Paper 2024/763

On SIS-problem-based random Feistel ciphers and its statistical evaluation of resistance against differential cryptanalysis

Yu Morishima, Tohoku Gakuin University
Masahiro Kaminaga, Tohoku Gakuin University
Abstract

Provable security based on a robust mathematical framework is the gold standard for security evaluation in cryptography. Several provable secure cryptosystems have been studied for public key cryptography. However, provably secure symmetric-key cryptography has received little attention. Although there are known provably secure symmetric-key cryptosystems based on the hardness of factorization and discrete logarithm problems, they are not only slower than conventional block ciphers but can also be broken by quantum computers. Our study aims to tackle this latter problem by proposing a new provably secure Feistel cipher using collision resistant hash functions based on a Short Integer Solution problem (SIS). Even if cipher primitives are resistant to quantum algorithms, it is crucial to determine whether the cipher is resilient to differential cryptanalysis, a fundamental and powerful attack against symmetric-key cryptosystems. In this paper, we demonstrate that the proposed cipher family is secure against differential cryptanalysis by deriving an upper bound on the maximum differential probability. In addition, we demonstrate the potential success of differential cryptanalysis for short block sizes and statistically evaluate the average resistance of cipher instances based on differential characteristic probabilities. This method approximates the S-box output using a folded two-dimensional normal distribution and employs a generalized extreme value distribution. This evaluation method is first introduced in this paper and serves as the basis for studying the differential characteristics of lattice matrices and the number of secure rounds. This study is foundational research on differential cryptanalysis against block ciphers using a lattice matrix based on SIS.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Preprint.
Keywords
Feistel ciphershort integer solution problemdifferential cryptanalysis
Contact author(s)
morishima @ mail tohoku-gakuin ac jp
History
2024-05-20: approved
2024-05-19: received
See all versions
Short URL
https://ia.cr/2024/763
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/763,
      author = {Yu Morishima and Masahiro Kaminaga},
      title = {On {SIS}-problem-based random Feistel ciphers and its statistical evaluation of resistance against differential cryptanalysis},
      howpublished = {Cryptology ePrint Archive, Paper 2024/763},
      year = {2024},
      note = {\url{https://eprint.iacr.org/2024/763}},
      url = {https://eprint.iacr.org/2024/763}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.