GNFS at... |
I am researching ASCON. I can find cryptanalytic attacks ASCON authenticated encryption and ASCON HASH, But I am not finding anything ASCON MAC. Anyone knows of any attacks, any research on this? |
I know that DES has 56 independent key bits, and that 3DES has 168 independent key bits by using 3 seperate 56-bit DES keys. 3DES also has a block size of 64 bits.
If I use 3DES as the underlying block cipher to construct a Davies-Meyer compression function, what would be the input/output size of this compression fu... |
Only if $r$ is prime.
Let $E[r] = \langle P,Q \rangle$ be the $r$-torsion subgroup. Its cyclic subgroup is defined by a generator of the form $[a]P + [b]Q$, but up to a (non-zero) scalar multiple: because $G$ and $[k]G$ generate the same subgroups.
How to count the subgroups? In the expression
$$G = [a]P + [b]Q$... |
normally, the chinese theorem looks like this:
x = a1 mod n1
x = a2 mod n2
x = a3 mod n3
but what to do if in my situation it looks like this:
c1 = x ** e mod n1
c2 = x ** e mod n2
c3 = x ** e mod n3
I know c1, c2, c3, e, n1, n2 and n3
so how do I find x? |
Suppose $\Pi=(Gen,Sign,Vrfy)$ is a secure signature scheme, is the following signature scheme $\Pi'$ secure?
- $Gen'$: The same as $Gen$, output public-private key pair $pk,sk$ on input $1^n$
- $Sign'$: On input a private key $sk$ and message $m\in\{0,1\}^n$, choose uniform $r\gets \{0,1\}^n$. Output $\sigma=(r,\si... |
Montgomery Reduction requires that $gcd(R,N) = 1$, where N is the original modulus and R is the selected modulus which is like $2^k,k\in\mathbb{N}$, because the computer adopts binary coding.
When N is odd, R and N must be prime, but when N is even, we cannot find the R in form $2^k,k\in\mathbb{N}$.
The paper “Mo... |
Suppose $\Pi=(Gen,Sign,Vrfy)$ is a secure signature scheme, is the following signature scheme $\Pi'$ secure?
- $Gen'$: The same as $Gen$, output public-private key pair $pk,sk$ on input $1^n$
- $Sign'$: On input a private key $sk$ and message $m\in\{0,1\}^n$, choose uniform $r\gets \{0,1\}^n$. Output $\sigma=(r,\si... |
**This is a partial answer**. The desired security goal (existential vs strong unforgeability or others?) hasn't been explicitly stated. Without restrictions, we can assume that (any) unforgeability is the target.
In general, this scheme does not need to be secure. In particular it doesn't need to be SUF-CMA secure... |
Montgomery Reduction requires that $gcd(R,N) = 1$, where N is the original modulus and R is the selected modulus which is like $2^k,k\in\mathbb{N}$, because the computer adopts binary coding.
When N is odd, R and N must be prime, but when N is even, we cannot find the R in form $2^k,k\in\mathbb{N}$.
The paper [“M... |
**This is a partial answer**. The desired security goal (existential vs strong unforgeability or others?) hasn't been explicitly stated. Without restrictions, we can assume that (any) unforgeability is the target.
In general, this scheme does not need to be secure. In particular it doesn't need to be SUF-CMA secure... |
Many blockchain users have wallets that hold a private key, which can interact with a website. For example, the website can request the wallet to sign a specific message.
'Do only sign this message if you trust the frontend and you want to give it access to your private key used for XYZ.'
From the deterministic s... |
Is it safe to derive a secrete from a signature? |
Is it safe to derive a secret from a signature? |
Research paper: "[Extended-Chacha20 Stream Cipher With
Enhanced Quarter Round Function][1]"
1. The initial matrix is 6x6, but what are the exact inputs for each index, in other words, how will you fill the two additional columns that are added to the matrix?
2. Is it possible to change the constant values? and is ... |
Is it possible to change the constant values of ChaCha20?
and how it will affect the security of the cipher. |
Do Safe and Sophie Germain primes maintain a relatively stable distribution as numbers get larger, or do they become rarified beyond a predictable value?
This is important in one area of triangular number comparison for some of my study.
What is the predicatable, stable distribution?
Is there a comparab... |
I have two secret numbers $A$ and $B$. Both are uniformly-distributed 32-bit numbers.
