Effects of optimizations for software implementations of small binary field arithmetic

Roberto Avanzi, Nicolas Thériault

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We describe an implementation of binary field arithmetic written in the C programming language. Even though the implementation targets 32-bit CPUs, the results can be applied also to CPUs with different granularity. We begin with separate routines for each operand size in words to minimize performance penalties that have a bigger relative impact for shorter operands - such as those used to implement modern curve based cryptography. We then proceed to use techniques specific to operand size in bits for several field sizes. This results in an implementation of field arithmetic where the curve representing field multiplication performance closely resembles the theoretical quadratic bit-complexity that can be expected for small inputs. This has important practical consequences: For instance, it will allow us to compare the performance of the arithmetic on curves of different genera and defined over fields of different sizes without worrying about penalties introduced by field arithmetic and concentrating on the curve arithmetic itself. Moreover, the cost of field inversion is very low, making the use of affine coordinates in curve arithmetic more interesting. These applications will be mentioned.

Original languageEnglish
Title of host publicationArithmetic of Finite Fields - First International Workshop, WAIFI 2007, Proceedings
PublisherSpringer Verlag
Number of pages16
ISBN (Print)9783540730736
StatePublished - 2007
Externally publishedYes
Event1st International Workshop on Arithmetic of Finite Fields, WAIFI 2007 - Madrid, Spain
Duration: 21 Jun 200722 Jun 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4547 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference1st International Workshop on Arithmetic of Finite Fields, WAIFI 2007


  • Binary fields
  • Curve-based cryptography
  • Efficient implementation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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