LFSR multipliers over GF(2m) defined by all-one polynomial

This paper presents two bit-serial modular multipliers based on the linear feedback shift register using an irreducible all one polynomial (AOP) over GF(2m). First, a new multiplication algorithm and its architecture are proposed for the modular AB multiplication. Then a new algorithm and architecture for the modular AB2 multiplication are derived based on the first multiplier. They have significantly smaller hardware complexity than the previous multipliers because of using the property of AOP. It simplifies the modular reduction compared with the case of using the generalized irreducible polynomial. Since the proposed multipliers have low hardware requirements and regular structures, they are suitable for VLSI implementation. The proposed multipliers can be used as the kernel architecture for the operations of exponentiation, inversion, and division.