I need a deterministic function $f(x)$ such that $f(A) = B$. $f(x)$ must not leak any information about $A$ or $B$.
Naively, what if $f(x) = x + C$, where $C = B - A$. What information is leaked, if any, in this case, and what w... |
Depending on the point/permute bits (color bits), the 1st and 2nd ciphertexts might involve the same $C_i$ value.
For example, imagine the point/permute bits are such that the basic garbled truth table is:
$$\begin{aligned}E(C_0) \\ E(C_0) \\ E(C_1) \\ E(C_0) \end{aligned}$$
Once you choose $C_0$ to make the fir... |
If I take a large truly random portion of data, I know that I can generate a 2048-bits key with it (assuming the random data has more entropy than the key). I read in this forum that Shake-256 has this ability.
I also read in [Wikipedia][1] this: "KangarooTwelve and MarsupilamiFourteen are Extendable-Output Function... |
Is KangarooTwelve hash function suitable for generating very large key material as Shake-256 is? |
normally, the chinese theorem looks like this:
$x = a_1$ mod $n_1$
$x = a_2$ mod $n_2$
$x = a_3$ mod $n_3$
but what to do if in my situation it looks like this:
$c_1 = x ** e$ mod $n_1$
$c_2 = x ** e$ mod $n_2$
$c_3 = x ** e$ mod $n_3$
I know $c_1$, $c_2$, $c_3$, $e$, $n_1$, $n_2$ and $n_3$
so ho... |
Normally, the chinese theorem looks like this:$$
x = a_1 \bmod n_1\\
x = a_2 \bmod n_2\\
x = a_3 \bmod n_3$$
but what to do if in my situation it looks like this:$$
c_1 = x^e \bmod n_1\\
c_2 = x^e \bmod n_2\\
c_3 = x^e \bmod n_3$$
I know $c_1$, $c_2$, $c_3$, $e$, $n_1$, $n_2$ and $n_3$. So how do I find $x$? |
Adding to the other answers, the questions leave a few things open to interpretation. Therefore, there are many ways to answer the question. The main thing that isn't clearly stated in the question is whether we think of a *keyed* hash function. Also, the quote in the question only considers random inputs (assumedly of... |
If we possess the knowledge that the expression $d^e \equiv c \pmod{n}$ holds for an **RSA** key pair, what would be the implication or consequence of this? Here, $e$, $n$, and $d$ represent the public exponent, modulus, and private exponent, respectively. |
What happens if we know that for an RSA key pair, the equation $d^e \equiv c \pmod{n}$ holds? |
I'm trying to analyze a stream of communication I captured from a game. I know the keys but I don't know how to apply them.
I've tried:
- Various AES-256 modes, splitting the message at different offsets into (nonce, ciphertext, MAC)
- RC4
- Debug the client binary for hints
But to no avail. The modes with ... |
Which cipher is used in this UDP stream? |
Can anyone please provide an example of an identification protocol that
1. With a private key
2. Resistant to attack with a fake ATM
3. Not resistant to eavesdropping attacks
? |
Example of an identification protocol that 1. With a private key 2. Resistant to attack with a fake ATM 3. Not resistant to eavesdropping attacks? |
I'm developing a program that uses a hybrid Key Encapsulation Mechanism (KEM) scheme, employing Kyber and X25519, with each producing a 32-byte shared secret. What would be the best scheme to combine these two shared secrets and derive a key for encryption?
I have a few schemes in mind:
- First scheme:
```
CONC... |
What scheme is the best for combining two shared secrets? |
I've read many e-voting papers that use El-Gamal scheme which I recall is vulnerable to man-in-the-middle attack, yet I find no discussion or even mentioning of it in those papers.
-Does anyone knows why?
-Is it completely solved or dealt with?
-I only found this old paper about it
https://www.semanticscholar.o... |
I am faced with a problem of selecting an appropriate message authentication code (MAC) for a particular application. These are the constraints:
I have two **64-bit integers** $r_a$ and $r_s$ **as input**, where:
1. $r_a < 2^{52}$ and $r_s < 2^{52}$
2. $r_a$ is a multiple of 4, i.e. $r_a = 0 \pmod{4}$
3. $r_s$ ... |
I am trying to understand some concepts such as DH problem and its variants. I have the following question from the book I read. (note that I translated the question from my language to english)
> Assume that two parties are using DH to make key exchange, so they
> need to use a group with an element x in it. Let's... |
which DH protocol is safer in communication with given condition? |
I have a noisy one-way communication channel where data is sent as a series of words of width *n* bits.
