Features

• Supports all Galois fields \(\mathrm{GF}(p^m)\), even arbitrarily-large fields!

• Faster than native NumPy! GF(x) * GF(y) is faster than (x * y) % p for \(\mathrm{GF}(p)\)

• Seamless integration with NumPy – normal NumPy functions work on Galois field arrays

• Linear algebra on Galois field matrices using normal np.linalg functions

• Functions to generate irreducible, primitive, and Conway polynomials

• Polynomials over Galois fields with galois.Poly

• Forward error correction codes with galois.BCH and galois.ReedSolomon

• Linear transforms over finite fields, such as the NTT with galois.ntt() and galois.intt()

• Fibonacci and Galois linear feedback shift registers with galois.LFSR, both binary and p-ary

• Various number theoretic functions

• Integer factorization and accompanying algorithms

• Prime number generation and primality testing