Parallelization of scalable elliptic curve cryptosystem processors in GF(2m)

Abstract

The parallelization of scalable elliptic curve cryptography (ECC) processors (ECPs) is investigated in this paper. The proposed scalable ECPs support all 5 pseudo-random curves or all 5 Koblitz curves recommended by the National Institute of Standards and Technology (NIST) without the need to reconfigure the hardware. The proposed ECPs parallelize the finite field arithmetic unit and the elliptic curve point multiplication (ECPM) algorithm to gain performance improvement. The finite field multiplication is separated such that the reduction step is executed in parallel with the next polynomial multiplication. Subsequently, the finite field arithmetic of the ECPs are further parallelized and the performance can be further improved by over 50%. Since the multiplier blocks consume a low number of hardware resources, the latency reduction outweighs the cost of the extra multiplier resulting in more efficient ECP designs. The technique is applied for both pseudo-random curve and Koblitz curve algorithms. A novel ECPM algorithm is also proposed for Koblitz curves that take advantage of the proposed finite field arithmetic architecture. The implementation results show that the proposed parallelized scalable ECPs have better performance compared to state-of-the-art scalable ECPs that support the same set of elliptic curves.