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In the past years several authors have considered finite fields extensions of odd characteristic optimised for a given architecture to ob- tain 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 w where w is a CPU related word length. PAFFs have several attractive properties for cryptography. In this paper we concen- trate on arithmetic aspects. We present some algorithms usually provid- ing better performance in PAFFs than in prime fields and in previously proposed instances of extension fields of comparable size.

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