Finding Practical Parameters for Isogeny-based Cryptography

Maria Corte-Real Santos; Jonathan Komada Eriksen; Michael Meyer; Francisco Rodríguez-Henríquez

Paper 2024/1150

Finding Practical Parameters for Isogeny-based Cryptography

Maria Corte-Real Santos

, University College London

Jonathan Komada Eriksen

, Norwegian University of Science and Technology

Michael Meyer

, University of Regensburg

Francisco Rodríguez-Henríquez

, Cryptography Research Center, Technology Innovation Institute

Abstract

Isogeny-based schemes often come with special requirements on the field of definition of the involved elliptic curves. For instance, the efficiency of SQIsign, a promising candidate in the NIST signature standardisation process, requires a large power of two and a large smooth integer to divide for its prime parameter . We present two new methods that combine previous techniques for finding suitable primes: sieve-and-boost and XGCD-and-boost. We use these methods to find primes for the NIST submission of SQIsign. Furthermore, we show that our methods are flexible and can be adapted to find suitable parameters for other isogeny-based schemes such as AprèsSQI or POKE. For all three schemes, the parameters we present offer the best performance among all parameters proposed in the literature.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published by the IACR in CIC 2024
DOI: https://doi.org/10.62056/ayojbhey6b
Keywords: Post-quantum cryptography isogenies parameter search SQIsign AprèsSQI POKE
Contact author(s): maria santos 20 @ ucl ac uk
jonathan k eriksen @ ntnu no
michael @ random-oracles org
francisco rodriguez @ tii ae
History: 2024-11-22: revised; 2024-07-15: received; See all versions
Short URL: https://ia.cr/2024/1150
License: CC BY

BibTeX

@misc{cryptoeprint:2024/1150,
      author = {Maria Corte-Real Santos and Jonathan Komada Eriksen and Michael Meyer and Francisco Rodríguez-Henríquez},
      title = {Finding Practical Parameters for Isogeny-based Cryptography},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1150},
      year = {2024},
      doi = {https://doi.org/10.62056/ayojbhey6b},
      url = {https://eprint.iacr.org/2024/1150}
}