On a Generalization of Substitution-Permutation Networks: The HADES Design Strategy

Lorenzo Grassi*, Reinhard Lüftenegger, Christian Rechberger, Dragos Rotaru, Markus Schofnegger

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


Keyed and unkeyed cryptographic permutations often iterate simple round functions. Substitution-permutation networks (SPNs) are an approach that is popular since the mid 1990s. One of the new directions in the design of these round functions is to reduce the substitution (S-Box) layer from a full one to a partial one, uniformly distributed over all the rounds. LowMC and Zorro are examples of this approach.

A relevant freedom in the design space is to allow for a highly non-uniform distribution of S-Boxes. However, choosing rounds that are so different from each other is very rarely done, as it makes security analysis and implementation much harder.

We develop the design strategy Hades and an analysis framework for it, which despite this increased complexity allows for security arguments against many classes of attacks, similar to earlier simpler SPNs. The framework builds upon the wide trail design strategy, and it additionally allows for security arguments against algebraic attacks, which are much more of a concern when algebraically simple S-Boxes are used.

Subsequently, this is put into practice by concrete instances and benchmarks for a use case that generally benefits from a smaller number of S-Boxes and showcases the diversity of design options we support: A candidate cipher natively working with objects in GF(p), for securing data transfers with distributed databases using secure multiparty computation (MPC). Compared to the currently fastest design MiMC, we observe significant improvements in online bandwidth requirements and throughput with a simultaneous reduction of preprocessing effort, while having a comparable online latency.
Original languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
Subtitle of host publicationLecture Notes in Computer Science
EditorsAnne Canteaut, Yuval Ishai
PublisherSpringer, Cham
Number of pages31
ISBN (Electronic)978-3-030-45724-2
ISBN (Print)978-3-030-45723-5
Publication statusPublished - 1 May 2020
EventEurocrypt 2020 -
Duration: 11 May 202015 May 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12106 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceEurocrypt 2020
Internet address


  • Hades strategy
  • Cryptographic permutations
  • Secure Multiparty Computation (MPC)

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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