carry-less multiplication optimization for ECC over GF(2^m) in MIRACL
c,cryptography,compiler-optimization,elliptic-curve,galois-field
The method outlined in fastgf2m.txt is for generating unrolled code associated with a fixed m value determined at compile time. The bmark program changes m at runtime, and so the unrolled code will often not be correct in this case. The documentation could be clearer on this point. Also make...
Errata (erasures+errors) Berlekamp-Massey for Reed-Solomon decoding
python,math,error-correction,galois-field,reed-solomon
After reading lots and lots of research papers and books, the only place where I have found the answer is in the book (readable online on Google Books, but not available as a PDF): "Algebraic codes for data transmission", Blahut, Richard E., 2003, Cambridge university press. Here are some extracts...
How to print all the additions and multiplications of a Galois Field in Sage
python,enumeration,sage,galois-field
You could simply use nested loops over the elements of k, instead of over the indices of the elements: sage: for e0 in k: ....: for e1 in k: ....: print '(%s) + (%s) = %s' % (e0, e1, e0+e1) ....: (0) + (0) = 0 (0) + (x) =...
Polynomial over final field library
c++,polynomials,finite-field,galois-field
Looks like NTL is the solution. It gives comfortable implementation of GF(2^n) polynomials modulo some polynomial and easy work with matrices (inverse, solving, etc..)