Questions tagged [coding-theory]

Question 1

Qi Cheng proved that the minimum distance for elliptic linear codes (AG codes for genus 1 curves) is NP-hard (see https://arxiv.org/abs/cs/0507026). Any instance of ECDLP for an elliptic curve $E/\...

Question 2

For any positive integer $k$, let $\boxplus_k$ be addition on $k$-bit unsigned integers and $\boxminus_k$ be subtraction on $k$-bit unsigned integers. Let $\operatorname{NH}_w((X,Y),(a,b)) = (a \...

Question 3

I'm a research student and previously specialized in Algebra and number theory. Currently I'm finding a research field in Crypto/coding theory. Algebraic geometry code seems interesting to me but some ...

Question 4

Let $$M= \begin{bmatrix}0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0\end{bmatrix}$$ which is used in the block ciphers MIDORI and MANTIS. Of course this matrix ...

Question 5

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 \...

Question 6

I want to find the minimum distance of an $[8,4]$ Near MDS code over a finite field F_4 (NMDS Code is a type of linear code). I want to know which programming language has a built-in function that ...

Question 7

Is there a better way than brute forcing (choose $k=\mathrm{rank}(A)$ first columns - test the determinant, if determinant = 0 choose new column set - there are $\binom nk$ many possibilities which is ...

Question 8

1. G known - how to decrypt Referring to this question: Basic attacks on McEliece; finding S and P (nobody answered) Take a McEliece cryptosystem with public generator matrix $G′=SGP$ where $G$ is a ...

Question 9

Having recently learned of coding based cryptography, it seems that they key size for post-quantum security might be a lot larger than what is required by Regev PKE (in the former keys include several ...

Question 10

An encryption scheme should be injective in the sense that each ciphertext should only be associated with at most one message, in order that decryption is unambiguous. An efficient signature ...

Question 11

I am implementing wet-paper codes (WPC) with randomly generated parity-check matrix $H$, based on this paper. As the wet DCT coefficients, I set DCT coefficients with value 0, or with values 0 and 1 (...

Question 12

From the literature, STC seems to be the current state-of-the-art for the coding part of steganography. From the description of the method, it appears to me it could be parallelized for GPU. Does ...

Question 13

From this Wiki page: given a Goppa code $\Gamma(g, L)$ and a binary word $v=(v_0,...,v_{n-1})$, its syndrome is defined as $$s(x)=\sum_{i=0}^{n-1}\frac{v_i}{x-L_i} \mod g(x).$$ To do error correction, ...

Question 14

I am currently reading about RS codes. I see that they are using a Galois Fields (Finite Fields) as vector spaces. Is there any other particular reason other than the fact that they simplify binary ...

Question 15

Is there a cryptographic reason for using an irreducible Goppa polynomial $g$ in the McEliece scheme? One doesn't need irreducibility to define a usable code, so I assume there is some structural ...

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Questions tagged [coding-theory]

NP-hardness of ECDLP

Is the NH hash family (from UMAC) AXU?

Is algebraic geometry code dead?

Is there a 4 by 4 NMDS matrix which is better than M= [[0,1,1,1], [1,0,1,1], [1,1,0,1], [1,1,1,0]] used in MIDORI?

Efficient decoding a code dual to a Goppa code?

Near Maximum Distance Separable Code

How to choose rank(A) independant columns of matrix A efficiently

Decrypting McEliece if security assumptions fail

What are the advantages of coding based cryptosytems over LWE (Regev)?

Covering codes for digital signatures

Too many wet positions in Wet-Paper Codes steganography with random H

Accelerating Syndrome-Trellis Codes (STC) for GPU [closed]

Patterson's decoding algorithm for Goppa codes

Can Reed-Solomon codes work on infinite fields like $\mathbb{Q}$?

Use of irreducible Goppa codes in McEliece scheme

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