Assume *n* is a constant roughly in the range of 16...48.
I don't want bit errors in one word to affect the other words.
To achieve confidentiality in such a scenario, one would use a stream cipher,
as that gu... |
[Monocypher][1] author here.
First, I can confirm Elligator only needs the sign of the y coordinate… which by definition of X25519, is always "positive". _Which by the way is not a good thing!_ You want instead to select the sign at random. X25519 is insensitive to the sign of its y coordinate anyway, so even if you... |
[Monocypher][1] author here.
First, I can confirm Elligator only needs the sign of the y coordinate… which by definition of X25519, is always "positive". _This is not a good thing!_ You want instead to select the sign at random. X25519 is insensitive to the sign of its y coordinate anyway, so even if you recover it ... |
Assume Bob is sender and Alice is future recipient.
In ideal situation Bob know Alice public key, and encrypt message with it.
But what if Bob don't know Alice public key (he only will know Alice public key when agreement met), I saw two solutions:
1) Bob encrypt message with Alice pub key after agreement met ... |
Possible to encrypt message without knowing recipient public key? |
since the NTT is a variant of the DFT respectively FFT, it seems possible to implement a recursive algorithm for the NTT of Kyber with a divide-and-conquer concept. This is the reason for my question here, I would be interested in how to recursively realize the NTT from the current Kyber [specification][1]. I am less i... |
Ive been assigned research involving online gaming companies and their use of cryptographic algorithms to produce 'provably fair' results. The largest player in the industry uses a method involving a client provided seed, which is then combined with a server seed and an incremental nonce. The server seed is shown to ... |
How do bad actors manipulate game results in real time within 'provably fair' gaming systems? |
Ive been assigned research involving online gaming companies and their use of cryptographic algorithms to produce 'provably fair' results. The largest player in the industry uses a method involving a client provided seed, which is then combined with a server seed and an incremental nonce. The server seed is shown to ... |
A company wants to poll employees about their view of the company (by using a web system, say). They would like to do it anonymously, but they don't want people filling out forms more than once. An intern in the company suggested the following.
Each employee has a certain identification number that only the employe... |
How to anonymously poll for information in a small group of people? |
Let's say we have Bob, Alice and third party.
Bob encrypt message with Alice pub key and send it to Alice, also he make message signature hash and upload to third party.
Alice receive message and decrypt it. She also ask third party for message hash and verify message.
However. What if Bob upload random sign... |
Let's say we have Bob, Alice and third party.
Bob make message signature hash and upload to third party, then encrypt message with Alice pub key and send it to Alice
Alice receive message and decrypt it. She also ask third party for message hash and verify message.
However. What if Bob upload random signatur... |
I was reading [Limits on the provable consequences of one way permutations](https://dl.acm.org/doi/10.1145/73007.73012) by Impagliazzo and Rudich when I got stuck on a sentence.
First of all, they define a polynomial relation that is any relation $ R $ verifiable in polynomial time in $ ||x|| + ||y|| $, i.e., $xRy$ ... |
RFC 2313 has this specific callout:
1. An RSA private key logically consists of only the
modulus n and the private exponent d. The presence of the
values p, q, d mod (p-1), d mod (p-1), and q-1 mod p is
intended for efficiency, as Quisquater and Couvreur have
... |
In RFC 2313 (PKCS1/RSA) said you could recreate the Private key from 'n' and 'd', which later versions removed. Why? |
> **2313 was obsoleted by RFC 2437. 2437 was obsoleted by 3447. 3447 might have been obsoleted by 8017 but does anyone use it?**
The version history on PKCS#1 v2.2 reads:
> Version 2.2 updates the list of allowed hashing algorithms to
align them with FIPS 180-4 [SHS], therefore adding SHA-224,
SHA-5... |
> **2313 was obsoleted by RFC 2437. 2437 was obsoleted by 3447. 3447 might have been obsoleted by 8017 but does anyone use it?**
The version history on PKCS#1 v2.2 reads:
> Version 2.2 updates the list of allowed hashing algorithms to
align them with FIPS 180-4 [SHS], therefore adding SHA-224,
SHA-5... |
The BFV algorithm is one type of fully homomorphic encryption algorithms.
