Efficient bit-parallel multipliers over finite fields GF(2m)

摘要: Hardware implementation of multiplication in finite field GF(2^m) based on sparse polynomials is found to be advantageous terms space-complexity as well the time-complexity. In this paper, we present a new permutation method construct irreducible like-trinomials form (x+1)^m+(x+1)^n+1 for efficient bit-parallel multipliers. For implementing multiplications such polynomials, have defined like-polynomial basis (LPB) an alternative original polynomial GF(2^m). We shown further that modular arithmetic binary equivalent trinomials. order design multipliers composite fields, another convert into forms (x^2+x+1)^m+(x^2+x+1)^n+1, (x^2+x)^m+(x^2+x)^n+1 and (x^4+x+1)^m+(x^4+x+1)^n+1. The proposed multiplier over GF(2^4^m) offer saving about 33% 42.8% additions corresponding existing architectures.