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Questions tagged [finite-field]

In algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains a finite number of elements.

In algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains a finite number of elements, called its order (the size of the underlying set). As with any field, a finite field is a set on which the operations of commutative multiplication, addition, subtraction and division (by anything except zero) have been defined.

Read more: http://en.wikipedia.org/wiki/Finite_field

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Gcd of polynomials modulo k

I want to ask Matlab to tell me, for example, the greatest common divisor of polynomials of x^4+x^3+2x+2 and x^3+x^2+x+1 over fields like Z_3[x] (where an answer is x+1) and Z_5[x] (where an answer is x^2-x+2). Any ideas how I would implement this?
Maths student
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Generating random element in $GF(2^x)$ in NTL

I'm trying to study part of the NTL functionality related to finite field arithmetics, but something weird is happening. I'm trying to generate 2 random elements in the field $GF(2^8)$ and do addition and subtraction with them. But it seems that the…
Bush
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how can I calculate order of an element in finite field using ntl?

I'm trying to calculate order of an element in finite field (Group) using ntl. but I did not find any function to do this! can anyone guide me please?
Habib Lotfi
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Finding GCD of two polynomial over field F2 (ield of integer residues modulo 2)

I am trying to find GCD of the following polynomials ( two separate questions ) in Field modulo 2 and field modulo 3. But I am stuck in the first one for some reasons. a(x) =x5+x3+x2+ 1, b(x) =x3+x for mod 2 a(x) = 2x3+2x2+x+1 b(x) =x2+2 …
kingmakerking
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Solving system of linear equations over a finite field python or java

Is there any package in python or java that can solve a system of linear equations over a finite field? I'm trying to solve 20+ equations with 20+ unknown variables and having this package would be great. This is a system of equations over a finite…
Quanquan Liu
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Which finite fields are generated automatically by Nemo (which uses flint)

I'm doing a lot of arithmetic in finite fields, using Julia and the Nemo package (https://nemocas.github.io/Nemo.jl/stable/finitefield/). The documentation says @doc raw""" gen(a::FqPolyRepField) Return the generator of the finite field. Note that…
Kevin O'Bryant
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Galois Reed Solomon

I work on a project about cryptosystem using Reed Solomon codes and it is using implementation of Galois package on Python. As I know, Reed Solomon codes based and work on polynomial representation but using the galois package, it can build the…
heidii
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In python, how to find a primitive element of finite field?

Say, I want a finite field containing $2^n$ elements for some positive $n$. How to get a single random primitive element in Python, different from that provided by the Conway polynomial? I know that Python's Galois library gives the option to…
Julian Osorio
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Is there no basic finite field calculation function on MATLAB?

I want to do some basic operations on finite fields, such as finding the greatest common factor of two polynomials, factoring polynomials, etc. I find few results on google. I'm new to matlab, doesn't matlab have a convenient function like the c++…
tom
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Is there a way to Forward Error Correct (FEC RS) an Alphabet of 36 chars?

Case: We want to Encode an 8 Character code to 10 Character code with adding 2 Forward Error Correcting Reed-Solomon Characters(so suffix 2 Error Correcting Chars). Example Code I'm using this Library C# FEC Reed-Solomon Library. I'm having a…
RennieM
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Optimal frequency of modulo operation in finite field arithmetic implementation

I'm trying to implement finite field arithmetic to use it in Elliptic Curve calculations. Since all that's ever used are arithmetic operations that commute with the modulo operator, I don't see a reason not to delaying that operation till the very…
popeye
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Is there any way to plot xy diagram of points of elliptic curve over finite field with huge number p defined by standard EC (p-192,p-256...)?

Is there any way to plot xy diagram of points of elliptic curve (such as NIST p-192,p-224,p-256...) over finite field? I tried with p-256, but it has very big number of p thus when I use for loop it takes huge amount of time to go through the loop.…
Alokin
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modulo reduction in field of non primitive order

I'm getting started with AES and need to calculate the inverse for S-byte table. I'm trying to generate exponential and logarithm table for inversion with generator 3. The exponents works fine till I reach 3 ^ 8 which is 0xff. Exponential table …
Shanks Limbu
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Factorizing multivariate polynomial over finite fields

I'm working on a project where I need to factorize a given bivariate polynomial over a finite field, is there any python library that can help me? Sympy cannot factorize multivariate polynomial over a finite field, so is there any other library that…
Ahmad Jabareen
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How to represent the elements of the Galois filed GF(2^8) and perform arithmetic in NTL library

I am new to NTL library for its GF2X, GF2E, GF2EX, etc. Now, I want to perform multiplication on the Galois field GF(2^8). The problem is as following: Rijndael (standardised as AES) uses the characteristic 2 finite field with 256 elements, which…
Land
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