Speed records for multi-prime RSA using AVX2 architectures

Shay Gueron, Vlad Krasnov

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


RSA is a popular public key algorithm. Its private key operation is modular exponentiation with a composite 2k-bit modulus that is the product of two kbit primes. Computing 2k-bit modular exponentiation can be sped up four fold with the Chinese Remainder Theorem (CRT), requiring two k-bit modular exponentiations (plus recombination). Multi-prime RSA is the generalization to the case where the modulus is a product of r ≥ 3 primes of (roughly) equal bit-length, 2k/r. Here, CRT trades 2k-bit modular exponentiation with r modular exponentiations, with 2k/r-bit moduli (plus recombination). This paper discusses multi-prime RSA with key lengths (=2k) of 2048/3072/4096 bits, and r = 3 or r = 4 primes. With these parameters, the security of multi-prime RSA is comparable to that of classical RSA. We show how to optimize multi-prime RSA on modern processors, by parallelizing r modular exponentiations and leveraging “vector” instructions, achieving performance gains of up to 5.07x.

Original languageEnglish
Title of host publicationInformation Technology
Subtitle of host publicationNew Generations - 13th International Conference on Information Technology
EditorsShahram Latifi
PublisherSpringer Verlag
Number of pages9
ISBN (Print)9783319324661
StatePublished - 2016
Event13th International Conference on Information Technology- New Generations, ITNG 2016 - Las Vegas, United States
Duration: 4 Apr 20166 Apr 2016

Publication series

NameAdvances in Intelligent Systems and Computing
ISSN (Print)2194-5357


Conference13th International Conference on Information Technology- New Generations, ITNG 2016
Country/TerritoryUnited States
CityLas Vegas

Bibliographical note

Funding Information:
This research was supported by the PQCRYPTO project, which was partially funded by the European Commission Horizon 2020 research Programme, grant #645622

Publisher Copyright:
© Springer International Publishing Switzerland 2016.


  • AVX2
  • AVX512
  • Haswell broadwell skylake
  • Multi-prime RSA
  • RSA

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science (all)


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