Paper 2021/267

Ciminion: Symmetric Encryption Based on Toffoli-Gates over Large Finite Fields

Christoph Dobraunig, Lorenzo Grassi, Anna Guinet, and Daniël Kuijsters

Abstract

Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), the need for symmetric encryption schemes that minimize the number of field multiplications in their natural algorithmic description is apparent. This development has brought forward many dedicated symmetric encryption schemes that minimize the number of multiplications in GF(2^n) or GF(p), with p being prime. These novel schemes have lead to new cryptanalytic insights that have broken many of said schemes. Interestingly, to the best of our knowledge, all of the newly proposed schemes that minimize the number of multiplications use those multiplications exclusively in S-boxes based on a power mapping that is typically x^3 or x^{-1}. Furthermore, most of those schemes rely on complex and resource-intensive linear layers to achieve a low multiplication count. In this paper, we present Ciminion, an encryption scheme minimizing the number of field multiplications in large binary or prime fields, while using a very lightweight linear layer. In contrast to other schemes that aim to minimize field multiplications in GF(2^n) or GF(p), Ciminion relies on the Toffoli gate to improve the non-linear diffusion of the overall design. In addition, we have tailored the primitive for the use in a Farfalle-like construction in order to minimize the number of rounds of the used primitive, and hence, the number of field multiplications as far as possible.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
A major revision of an IACR publication in EUROCRYPT 2021
Keywords
Symmetric EncryptionLow Multiplicative Complexity
Contact author(s)
christoph dobraunig @ lamarr at
lgrassi @ science ru nl
email @ annagui net
Daniel Kuijsters @ ru nl
History
2021-03-03: received
Short URL
https://ia.cr/2021/267
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2021/267,
      author = {Christoph Dobraunig and Lorenzo Grassi and Anna Guinet and Daniël Kuijsters},
      title = {Ciminion: Symmetric Encryption Based on Toffoli-Gates over Large Finite Fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/267},
      year = {2021},
      url = {https://eprint.iacr.org/2021/267}
}
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