Generic Efficient Arithmetic Algorithms for PAFFs (Processor Adequate Finite Fields) and Related Algebraic Structures

摘要

In the past years several authors have considered finite fields extensions of odd characteristic optimised for a given architecture to obtain performance gains. The considered fields were however very specific. We define a Processor Adequate Finite Field (PAFF) as a field of odd characteristic p < 2~ω where ω is a CPU related word length. PAFFs have several attractive properties for cryptography. In this paper we concentrate on arithmetic aspects. We present some algorithms usually providing better performance in PAFFs than in prime fields and in previously proposed instances of extension fields of comparable size.