Speeding up big-numbers squaring

Shay Gueron, Vlad Krasnov

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

Abstract

This paper deals with optimizations for big-numbers (multi-precision) squaring, and their efficient implementation on x86-64 platforms. Such optimizations have various usages, and a most prominent one is RSA acceleration, where big-numbers squaring consumes a significant portion of the computations. We introduce an algorithm for big-numbers squaring, that reduces the number of single precision add-with-carry operations, and trades several additions with a single left shift operation. When measured on the 2nd Generation Intel® Core™ processor, for 512-bit operands, our algorithm is roughly 1.4 times faster than the implementation of GMP library 5.0.2. For 1024-bit operands, our implementation is 1.2 times faster than that of the GMP library 5.0.2. Our optimization is used in a recently posted Open SSL patch [4] for accelerating modular exponentiation for RSA.

Original languageEnglish
Title of host publicationProceedings of the 9th International Conference on Information Technology, ITNG 2012
Pages821-823
Number of pages3
DOIs
StatePublished - 2012
Event9th International Conference on Information Technology, ITNG 2012 - Las Vegas, NV, United States
Duration: 16 Apr 201218 Apr 2012

Publication series

NameProceedings of the 9th International Conference on Information Technology, ITNG 2012

Conference

Conference9th International Conference on Information Technology, ITNG 2012
Country/TerritoryUnited States
CityLas Vegas, NV
Period16/04/1218/04/12

Keywords

  • RSA
  • multi-precision arithmetic

ASJC Scopus subject areas

  • Computer Networks and Communications

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