A Simple Architectural Enhancement for Fast and Flexible Elliptic Curve Cryptography over Binary Finite Fields GF(2 m )

Abstract

AbstractMobile and wireless devices like cell phones and network-enhanced PDAs have become increasingly popular in recent years. The security of data transmitted via these devices is a topic of growing importance and methods of public-key cryptography are able to satisfy this need. Elliptic curve cryptography (ECC) is especially attractive for devices which have restrictions in terms of computing power and energy supply. The efficiency of ECC implementations is highly dependent on the performance of arithmetic operations in the underlying finite field. This work presents a simple architectural enhancement to a general-purpose processor core which facilitates arithmetic operations in binary finite fields GF(2m). A custom instruction for a multiply step for binary polynomials has been integrated into a SPARC V8 core, which subsequently served to compare the merits of the enhancement for two different ECC implementations. One was tailored to the use of GF(2191) with a fixed reduction polynomial. The tailored implementation was sped up by 90% and its code size was reduced. The second implementation worked for arbitrary binary fields with a range of reduction polynomials. The flexible implementation was accelerated by a factor of nearly 10.KeywordsElliptic curve cryptographyapplication-specific instruction set extensionbinary finite fieldsSPARC V8multiply step instruction