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How to Build Fully Secure Tweakable Blockciphers from Classical Blockciphers

  • Lei Wang
  • Jian Guo
  • Guoyan Zhang
  • Jingyuan Zhao
  • Dawu Gu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10031)

Abstract

This paper focuses on building a tweakable blockcipher from a classical blockcipher whose input and output wires all have a size of n bits. The main goal is to achieve full \(2^n\) security. Such a tweakable blockcipher was proposed by Mennink at FSE’15, and it is also the only tweakable blockcipher so far that claimed full \(2^n\) security to our best knowledge. However, we find a key-recovery attack on Mennink’s proposal (in the proceeding version) with a complexity of about \(2^{n/2}\) adversarial queries. The attack well demonstrates that Mennink’s proposal has at most \(2^{n/2}\) security, and therefore invalidates its security claim. In this paper, we study a construction of tweakable blockciphers denoted as \(\widetilde{\mathbb {E}}[s]\) that is built on s invocations of a blockcipher and additional simple XOR operations. As proven in previous work, at least two invocations of blockcipher with linear mixing are necessary to possibly bypass the birthday-bound barrier of \(2^{n/2}\) security, we carry out an investigation on the instances of \(\widetilde{\mathbb {E}}[s]\) with \(s \ge 2\), and find 32 highly efficient tweakable blockciphers \(\widetilde{E1}\), \(\widetilde{E2}\), \(\ldots \), \(\widetilde{E32}\) that achieve \(2^n\) provable security. Each of these tweakable blockciphers uses two invocations of a blockcipher, one of which uses a tweak-dependent key generated by XORing the tweak to the key (or to a secret subkey derived from the key). We point out the provable security of these tweakable blockciphers is obtained in the ideal blockcipher model due to the usage of the tweak-dependent key.

Keywords

Tweakable blockcipher Full security Ideal blockcipher Tweak-dependent key 

Notes

Acknowledgements

Lei Wang and Dawu Gu are sponsored by the Natural Science Foundation of Shanghai (16ZR1416400), Major State Basic Research Development Program (973 Plan), the National Natural Science Foundation of China (61472250), and Innovation Plan of Science and Technology of Shanghai (14511100300). Guoyan Zhang is sponsored by National Natural Science Foundation of China (61602276). Jingyuan Zhao is sponsored by the National Science Foundation of China (no. 61379139) and the Strategic Priority Research Program of the Chinese Academy of Sciences (no. XDA06100701).

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Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  • Lei Wang
    • 1
    • 4
  • Jian Guo
    • 2
  • Guoyan Zhang
    • 3
  • Jingyuan Zhao
    • 4
  • Dawu Gu
    • 1
  1. 1.Department of Computer Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Nanyang Technological UniversitySingaporeSingapore
  3. 3.School of Computer Science and TechnologyShandong UniversityJinanChina
  4. 4.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina

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