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XPX: generalized tweakable Even-Mansour with improved security guarantees. (English) Zbl 1351.94058

Robshaw, Matthew (ed.) et al., Advances in cryptology – CRYPTO 2016. 36th annual international cryptology conference, Santa Barbara, CA, USA, August 14–18, 2016. Proceedings. Part I. Berlin: Springer (ISBN 978-3-662-53017-7/pbk; 978-3-662-53018-4/ebook). Lecture Notes in Computer Science 9814, 64-94 (2016).
Summary: We present \(\mathrm {XPX}\), a tweakable blockcipher based on a single permutation \(P\). On input of a tweak \((t_{11},t_{12},t_{21},t_{22})\in \mathcal {T}\) and a message \(m\), it outputs ciphertext \(c=P(m\oplus \varDelta_1)\oplus \varDelta_2\), where \(\varDelta_1=t_{11}k\oplus t_{12}P(k)\) and \(\varDelta_2=t_{21}k\oplus t_{22}P(k)\). Here, the tweak space \(\mathcal {T}\) is required to satisfy a certain set of trivial conditions (such as \((0,0,0,0)\not \in \mathcal {T}\)). We prove that \(\mathrm {XPX}\) with any such tweak space is a strong tweakable pseudorandom permutation. Next, we consider the security of \(\mathrm {XPX}\) under related-key attacks, where the adversary can freely select a key-deriving function upon every evaluation. We prove that \(\mathrm {XPX}\) achieves various levels of related-key security, depending on the set of key-deriving functions and the properties of \(\mathcal {T}\). For instance, if \(t_{12}, t_{22}\neq 0\) and \((t_{21}, t_{22})\neq (0,1)\) for all tweaks, \(\mathrm {XPX}\) is XOR-related-key secure. \(\mathrm {XPX}\) generalizes Even-Mansour (\(\mathrm {EM}\)), but also Rogaway’s \(\mathrm {XEX}\) based on \(\mathrm {EM}\), and various other tweakable blockciphers. As such, \(\mathrm {XPX}\) finds a wide range of applications. We show how our results on \(\mathrm {XPX}\) directly imply related-key security of the authenticated encryption schemes Prøst-\(\mathrm {COPA}\) and \(\mathrm {Minalpher}\), and how a straightforward adjustment to the MAC function \(\mathrm {Chaskey}\) and to keyed Sponges makes them provably related-key secure.
For the entire collection see [Zbl 1344.94001].

MSC:

94A60 Cryptography

Software:

ELmD; Minalpher
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References:

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