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2018 | OriginalPaper | Buchkapitel

Rasta: A Cipher with Low ANDdepth and Few ANDs per Bit

verfasst von : Christoph Dobraunig, Maria Eichlseder, Lorenzo Grassi, Virginie Lallemand, Gregor Leander, Eik List, Florian Mendel, Christian Rechberger

Erschienen in: Advances in Cryptology – CRYPTO 2018

Verlag: Springer International Publishing

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Abstract

Recent developments in multi party computation (MPC) and fully homomorphic encryption (FHE) promoted the design and analysis of symmetric cryptographic schemes that minimize multiplications in one way or another. In this paper, we propose with Rastaa design strategy for symmetric encryption that has ANDdepth d and at the same time only needs d ANDs per encrypted bit. Even for very low values of d between 2 and 6 we can give strong evidence that attacks may not exist. This contributes to a better understanding of the limits of what concrete symmetric-key constructions can theoretically achieve with respect to AND-related metrics, and is to the best of our knowledge the first attempt that minimizes both metrics simultaneously. Furthermore, we can give evidence that for choices of d between 4 and 6 the resulting implementation properties may well be competitive by testing our construction in the use-case of removing the large ciphertext-expansion when using the BGV scheme.

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Note here that an attacker could rename the variables obtained after the linear layer, making the number of quadratic terms drops to only k. However, this renaming would only be valid for one message, while many messages are necessary to solve the system, which makes this process unlikely to have any impact.

We do not extend this analysis to linear hulls as even for more suitable designs doing this analytically is beyond the state of the art.

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Titel: Rasta: A Cipher with Low ANDdepth and Few ANDs per Bit
verfasst von: Christoph Dobraunig
Maria Eichlseder
Lorenzo Grassi
Virginie Lallemand
Gregor Leander
Eik List
Florian Mendel
Christian Rechberger
Verlag: Springer International Publishing
Buch: Advances in Cryptology – CRYPTO 2018
Print ISBN: 978-3-319-96883-4

Electronic ISBN: 978-3-319-96884-1

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-96884-1_22

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