Paper 2024/121

An acceleration of the AKS prime identification algorithm

Stephen Meredith Williams, Barcombe Services
Abstract

In its standard form, the AKS prime identification algorithm is deterministic and polynomial time but too slow to be of practical use. By dropping its deterministic attribute, it can be accelerated to an extent that it is practically useful, though still much slower than the widely used Miller-Rabin-Selfridge-Monier (MRSM) algorithm based on the Fermat Little Theorem or the Solovay-Strassen algorithm based on the Euler Criterion. The change made, in the last stage of AKS, is to check a modular equation not for a long sequence of values but for a single one. Another change is to reduce, arbitrarily, the size of the parameter $r$ giving the degree of the polynomial used for the last stage.

Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Preprint.
Keywords
AKS primality testingsingle–valueCarmichael numbersbinomial theoremaccelerationalgorithm
Contact author(s)
zen323167 @ zen co uk
History
2024-01-29: approved
2024-01-27: received
See all versions
Short URL
https://ia.cr/2024/121
License
Creative Commons Attribution-NonCommercial
CC BY-NC

BibTeX

@misc{cryptoeprint:2024/121,
      author = {Stephen Meredith Williams},
      title = {An acceleration of the {AKS} prime identification algorithm},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/121},
      year = {2024},
      url = {https://eprint.iacr.org/2024/121}
}
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