Digit-Serial Systolic Architectures for Inversions over GF(2m)

Digit-serial architectures for finite field arithmetic operations are of interest since hardware costs can be optimized by minimizing the digit size to satisfy throughput requirements. Based on a reformulation of the extended Euclidean algorithm, we design digit-serial systolic architectures with digit size L for inversions over GF(2^m) using a systematic approach. Compared with previously proposed digit-serial inversion architectures, our new architectures require significantly less hardware and reduce critical path delays by 50% while achieving the same throughput L/m and latency. Unlike previously proposed digit-serial inversion architectures, for which L has to be a divisor of m, our systematic approach is applicable even when L is not a divisor of m