Comparative cost/performance evaluation of digit-serial multipliers for finite fields of type GF(2n)

Multiplication in finite fields (Galois fields) is a basic operation for cryptography applications. Recent proposals for elliptic code cryptography, require efficient computation of multiplication in finite fields of type GF(2n) for large values of n (150, 200 bits). Digit-serial multiplier VLSI architectures are an attractive solution, being a compromise between purely parallel and serial ones. A comparative study of digit-serial multiplier VLSI architectures, for fields of type GF(2n), is carried out. Such architectures are reviewed, some further optimisations are proposed, and are then implemented in VHDL (CMOS cell library, 0.35 μm, by ST Microelectronics). Figures of merit like time latency, silicon area and power consumption are evaluated by simulation with Synopsis tools, varying parameters like the size n of the field elements and the size k of the blocks of bits being processed in parallel by the digit-serial architectures.