A Chinese Remainder Theorem Approach to Bit-Parallel Polynomial Basis Multipliers for Irreducible Trinomials

摘要

We show that the step “modulo the degree- field generating irreducible polynomial” in the classical definition of the 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 multipliers for irreducible trinomials on where . For some values of , 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 for example, the space complexity of the proposed - esign is reduced by about , while the time complexity matches the best result. Our experimental results show that among the 539 values of such that and is irreducible over for some in the range , the proposed multipliers beat the current fastest parallel multipliers for 290 values of when : they have the same time complexity, but the space complexities are reduced by