How can I encode an integer to polynomial ring by using batch encoder based on $R_t := {Z_t[X] \over ⟨(X^n)+1⟩}$? The plaintext space $(R \bmod t)$ is $R_t := {R \over t \cdot R}$ for some integers $t$ and encryption of the element $m(X) \in R... |
There are probabilistic algorithms to factor $n$ into $p$ and $q$ from $n$, $e$, $d$. It's then easy to rebuild the full private key $(n,e,d,p,q,d_p,d_q,q_\text{inv})$. One such algorithm is [there][1]. A similar one is in OpenSSL key import, and other libraries. The time it takes in practice is acceptable (comparable ... |
There are probabilistic algorithms to factor $n$ into $p$ and $q$ from $n$, $e$, $d$. It's then easy to rebuild the full private key $(n,e,d,p,q,d_p,d_q,q_\text{inv})$. One such algorithm is [there][1]. A similar one is in OpenSSL key import, and other libraries. The time it takes in practice is acceptable (comparable ... |
> In a naive encrypted store, I would have some data, and the key would remain sha256(data) and the data would be, say, aes-gcm(data). But is this safe? Does knowledge of the sha256 of the cleartext data aid an attacker in figuring out how to decrypt data?
Yesno. The attacker can guess the data, but they won't learn... |
There are probabilistic algorithms to factor $n$ into $p$ and $q$ from $n$, $e$, $d$. It's then easy to rebuild the full private key $(n,e,d,p,q,d_p,d_q,q_\text{inv})$. One such algorithm is [there][1]. A similar one is in OpenSSL key import, and other libraries. The time it takes in practice is acceptable (comparable ... |
There are probabilistic algorithms to factor $n$ into $p$ and $q$ from $n$, $e$, $d$. It's then easy to rebuild the full private key $(n,e,d,p,q,d_p,d_q,q_\text{inv})$. One such algorithm is [there][1]. A similar one is in OpenSSL key import, and other libraries. The time it takes in practice is acceptable (comparable ... |
So I read parts of the following article:
https://blog.cr.yp.to/20231003-countcorrectly.html
But I quite dont understand it. NIST assumes Kyber 512 is just as hard as AES128 nowadays, in presence of quantum computers. The error they mention is that Kyber has the security level of 2^41 bits, instead of 2^80 bits, bu... |
The plain, normal-form, decisional LWE problem over $\mathbb{Z}/q\mathbb{Z}$ is: given a *uniformly random* $n\times n$ matrix $A$ and vector $b\in \mathbb{Z}/q\mathbb{Z}^n$, decide if $b=As+e$ for small $s$ and small $e$.
The decisional ring LWE problem is, in $R_q:=\mathbb{Z}[x]/(q,p(x))$, given uniformly random ... |
Do we know that LWE is harder than Ring LWE? |
Few things: Circulant LWE is easy --- it corresponds to RLWE in $\mathbb{Z}_q[x]/(x^n-1)$, which (for $n = 2^k$) is (ring) isomorphic to $\mathbb{Z}_q[x]/(x-1)\times \prod_i \mathbb{Z}_q[x]/(x^{2^i}+1)$. In particular, one can project down onto the $\mathbb{Z}_q[x]/(x-1)$ component (corresponding to evaluation of the p... |
secp256k1 Generator:(G_X, G_Y, 0x1),
secp256k1 any public key using affine coordinates : B=(X, Y)
secp256k1 any Public key using jacobian coordinates:BB=(P_X, P_Y, P_Z)
(B's private key)==(BB's private key)
I consider projective Jacobian coordinates for secp256k1.
Given any public key B, if the z-coordin... |
I am currently exploring the workings of the Tor network, specifically how the Diffie-Hellman (DH) key exchange protocol is employed to establish shared secret keys between the client and each relay in the circuit.
While I understand how the client exchanges keys with the entry node, I am seeking clarity on how the... |
secp256k1 Generator:(G_X, G_Y, 0x1),
secp256k1 any public key using affine coordinates : B=(X, Y)
secp256k1 any Public key using jacobian coordinates:BB=(P_X, P_Y, P_Z)
(B's private key)==(BB's private key)
I consider projective Jacobian coordinates for secp256k1.
Given any public key B, if the z-coordin... |
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