## Cryptology ePrint Archive: Report 2012/450

Tweakable Blockciphers with Beyond Birthday-Bound Security

Will Landecker and Thomas Shrimpton and R. Seth Terashima

Abstract: Liskov, Rivest and Wagner formalized the tweakable blockcipher (TBC) primitive at CRYPTO'02. The typical recipe for instantiating a TBC is to start with a blockcipher, and then build up a construction that admits a tweak. Almost all such constructions enjoy provable security only to the birthday bound, and the one that does achieve security beyond the birthday bound (due to Minematsu) severely restricts the tweak size and requires per-invocation blockcipher rekeying.

This paper gives the first TBC construction that simultaneously allows for arbitrarily “wide” tweaks, does not rekey, and delivers provable security beyond the birthday bound. Our construction is built from a blockcipher and an $\eAXU$ hash function.

As an application of the TBC primitive, LRW suggest the TBC-MAC construction (similar to CBC-MAC but chaining through the tweak), but leave open the question of its security. We close this question, both for TBC-MAC as a PRF and a MAC. Along the way, we find a nonce-based variant of TBC-MAC that has a tight reduction to the security of the underlying TBC, and also displays graceful security degradation when nonces are misused. This result is interesting on its own, but it also serves as an application of our new TBC construction, ultimately giving a variable input-length PRF with beyond birthday-bound security.

Category / Keywords: secret-key cryptography / tweakable blockcipher, beyond birthday bound, pseudorandom function, message authentication code, unforgeability

Publication Info: The conference version of this paper will appear in CRYPTO 2012. This is the full version.

Date: received 6 Aug 2012, last revised 8 Aug 2012

Contact author: seth at cs pdx edu

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2012/450

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