Title :
Instruction set extension for fast elliptic curve cryptography over binary finite fields GF(2m)
Author :
Groszschaedl, J. ; Kamendje, Guy-Armand
Author_Institution :
Inst. for Appl. Inf. Process. & Commun., Graz Univ. of Technol., Austria
Abstract :
The performance of elliptic curve (EC) cryptosystems depends essentially on efficient arithmetic in the underlying finite field. Binary finite fields GF(2m) 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. 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(2m) 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.
Keywords :
digital arithmetic; hardware-software codesign; instruction sets; polynomials; public key cryptography; reduced instruction set computing; smart cards; 16 bit; 191 bit; 5 MHz; ECDSA signature; RISC processor; binary finite field; binary polynomial; carry-free addition; constrained device; conventional software; elliptic curve cryptography; general-purpose processor; hardware/software approach; instruction set extension; multiple-precision arithmetic; multiplier datapath; polynomial arithmetic; single-precision multiplication; smart card; Elliptic curve cryptography; Galois fields;
Conference_Titel :
Application-Specific Systems, Architectures, and Processors, 2003. Proceedings. IEEE International Conference on
Print_ISBN :
0-7695-1992-X
DOI :
10.1109/ASAP.2003.1212868