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New observation on the key schedule of RECTANGLE

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Abstract

We evaluate the security of RECTANGLE from the perspective of actual key information (AKI). Insufficient AKI permits the attackers to deduce some subkey bits from some other subkey bits, thereby lowering the overall attack complexity or getting more attacked rounds. By considering the interaction between the key schedule’s diffusion and the round function’s diffusion, we find there exists AKI insufficiency in 4 consecutive rounds for RECTANGLE-80 and 6 consecutive rounds for RECTANGLE-128, although the master key bits achieve complete diffusion in 2 and 4 rounds, respectively. With such weakness of the key schedule, we give a generic meet-in-the-middle attack on 12-round reduced RECTANGLE-128 with only 8 known plaintexts. Moreover, we calculate AKI of variants of RECTANGLE as well as PRESENT. Surprisingly we find that both RECTANGLE-128 and PRESENT-128 with no key schedule involve more AKI than the original one. Based on this finding, we slightly modify the key schedule of RECTANGLE-128. Compared with the original one, this new key schedule matches better with the round function in terms of maximizing AKI. Our work adds more insight to the design of block ciphers’ key schedule.

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References

  1. Bogdanov A, Knudsen L R, Leander G, et al. PRESENT: an ultra-lightweight block cipher. In: Proceedings of International Workshop on Cryptographic Hardware and Embedded Systems. Berlin: Springer, 2007. 450–466

    Google Scholar 

  2. Guo J, Peyrin T, Poschmann A. The LED block cipher. In: Proceedings of Cryptographic Hardware and Embedded Systems-CHES 2011, 2011

    Book  MATH  Google Scholar 

  3. Banik S, Bogdanov A, Isobe T, et al. Midori: a block cipher for low energy. In: Proceedings of International Conference on the Theory and Application of Cryptology and Information Security. Berlin: Springer, 2014. 411–436

    Google Scholar 

  4. Beierle C, Jean J, Kölbl S, et al. The SKINNY family of block ciphers and its low-latency variant MANTIS. In: Proceedings of Annual Cryptology Conference. Berlin: Springer, 2016. 123–153

    Google Scholar 

  5. Avanzi R. The QARMA block cipher family. IACR Trans Symmetric Cryptol, 2017, 2017: 4–44

    Google Scholar 

  6. Banik S, Pandey S K, Peyrin T, et al. GIFT: a small PRESENT. In: Proceedings of International Conference on Cryptographic Hardware and Embedded Systems. Berlin: Springer, 2017. 321–345

    Google Scholar 

  7. Beaulieu R, Treatman-Clark S, Shors D, et al. The SIMON and SPECK lightweight block ciphers. In: Proceedings of the 52nd ACM/EDAC/IEEE Design Automation Conference (DAC), 2015. 1–6

    Google Scholar 

  8. Wu W, Zhang L. LBlock: a lightweight block cipher. In: Proceedings of International Conference on Applied Cryptography and Network Security. Berlin: Springer, 2011. 327–344

    Chapter  Google Scholar 

  9. Suzaki T, Minematsu K, Morioka S, et al. TWINE: a lightweight block cipher for multiple platforms. In: Proceedings of International Conference on Selected Areas in Cryptography. Berlin: Springer, 2012. 339–354

    Google Scholar 

  10. Hong D, Sung J, Hong S, et al. HIGHT: a new block cipher suitable for low-resource device. In: Proceedings of International Workshop on Cryptographic Hardware and Embedded Systems. Berlin: Springer, 2006. 46–59

    Google Scholar 

  11. Needham R M, Wheeler D J. Tea Extensions. Technical Report. Cambridge: Cambridge University, 1997

    Google Scholar 

  12. Knudsen L, Leander G, Poschmann A, et al. PRINTcipher: a block cipher for IC-printing. In: Proceedings of International Workshop on Cryptographic Hardware and Embedded Systems. Berlin: Springer, 2010. 16–32

    Google Scholar 

  13. Diffie W, Hellman M E. Special feature exhaustive cryptanalysis of the NBS data encryption standard. Computer, 1977, 10: 74–84

    Article  Google Scholar 

  14. Huang J, Lai X. Revisiting key schedule’s diffusion in relation with round function’s diffusion. Des Codes Cryptogr, 2014, 73: 85–103

    Article  MathSciNet  MATH  Google Scholar 

  15. Huang J, Vaudenay S, Lai X. On the key schedule of lightweight block ciphers. In: Proceedings of International Conference in Cryptology in India. Berlin: Springer, 2014. 124–142

    Google Scholar 

  16. Lin L, Wu W, Zheng Y. Automatic search for key-bridging technique: applications to LBlock and TWINE. In: Proceedings of International Conference on Fast Software Encryption. Berlin: Springer, 2016. 247–267

    Chapter  Google Scholar 

  17. Dunkelman O, Keller N, Shamir A. Improved single-key attacks on 8-round AES-192 and AES-256. In: Proceedings of International Conference on the Theory and Application of Cryptology and Information Security. Berlin: Springer, 2010. 158–176

    Google Scholar 

  18. Zhang W T, Bao Z Z, Lin D D, et al. RECTANGLE: a bit-slice lightweight block cipher suitable for multiple platforms. Sci China Inf Sci, 2015, 58: 1–15

