Elliptic Curve Cryptography for the masses: Simple and fast finite field arithmetic

Michael Scott

Paper 2024/779

Elliptic Curve Cryptography for the masses: Simple and fast finite field arithmetic

Michael Scott, Technology Innovation Institute

Abstract

Shaped prime moduli are often considered for use in elliptic curve and isogeny-based cryptography to allow for faster modular reduction. Here we focus on the most common choices for shaped primes that have been suggested, that is pseudo-Mersenne, generalized Mersenne and Montgomery-friendly primes. We consider how best to to exploit these shapes for maximum efficiency, and provide an open source tool to automatically generate, test and time working high-level language finite-field code. Next we consider the advantage to be gained from implementations that are written in assembly language and which exploit special instructions, SIMD hardware if present, and the particularities of the algorithm being implemented.

Note: Fixed typo

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint.
Contact author(s): michael scott @ tii ae
History: 2024-10-05: last of 4 revisions; 2024-05-21: received; See all versions
Short URL: https://ia.cr/2024/779
License: CC BY

BibTeX

@misc{cryptoeprint:2024/779,
      author = {Michael Scott},
      title = {Elliptic Curve Cryptography for the masses: Simple and fast finite field arithmetic},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/779},
      year = {2024},
      url = {https://eprint.iacr.org/2024/779}
}