Elixir: High-Throughput Cost-Effective Dual-Field Processors and the Design Framework for Elliptic Curve Cryptography

We present a design framework that consists of a high-throughput, parallel, and scalable elliptic curve cryptographic (ECC) processor, and its cost-effectiveness methodology for the design exploration. A two-phase scheduling methodology is proposed to optimize the ECC arithmetic over both GF(p) and GF(2m). Based on the methodology, a parallel and scalable ECC architecture is also proposed. Our dual-field ECC architecture supports arbitrary elliptic curves and arbitrary finite fields with different field sizes. The optimization to a variety of applications with different area/throughput requirements can be achieved rapidly and efficiently. Using 0.13-mum CMOS technology, a 160-bit ECC processor core is implemented, which can perform elliptic-curve scalar multiplication in 340 mus over GF(p) and 155 mus over GF(2m), respectively. The comparison of speed and area overhead among different ECC designs justifies the cost-effectiveness of the proposed ECC architecture with its design methodology.