Architectural Support for Arithmetic in Optimal Extension Fields

Public-key cryptosystems generally involve computation-intensive arithmetic operations, making them impractical for software implementation on constrained devices such as smart cards. In this paper we investigate the potential of architectural enhancements and instruction set extensions for low-level arithmetic used in public-key cryptography, most notably multiplication in finite fields of large order. The focus of the present work is directed towards a special type of finite fields, the so-called Optimal Extension Fields GF(pm) where p is a pseudo-Mersenne (PM) prime of the form p = 2n -c that fits into a single register. Based on the MIPS32 instruction set architecture, we introduce two custom instructions to accelerate the reduction modulo a PM prime. Moreover, we show that the multiplication in an Optimal Extension Field can take advantage of a multiply/accumulate unit with a wide accumulator so that a certain number of 64-bit products can be summed up without overflow. The propo...

• Type: Conference
• Year: 2004
• Where: ASAP
• Authors: Johann Großschädl, Sandeep S. Kumar, Christof Paar
• Keywords: ASAP 2004, Finite Fields, Hardware, Optimal Extension Field, Reduction Modulo