Programmable LSB-first and MSB-first modular multipliers for ECC in GF(2m)

In this paper, we propose programmable serial- in parallel-out LSB-first and MSB-first modular multipliers for elliptic curve cryptosystems (ECCs). The proposed multipliers can operate in any arbitrary field GF(2^m) such that m is less than a maximum field order M. A linear array of processing elements is designed with a parallel switching circuitry to incorporate programmability in the fixed order multipliers. The proposed architectures are qualitatively compared against existing programmable multipliers in terms of gate count, delay and latency. The application specific integrated circuit (ASIC) implementation of the proposed multipliers using TSMC 0.18 mum standard cell library is also analyzed.