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A New General Method of Searching for Cubes in Cube Attacks

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Information and Communications Security (ICICS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12282))

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Abstract

Cube attack, proposed by Dinur and Shamir at EUROCRYPT 2009, is one of general and powerful cryptanalytic techniques against symmetric-key cryptosystems. However, it is quite time consuming to search for large cubes using the existing techniques, e.g., random walk, and practically infeasible to execute the cube attack when the size of cube exceeds an experimental range, e.g., 50. Thus, how to find favorite cubes is still an intractable problem. In this paper, a new general method of searching for cubes in cube attacks, called iterative walk, is proposed. Iterative walk takes the technique numeric mapping proposed at CRYPTO 2017 as a tool, which is used to test cubes and find out the best cubes among them. This new method consists of two concrete techniques, called incremental iterative walk and decremental iterative walk, respectively. Both of them split the process of searching for cubes with large size into several iterative processes, each of which aims at searching for a ‘best’ set of input variables with small size. After each iterative process, the input variables in the obtained ‘best’ set are added to (or dropped from) the cube in incremental (or decremental) iterative walk. As illustrations, we apply it to the authenticated encryption cipher ACORN v3, which was selected as one of seven finalists of CAESAR competition. Some new distinguishing attacks on round reduced variants of ACORN v3 are obtained.

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Notes

  1. 1.

    Only 670 initialization rounds of ACORN v3 was attacked when it was formally published in [28].

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China under Grant 61602514, 61802437, 61272488, 61202491, 61572516, 61272041, 61772547, National Cryptography Development Fund under Grant MMJJ20170125 and National Postdoctoral Program for Innovative Talents under Grant BX201700153.

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Authors and Affiliations

  1. PLA SSF Information Engineering University, Zhengzhou, 450001, China

    Lin Ding, Chenhui Jin & Jie Guan

  2. Shanghai Jiao Tong University, Shanghai, 200240, China

    Lin Ding, Lei Wang & Dawu Gu

  3. Westone Cryptologic Research Center, Beijing, 100000, China

    Lei Wang

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  1. Lin Ding
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  2. Lei Wang
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  3. Dawu Gu
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  4. Chenhui Jin
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  5. Jie Guan
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Correspondence to Lin Ding .

Editor information

Editors and Affiliations

  1. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

  2. Hamburg University of Technology, Hamburg, Germany

    Dieter Gollmann

  3. Technical University of Denmark, Kongens Lyngby, Denmark

    Christian D. Jensen

  4. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

Appendix A

Appendix A

figure e

(See Table 5)

Table 5. The cubes used in Table 4
Full size table

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Ding, L., Wang, L., Gu, D., Jin, C., Guan, J. (2020). A New General Method of Searching for Cubes in Cube Attacks. In: Meng, W., Gollmann, D., Jensen, C.D., Zhou, J. (eds) Information and Communications Security. ICICS 2020. Lecture Notes in Computer Science(), vol 12282. Springer, Cham. https://doi.org/10.1007/978-3-030-61078-4_21

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  • DOI: https://doi.org/10.1007/978-3-030-61078-4_21

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