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Designs, Codes and Cryptography

, Volume 87, Issue 6, pp 1271–1296 | Cite as

MILP-aided cube-attack-like cryptanalysis on Keccak Keyed modes

  • Wenquan Bi
  • Xiaoyang DongEmail author
  • Zheng Li
  • Rui Zong
  • Xiaoyun WangEmail author
Article

Abstract

Cube-attack-like cryptanalysis was proposed by Dinur et al. at EUROCRYPT 2015, which recovers the key of Keccak keyed modes in a divide-and-conquer manner. In their attack, one selects cube variables manually, which leads to more key bits involved in the key-recovery attack, so the complexity is too high unnecessarily. In this paper, we introduce a new MILP model and make the cube attacks better on the Keccak keyed modes. Using this new MILP tool, we find the optimal cube variables for Keccak-MAC, Keyak and Ketje, which makes that a minimum number of key bits are involved in the key-recovery attack. For example, when the capacity is 256, we find a new 32-dimension cube for Keccak-MAC that involves only 18 key bits instead of Dinur et al.’s 64 bits and the complexity of the 6-round attack is reduced to \(2^{42}\) from \(2^{66}\). More impressively, using this new tool, we give the very first 7-round key-recovery attack on Keccak-MAC-512. We get the 8-round key-recovery attacks on Lake Keyak in nonce-respected setting. In addition, we get the best attacks on Ketje Major/Minor. For Ketje Major, when the length of nonce is 9 lanes, we could improve the best previous 6-round attack to 7-round. Our attacks do not threaten the full-round (12) Keyak/Ketje or the full-round (24) Keccak-MAC. When comparing with Huang et al.’s conditional cube attack, the MILP-aided cube-attack-like cryptanalysis has larger effective range and gets the best results on the Keccak keyed variants with relatively smaller number of degrees of freedom.

Keywords

Keccak-MAC Keyak Ketje MILP Cube attack 

Mathematics Subject Classification

94A60 

Notes

Acknowledgements

This work is supported by National Key Research and Development Program of China (No. 2017YFA0303903), National Cryptography Development Fund (Nos. MMJJ20180101, MMJJ20170121), National Natural Science Foundation of China (No. 61672019).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Cryptologic Technology and Information Security, Ministry of EducationShandong UniversityJinanChina
  2. 2.Institute for Advanced StudyTsinghua UniversityBeijingChina

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