An Implementation Scheme of σ-LFSR Based on Trinomial Primitive Polynomial
Zehui Wang · Journal of Wuhan University · 2008
Deterministic irreducible polynomial and primitive polynomial over finite rings,i.e.polynomial rings with coefficients in finite fields,are obtained.With these polynomials,an efficient algorithm for obtaining the longest period of output stream is constructed.It is proved that the algorithm needs only 2(lb p) times additions modulo p for determining every value of the output stream.An implementation scheme of σ-LFSR based on trinomial primitive polynomial is given.The theoretical analysis and the computer simulation results show that this σ-LFSR generator has good randomness and can be implemented easily in both software and hardware.This approach can be used to construct new efficient cryptosystems for stream ciphers.