Systolic and Scalable Architectures for Digit-Serial Multiplication in Fields GF(p ^m)

Abstract

This contribution defines systolic digit-serial architectures for fields G(p ^m). These architectures are scalable in the sense that their instantiations support multiplication in different fields GF(p ^m) for which p is fixed and m is variable. These features make the multiplier architectures suitable for ASIC as well as FPGA implementations. In addition, the same architectures are easily applicable to tower fields GF(q ^m) for a given ground field GF(q), where q itself is a prime power. We simulated the basic cell of a systolic LSDE multiplier on 0.18 μm CMOS technology to verify the functionality of the architectures. Finally, we provide specific values for GF(2^m) and GF(3^m) fields which are of particular interest in recent cryptographic applications, for example, the implementation of short signature schemes based on the Tate pairing.