Horner's Rule-Based Multiplication over Fp and Fp^n: A Survey

Jean-Michel Muller (1) , Jean-Luc Beuchat (2) , Takanori Miyoshi (2) , Eiji Okamoto (2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 Laboratory of Cryptography and Information Security

This paper aims at surveying multipliers based on Horner's rule for finite field arithmetic. We present a generic architecture based on five processing elements and introduce a classification of several algorithms based on our model. We provide the readers with a detailed description of each scheme which should allow them to write a VHDL description or a VHDL code generator.

Keywords: Modular multiplication; Horner's rule; carry-save; high-radix carry-save; borrow-save; finite field; FPGA

Domains: Computer Science [cs]; Other [cs.OH]

Jean-Michel Muller, Jean-Luc Beuchat, Takanori Miyoshi, Eiji Okamoto. Horner's Rule-Based Multiplication over Fp and Fp^n: A Survey. International Journal of Electronics, 2008, 95 (7), pp.669-685. ⟨ensl-00148210⟩