Instruction set extension for fast elliptic curve cryptography over binary finite fields GF(2m)

The performance of elliptic curve (EC) cryptosystems depends essentially on efficient arithmetic in the underlying finite field. Binary finite fields GF(2(m)) have the advantage of "carry-free" addition. Multiplication, on the other hand, is rather costly since polynomial arithmetic is not supported by general-purpose processors. In this paper we propose a combined hardware/software approach to overcome this problem. First, we outline that multiplication of binary polynomials can be easily integrated into a multiplier datapath for integers without significant additional hardware. Then, we present new algorithms for multiple-precision arithmetic in GF(2(m)) based on the availability of an instruction for single-precision multiplication of binary polynomials. The proposed hardware/software approach is considerably faster than a "conventional" software implementation and well suited for constrained devices like smart cards. Our experimental results show that an enhanced 16-bit RISC processor is able to generate a 191-bit ECDSA signature in less than 650 msec when the core is clocked at 5 MHz.