    Google Scholar 

  19. Biham E, Shamir A. Differential cryptanalysis of DES-like cryptosystems. J Cryptology, 1991, 4: 3–72

    Article  MathSciNet  MATH  Google Scholar 

  20. Biham E, Biryukov A, Shamir A. Cryptanalysis of Skipjack reduced to 31 rounds using impossible differentials. In: Proceedings of International Conference on the Theory and Applications of Cryptographic Techniques. Berlin: Springer, 1999. 12–23

    Google Scholar 

  21. Matsui M. Linear cryptanalysis method for DES cipher. In: Proceedings of Workshop on the Theory and Application of of Cryptographic Techniques. Berlin: Springer, 1993. 386–397

    Google Scholar 

  22. Daemen J, Knudsen L, Rijmen V. The block cipher Square. In: Proceedings of International Workshop on Fast Software Encryption. Berlin: Springer, 1997. 149–165

    Chapter  Google Scholar 

  23. Knudsen L,Wagner D. Integral cryptanalysis. In: Proceedings of International Workshop on Fast Software Encryption. Berlin: Springer, 2002. 112–127

    Chapter  Google Scholar 

  24. Collard B, Standaert F X. A statistical saturation attack against the block cipher PRESENT. In: Proceedings of Cryptographers’ Track at the RSA Conference. Berlin: Springer, 2009. 195–210

    Google Scholar 

  25. Shan J Y, Hu L, Song L, et al. Related-key differential attack on 19-round reduced RECTANGLE-80 (in Chinese). J Cryptologic Reseatch, 2015, 2: 54–65

    Google Scholar 

  26. Kosuge H, Tanaka H, Iwai K, et al. Integral attack on reduced-round Rectangle. In: Proceedings of IEEE 2nd International Conference on Cyber Security and Cloud Computing (CSCloud), 2015. 68–73

    Google Scholar 

  27. Sun L, Wang M Q. Toward a further understanding of bit-based division property. Sci China Inf Sci, 2017, 60: 128101

    Article  MathSciNet  Google Scholar 

  28. Xiang Z, Zhang W, Bao Z, et al. Applying MILP method to searching integral distinguishers based on division property for 6 lightweight block ciphers. In: Proceedings of International Conference on the Theory and Application of Cryptology and Information Security. Berlin: Springer, 2016. 648–678

    Google Scholar 

  29. Sasaki Y, Todo Y. New impossible differential search tool from design and cryptanalysis aspects. In: Proceedings of Annual International Conference on the Theory and Applications of Cryptographic Techniques. Berlin: Springer, 2017. 185–215

    Google Scholar 

  30. Zhang W, Bao Z, Rijmen V, et al. A new classification of 4-bit optimal s-boxes and its application to PRESENT, RECTANGLE and SPONGENT. In: Proceedings of International Workshop on Fast Software Encryption. Berlin: Springer, 2015. 494–515

    Chapter  Google Scholar 

  31. Stoffelen K. Optimizing s-box implementations for several criteria using SAT solvers. In: Proceedings of International Conference on Fast Software Encryption. Berlin: Springer, 2016. 140–160

    Chapter  Google Scholar 

  32. Bao Z, Luo P, Lin D. Bitsliced implementations of the PRINCE, LED and RECTANGLE block ciphers on AVR 8-bit microcontrollers. In: Proceedings of International Conference on Information and Communications Security. Berlin: Springer, 2015. 18–36

    Google Scholar 

  33. Maene P, Verbauwhede I. Single-cycle implementations of block ciphers. In: Proceedings of International Workshop on Lightweight Cryptography for Security and Privacy. Berlin: Springer, 2015. 131–147

    Google Scholar 

  34. Feizi S, Nemati A, Ahmadi A, et al. A high-speed FPGA implementation of a Bit-slice Ultra-Lightweight block cipher, RECTANGLE. In: Proceedings of the 5th International Conference on Computer and Knowledge Engineering (ICCKE), 2015. 206–211

    Google Scholar 

  35. Biryukov A, Derbez P, Perrin L. Differential analysis and meet-in-the-middle attack against round-reduced TWINE. In: Proceedings of International Workshop on Fast Software Encryption. Berlin: Springer, 2015. 3–27

    Chapter  Google Scholar 

  36. Bouillaguet C, Derbez P, Fouque P A. Automatic search of attacks on round-reduced AES and applications. In: Proceedings of Annual Cryptology Conference. Berlin: Springer, 2011. 169–187

    Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61702331, 61472251, 61402280, U1536101), China Postdoctoral Science Foundation (Grant No. 2017M621471), National Cryptography Development Fund (Grant No. MMJJ20170105), and Science and Technology on Communication Security Laboratory.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Hailun Yan, Mo Chen & Xuejia Lai

  2. School of Electronics and Information, Shanghai Dianji University, Shanghai, 201306, China

    Yiyuan Luo

  3. Westone Cryptologic Research Center, Beijing, 100070, China

    Xuejia Lai

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  1. Hailun Yan
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  2. Yiyuan Luo
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  3. Mo Chen
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  4. Xuejia Lai
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Correspondence to Xuejia Lai.

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Yan, H., Luo, Y., Chen, M. et al. New observation on the key schedule of RECTANGLE. Sci. China Inf. Sci. 62, 32108 (2019). https://doi.org/10.1007/s11432-018-9527-8

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  • DOI: https://doi.org/10.1007/s11432-018-9527-8

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