Generic efficient arithmetic algorithms for PAFFs (Processor Adequate Finite Fields) and related algebraic structures (extended abstract)

Roberta Maria Avanzi, Preda Mihǎilescu

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

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 < 2w where w 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.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsMitsuru Matsui, Robert Zuccherato
PublisherSpringer Verlag
Pages320-334
Number of pages15
ISBN (Print)3540213708, 9783540213703
DOIs
StatePublished - 2004
Externally publishedYes

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3006
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Keywords

  • Discrete logarithm systems
  • Exponentiation algorithms
  • Finite extension fields
  • Modular reduction

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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