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Erschienen in:
Boosting Authenticated Encryption Robustness with Minimal Modifications Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Encrypted Davies-Meyer and Its Dual: Towards Optimal Security Using Mirror Theory

verfasst von : Bart Mennink, Samuel Neves

Erschienen in: Advances in Cryptology – CRYPTO 2017

Verlag: Springer International Publishing

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Abstract

At CRYPTO 2016, Cogliati and Seurin introduced the Encrypted Davies-Meyer construction, \(p_2(p_1(x) \oplus x)\) for two n-bit permutations \(p_1,p_2\), and proved security up to \(2^{2n/3}\). We present an improved security analysis up to \(2^n/(67n)\). Additionally, we introduce the dual of the Encrypted Davies-Meyer construction, \(p_2(p_1(x)) \oplus p_1(x)\), and prove even tighter security for this construction: \(2^n/67\). We finally demonstrate that the analysis neatly generalizes to prove almost optimal security of the Encrypted Wegman-Carter with Davies-Meyer MAC construction. Central to our analysis is a modernization of Patarin’s mirror theorem and an exposition of how it relates to fundamental cryptographic problems.

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Vorheriges Kapitel Indifferentiability of Iterated Even-Mansour Ciphers with Non-idealized Key-Schedules: Five Rounds Are Necessary and Sufficient
Nächstes Kapitel A Formal Treatment of Multi-key Channels
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Fußnoten
1
Another notable approach is data-dependent rekeying by Bellare et al. [7]: given a block cipher \(E_k\), data-dependent rekeying computes \(E_{E_k(x)}(x)\). However, this approach only achieves approximately \(2^{n/2}\) security, and it inherently requires rekeying of the block cipher which could be a costly operation in practice.
 
2
Generalizations to multiple unknowns are possible [40, 43], but are irrelevant for our work.
 
3
The issue does not appear for \(\mathrm {EDM}^{p_1,p_2}\) or \(\mathrm {EWCDM}^{h,p_1,p_2}\). It even does not appear for \(\mathrm {EDMD}^{p_1,p_2}\) as the inputs to the second permutation are always distinct.
 
4
Closer inspection of the proof reveals that \(2u\le 2^n/16\) suffices.
 
5
We remark that Patarin derived upper bound \(2^n/67\): he stated the claim on \(h'_{2u}(i,j)\) for unknown constants, subsequently derived the side condition, and only then derived the constants (and hence the 67). Knowing the constants in retrospect allows us to obtain a better bounding. In the end, the side condition in the theorem statement is the most dominant one (the one of the second claim).
 
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Metadaten
Titel
Encrypted Davies-Meyer and Its Dual: Towards Optimal Security Using Mirror Theory
verfasst von
Bart Mennink
Samuel Neves
Copyright-Jahr
2017
Buch
Advances in Cryptology – CRYPTO 2017

Print ISBN: 978-3-319-63696-2

Electronic ISBN: 978-3-319-63697-9

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-63697-9_19

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