A new bit-serial multiplier over GF(pm) using irreducible trinomials

Abstract

Pairing-based schemes, such as identity-based cryptosystem, are widely used for future computing environments. Hence the work of hardware architectures for G F ( p m ) has been brought to public attention for the past few years since most of the pairing-based schemes are implemented using arithmetic operations over G F ( p m ) defined by irreducible trinomials. This paper proposes a new most significant elements (MSE)-first serial multiplier for G F ( p m ) , where p > 2 , which is more efficient than least significant elements (LSE)-first multipliers from the point of view of both the time delay and the size of registers. In particular, the proposed multiplier has an advantage when the extension degree of finite fields m is large and the characteristic of finite fields p is small like G F ( 3 m ) , G F ( 5 m ) , and G F ( 7 m ) used in pairing-based cryptosystems.