International Association
for Cryptologic Research

We show that the step \"modulo the degree-n field generating irreducible polynomial\" in the classical definition of the GF(2^n) multiplication operation can be avoided. This leads to an alternative representation of the finite field multiplication operation. Combining this representation and the Chinese Remainder Theorem, we design bit-parallel GF(2^n) multipliers for irreducible trinomials u^n + u^k + 1 on GF(2). For some values of n, our architectures have the same time complexity as the fastest bit-parallel multipliers - the quadratic multipliers, but their space complexities are reduced. Take the special irreducible trinomial u^2k +u^k +1 for example, the space complexity of the proposed design is reduced by about 1/8, while the time complexity matches the best result. Our experimental results show that among the 539 values of n such that 4