Security research with Square attack to a variant Camellia cipher

Abstract

This paper investigates the relation between the choice of S-boxes and Square attack. A variant Camellia, which uses only a single S-box instead of four, is proposed. The security of the variant Camellia against Square attack is studied in detail. Result shows that it needs only 28 chosen plaintexts to recover a byte of the 6th round-key of variant Camellias, while the original Camellia needs either 28 chosen plaintexts to recover a byte of the 6th round-key and a byte of some constant or 216 chosen plaintexts to recover a byte of the 6th round-key. Furthermore, Square attacks on other round-reduced variant Camellia are proposed, and the time complexity of 11-round attack is reduced from 2²⁵⁰ to 2^225.5. The weaker variant Camellia indicates that the choice of S-box and the order of different S-boxes have influence on Square attack.

Keywords

block cipher / Camellia / Square attack

References

[1] Daemen J, Knudsen L R, Rijmen V. The block cipher Square. In: Proceedings of the 4th International Workshop on Fast Software Encryption. Lecture Notes in Computer Science, 1997, 1267: 149–165

[2] Lucks S. The saturation attack—a bait for Twofish. In: Proceedings of the 8th International Workshop on Fast Software Encryption. Lecture Notes in Computer Science, 2002, 2355: 1–15

[3] Biryukov A, Shamir A. Structural cryptanalysis of SASAS. In: Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology. Lecture Notes in Computer Science, 2001, 2045: 395–405

[4] Knudsen L R, Wagner D. Integral cryptanalysis. In: Proceedings of the 9th International Workshop on Fast Software Encryption. Lecture Notes in Computer Science, 2002, 2365: 112–127

[5] Reza Z’aba M, Raddum H, Henricksen M, Dawson E. Bit-pattern based integral attack. In: Proceedings of the 15th International Workshop on Fast Software Encryption. Lecture Notes in Computer Science, 2008, 5086: 363–381

[6] Aoki K, Ichikawa T, Kanda M, Matsui M, Moriai S, Nakajima J, Tokita T. Camellia: a 128-bit block cipher suitable for multiple platforms—design and analysis. In: Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography. Lecture Notes in Computer Science, 2001, 2012: 39–56

[7] Kanda M, Matsumoto T. Security of Camellia against truncated differential cryptanalysis. In: Proceedings of the 8th International Workshop on Fast Software Encryption. Lecture Notes in Computer Science, 2002, 2355: 286–299

[8] Hatano Y, Sekine H, Kaneko T. Higher order differential attack of Camellia (II). In: Proceedings of the 9th Annual International Workshop on Selected Areas in Cryptography, Lecture Notes in Computer Science, 2003, 2595: 129–146

[9] He Y P, Qing S H. Square attack on reduced Camellia cipher. In: Proceedings of the 3rd International Conference on Information and Communications Security. Lecture Notes in Computer Science, 2001, 2229: 238–245

[10] Yeom Y, Park S, Kim I. On the security of Camellia against the Square attack. In: Proceedings of the 9th International Workshop on Fast Software Encryption. Lecture Notes in Computer Science, 2002, 2365: 89–99

[11] Lei D, Chao L, Feng K Q. New observation on Camellia. In: Proceedings of the 12th International Workshop on Selected Areas in Cryptography. Lecture Notes in Computer Science, 2006, 3897: 51–64

[12] Wu W L, Feng D G. Collision attack on reduced-round Camellia. Science in China, Series F: Information Sciences, 2005, 48(1): 78–90

[13] Wu W L, Zhang W T, Feng D G. Impossible differential cryptanalysis of reduced-round ARIA and Camellia. Journal of Compute Science and Technology, 2007, 22(3): 449–456

[14] Lu J Q, Kim J, Keller N, Dunkelman O. Improving the efficiency of impossible differential cryptanalysis of reduced Camellia and MISTY1. In: Proceedings of the Cryptopgraphers’ Track at the RSA conference on Topics in cryptology. Lecture Notes in Computer Science, 2008, 4964: 370–386

[15] Kwon D, Kim J, Park S, Sung S H, Sohn Y, Song J H, Yeom Y, Yoon E-J, Lee S, Lee J, Chee S, Han D, Hong J. New block cipher: ARIA. In: Proceedings of the 6th International Conference on Information Security and Cryptology. Lecture Notes in Computer Science, 2004, 2971: 432–445

[16] Li P, Sun B, Li C. Integral cryptanalysis of ARIA. In: Proceedings of Information Security and Cryptology—Inscrypt2009

Acknowledgements

This work was supported by the Planned Science and Technology Project of Hunan Province of China (Grant No. 2010GK3063 ) and A Project Supported by Scientific Research Fund of Hunan Provincial Education Department.

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg