Simon’s Algorithm and Symmetric Crypto: Generalizations and Automatized Applications

Federico Canale; Gregor Leander; Lukas Stennes

Paper 2022/782

Simon’s Algorithm and Symmetric Crypto: Generalizations and Automatized Applications

Federico Canale, Ruhr University Bochum

Gregor Leander

, Ruhr University Bochum

Lukas Stennes, Ruhr University Bochum

Abstract

In this paper we deepen our understanding of how to apply Simon’s algorithm to break symmetric cryptographic primitives. On the one hand, we automate the search for new attacks. Using this approach we automatically find the first efficient key-recovery attacks against constructions like 5-round MISTY L-FK or 5-round Feistel-FK (with internal permutation) using Simon’s algorithm. On the other hand, we study generalizations of Simon’s algorithm using non-standard Hadamard matrices, with the aim to expand the quantum symmetric cryptanalysis toolkit with properties other than the periods. Our main conclusion here is that none of these generalizations can ac- complish that, and we conclude that exploiting non-standard Hadamard matrices with quantum computers to break symmetric primitives will require fundamentally new attacks.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint.
Keywords: Symmetric Cryptanalysis Simon’s algorithm Bernstein-Vazirani algorithm Fourier transform automatic search
Contact author(s): federico canale @ rub de
gregor leander @ rub de
lukas stennes @ rub de
History: 2022-06-20: approved; 2022-06-17: received; See all versions
Short URL: https://ia.cr/2022/782
License: CC BY

BibTeX

@misc{cryptoeprint:2022/782,
      author = {Federico Canale and Gregor Leander and Lukas Stennes},
      title = {Simon’s Algorithm and Symmetric Crypto: Generalizations and Automatized Applications},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/782},
      year = {2022},
      url = {https://eprint.iacr.org/2022/782}
}