A low-cost ECC coprocessor for smartcards

Abstract

In this article we present a low-cost coprocessor for smartcards which supports all necessary mathematical operations for a fast calculation of the Elliptic Curve Digital Signature Algorithm (ECDSA) based on the finite field GF(2m). These ECDSA operations are GF(2m) addition, 4-bit digit-serial multiplication in GF(2m), inversion in GF(2 m), and inversion in GF(p). An efficient implementation of the multiplicative inversion which breaks the 11:1 limit regarding multiplications makes it possible to use affine instead of projective coordinates for point operations on elliptic curves. A bitslice architecture allows an easy adaptation for different bit lengths. A small chip area is achieved by reusing the hardware registers for different operations. © International Association for Cryptologic Research 2004.