Low-complexity bit-parallel systolic architectures for computing A(x)B2(x) over GF(2m)

Abstract

Cryptographic applications based on finite fields have recently attracted considerable interest. This work develops two new algorithms, called the time-dependent and time-independent multiplication algorithms, for computing A(x)B2(x) over a finite field GF(2m) using an interleaved conventional multiplication approach. The proposed algorithms allow efficient realisation of the bit-parallel multiplication using iterative arrays. The results reveal that our proposed time-dependent and time-independent multipliers save approximately 34% and 62% less space complexity, respectively, compared to the traditional multipliers for a general polynomial basis of GF(2m). Additionally, the presented multiplication algorithms can also be effective Montgomery multiplication algorithms to yield low-complexity architectures.