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Questions tagged [galois-field]

Galois field also knows as finite field in abstract algebra is a field that contains a finite number of elements.

A Galois field, also knows as finite field in abstract algebra, is a field that contains a finite number of elements.

A field is an algebraic structure with multiplication and addition, where every element has a multiplicative inverse, and all elements commute with each other.

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questions about AES irreducible polynomials

For galois field GF(2^8), the polynomial's format is a7x^7+a6x^6+...+a0. For AES, the irreducible polynomial is x^8+x^4+x^3+x+1. Apparently, the max power in GF(2^8) is x^7, but why the max power of irreducible polynomial is x^8? How will the max…
Junjie Zhou
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Euclidean algorithm for polynomials in GF(2^8)

I am trying to create an Euclidean algorithm (to solve Bezout's Relation) for 2 polynomials in the GF(2^8). I currently have this code for my different operations class ReedSolomon: gfSize = 256 genPoly = 285 log = [0]*gfSize …
Paul
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Template Parameter Array

I'm trying to create a class that uses the value of an array as a value/type template parameter. See below template< std::array arr> class gf { ... }; I believe my rationale for doing this is sane. This class implements operator…
ytgsyk4h
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Use of Reed-Solomon error correction algorithm with 4-state barcodes

I have a combined data information that requires minimum 35 bits. Using a 4-state barcode, each bar represents 2 bits, so the above mentioned information can be translated into 18 bars. I would like to add some strong error correction to this…
Ωmega
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How to do multiplication for two 4-bit numbers treating them as polynomials in C++

I am simulating a mini AES encryption/decryption algorithm using C++. For this I need to multiply two 4-bit numbers while treating them as polynomials. It goes through some stages that are converting them to polynomials, multiplying the two…
Pts
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How to convert a Galois Field Matrix to a binary matrix

I have a output matrix (3,63) of a encoder BCH but this matrix is a Galois Field and i need convert this Galois field in a matrix binary, because matlab treats the elements the Galois field as string and i need treats this values as binary…
zurbaranf
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How to keep the value of multiplication within the finite field range? I am implementing GF(8) multiplication

I am implementing GF(8) Multiplication. Primitive Polynomial is x^3 + x + 1. I know the basics: if multiplication overflows, I can xor it with my primitive polynomial and bring it into the range of finite field. However the trouble occurs when the…
Saurabh Singh
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Reed solomon encoding over Galois Field

I am passing a secret key (length of 16 ASCII chars = 128 bits) through Reed Solomon encoder which is operating over Galois field 16 (2^16). My question is: should this key be considered as 128 bits or 256? I got lost here because I know that ASCII…
user9680269
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solving a galois field matrix equation in matlab

I have the equation AX * C = AXB where all of the variables are square gf matrices of size n and the values are 0 or 1. AXB and AX are known, while C should be solved to B or an equivalent of it (there should be multiple solutions). Because X most…
psos
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Galois field algorithm from C to Matlab

I'm transcribing a C code for Matlab from a multiplication by 2 in the Gallois field, the problem is that my matlab code is not displaying the same value as the C code. Apparently everything is ok, I commented the code in matlab to identify the…
Mutante
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error 'int' object is not subscriptable python

i am learning python can you please help me with this code for galois field xor code is def generateGF(a,b): for x in range(a**b-1): for y in range(a**b-1): a[x][y] = bin(x)[2:].zfill(3) + bin(y)[2:].zfill(3) # limited for…
xeon zolt
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Gaussian Elimination over GF(3)

I'm trying to implement a gaussian algorithm that would work over Galois Field(3). I've already successfully implemented the algorithm over GF(2) but GF(3) seems a bit more tricky. My main problem is : when the value of the pivot line i've chosen is…
FreeRide
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How to print all the additions and multiplications of a Galois Field in Sage

My command line takes two inputs, a prime p and a positive integer n. I put them in a Galois Field in the form of GF(p^n). My goal is to print out all the elements of the field, the additions, and multiplications. I can print out the elements of…
umdcoder
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Polynomial over final field library

I'm trying to find a C++ library that handles polynomials over some finite field GF(2^n) and have support of matrix representation with support for rank finding/inverse or even solving A=X*B. I'm trying to use Linbox, but there's very little…
G. Ko
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Fast matrix Exponentiation computation in Galois field

I am looking for a fast way to compute power of matrix A in galois field 2 (GF(2)). A is a double matrix and its exponentiation of x denoted by A^x = A * A * A * ... * A (x times) The simple way is that converts A to GF(2) (because given matrix…
John
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