Elliptic curve digital signature algorithm over GF(p) on a residue number system enabled microprocessor

Abstract

We describe a residue number system (RNS) implementation of the 192-bit elliptic curve digital signature algorithm over GF(p). It uses a Tensilica Xtensa LX2.1 microprocessor core with hardware extensions to improve the performance of RNS operations. The low power and small area of the enhanced Xtensa LX2.1 core make it suitable for smart cards. This implementation is the first to use the RNS for elliptic curve cryptography on a sequential microprocessor. The RNS-enabled microprocessor performs a 192-bit point multiplication in approximately 2 million clock cycles, a performance that compares well to other minimally enhanced elliptic curve cryptography implementations.