Applications of the montgomery exponent

Shay Gueron*, Or Zuk

*Corresponding author for this work

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

3 Scopus citations


We de£ne here the Montgomery Exponent of order s, modulo the odd integer N, by MEXP = MEXP(A, X, N, s) = AX2-s(X-1) (mod N), and illustrate some properties and usage of this operator. We show how AX (mod N) can be obtained from MEXP(A, X, N, s) by one Montgomery multiplication. This suggests a new modular exponentiation algorithm that uses one Montgomery multiplication less than the number required with the standard method. This improves the performance, although the improvement is signi£cant only when the exponent X is short (e.g., modular squaring or RSA veri£cation). However, and even more important, this achieves code size reduction, which is appreciated when the exponentiation algorithm is written in a low level language and stored in (expensive) ROM. We also illustrate the potential advantage in performance and code size when known cryptographic applications are modi£ed in a way that MEXP replaces the standard modular exponentiation.

Original languageAmerican English
Title of host publicationProceedings ITCC 2005 - International Conference on Information Technology
Subtitle of host publicationCoding and Computing
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)0769523153, 9780769523156
StatePublished - 2005
Externally publishedYes
EventITCC 2005 - International Conference on Information Technology: Coding and Computing - Las Vegas, NV, United States
Duration: 4 Apr 20056 Apr 2005

Publication series

NameInternational Conference on Information Technology: Coding and Computing, ITCC


ConferenceITCC 2005 - International Conference on Information Technology: Coding and Computing
Country/TerritoryUnited States
CityLas Vegas, NV


  • Ef£cient implementations
  • Modular exponentiation
  • Montgomery multiplication


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