Incorporating SIS Problem into Luby-Rackoff Cipher

Yu Morishima; Masahiro Kaminaga

Paper 2024/763

Incorporating SIS Problem into Luby-Rackoff Cipher

Yu Morishima

, Tohoku Gakuin University

Masahiro Kaminaga, Tohoku Gakuin University

Abstract

With the rise of quantum computing, the security of traditional cryptographic systems, especially those vulnerable to quantum attacks, is under threat. While public key cryptography has been widely studied in post-quantum security, symmetric-key cryptography has received less attention. This paper explores using the Ajtai-Micciancio hash function, based on the Short Integer Solution (SIS) problem, as a pseudorandom function in the Luby-Rackoff cipher. Since lattice-based problems like SIS are believed to resist quantum algorithms, this approach provides the potential for a quantum-resistant block cipher. We also propose a novel statistical method based on the Generalized Extreme Value distribution to evaluate the number of secure rounds and resistance to differential cryptanalysis.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint.
Keywords: Luby-Rackoff cipher Short integer solution problem Differential cryptanalysis
Contact author(s): morishima @ mail tohoku-gakuin ac jp
History: 2024-10-26: revised; 2024-05-19: received; See all versions
Short URL: https://ia.cr/2024/763
License: CC BY

BibTeX

@misc{cryptoeprint:2024/763,
      author = {Yu Morishima and Masahiro Kaminaga},
      title = {Incorporating {SIS} Problem into Luby-Rackoff Cipher},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/763},
      year = {2024},
      url = {https://eprint.iacr.org/2024/763}
}