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Tweak-Length Extension for Tweakable Blockciphers

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Cryptography and Coding (IMACC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9496))

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Abstract

Tweakable blockcipher (TBC) is an extension of standard blockcipher introduced by Liskov, Rivest and Wagner in 2002. TBC is a versatile building block for efficient symmetric-key cryptographic functions, such as authenticated encryption.

In this paper we study the problem of extending tweak of a given TBC of fixed-length tweak, which is a variant of popular problem of converting a blockcipher into a TBC, i.e., blockcipher mode of operation. The problem is particularly important for known dedicated TBCs since they have relatively short tweak. We propose a simple and efficient solution, called \(\text {XTX}\), for this problem. \(\text {XTX}\) converts a TBC of fixed-length tweak into another TBC of arbitrarily long tweak, by extending the scheme of Liskov, Rivest and Wagner that converts a blockcipher into a TBC. Given a TBC of n-bit block and m-bit tweak, \(\text {XTX}\) provides \((n+m){/}2\)-bit security while conventional methods provide n / 2 or m / 2-bit security. We also show that \(\text {XTX}\) is even useful when combined with some blockcipher modes for building TBC having security beyond the birthday bound.

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Notes

  1. 1.

    The two schemes shown by [17] are also called LRW1 and LRW2, and we refer to LRW2 throughout this paper.

  2. 2.

    Originally proved by [17] with a slightly larger constant, then improved by [22].

  3. 3.

    In some special cases the result obtained by the method of [18] cannot be converted into computational counterparts [19, 25]. However the proof presented here does not have such difficulty. A bug in a theorem of [18] was pointed out by Jetchev, Özen and Stam [14], however we did not use it.

  4. 4.

    The name CLRW2 means it is a chain of the second construction of [17], which we simply call LRW.

  5. 5.

    Originally the constant was 6, however an error in the proof was pointed out by Procter [26]. He fixed the proof with an increased constant, 8.

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Acknowledgments

The authors would like to thank the anonymous reviewers for highly constructive and insightful comments. The work by Tetsu Iwata was supported in part by JSPS KAKENHI, Grant-in-Aid for Scientific Research (B), Grant Number 26280045.

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Authors and Affiliations

  1. NEC Corporation, Kawasaki, Japan

    Kazuhiko Minematsu

  2. Nagoya University, Nagoya, Japan

    Tetsu Iwata

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  1. Kazuhiko Minematsu
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  2. Tetsu Iwata
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Correspondence to Kazuhiko Minematsu .

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  1. University College London, Cambridge, United Kingdom

    Jens Groth

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Minematsu, K., Iwata, T. (2015). Tweak-Length Extension for Tweakable Blockciphers. In: Groth, J. (eds) Cryptography and Coding. IMACC 2015. Lecture Notes in Computer Science(), vol 9496. Springer, Cham. https://doi.org/10.1007/978-3-319-27239-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-27239-9_5

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