Abstract
The division property proposed at Eurocrypt’15 is a novel technique to find integral distinguishers, which has been applied to most kinds of symmetric ciphers such as block ciphers, stream ciphers, and authenticated encryption, etc. The original division property is word-oriented, and later the bit-based one was proposed at FSE’16 to get better integral property, which is composed of conventional bit-based division property (two-subset division property) and bit-based division property using three subsets (three-subset division property). Three-subset division property has more potential to achieve better integral distinguishers compared with the two-subset division property. The bit-based division property could not be to apply to ciphers with large block sizes due to its unpractical complexity. At Asiacrypt’16, the two-subset division property was modeled using Mixed Integral Linear Programming (MILP) technique, and the limits of block sizes were eliminated. However, there is still no efficient method searching for three-subset division property. The propagation rule of the XOR operation for \(\mathbb {L}\) (The definition of \(\mathbb {L}\) and \(\mathbb {K}\) is introduced in Sect. 2.), which is a set used in the three-subset division property but not in two-subset one, requires to remove some specific vectors, and new vectors generated from \(\mathbb {L}\) should be appended to \(\mathbb {K}\) when Key-XOR operation is applied, both of which are difficult for common automatic tools such as MILP, SMT or CP. In this paper, we overcome one of the two challenges, concretely, we address the problem to add new vectors into \(\mathbb {K}\) from \(\mathbb {L}\) in an automatic search model. Moreover, we present a new model automatically searching for a variant three-subset division property (VTDP) with STP solver. The variant is weaker than the original three-subset division property (OTDP) but it is still powerful in some ciphers. Most importantly, this model has no constraints on the block size of target ciphers, which can also be applied to ARX and S-box based ciphers. As illustrations, some improved integral distinguishers have been achieved for SIMON32, SIMON32/48/64(102), SPECK32 and KATAN/KTANTAN32/48/64 according to the number of rounds or number of even/odd-parity bits.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We can implement the model of S-box using the exclusion method as those of Copy, AND and XOR, also.
References
Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK lightweight block ciphers. In: PADAC 2015, pp. 175:1–175:6 (2015)
Bogdanov, A., et al.: PRESENT: an ultra-lightweight block cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74735-2_31
Boura, C., Canteaut, A.: Another view of the division property. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 654–682. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_24
De Cannière, C., Dunkelman, O., Knežević, M.: KATAN and KTANTAN—a family of small and efficient hardware-oriented block ciphers. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 272–288. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04138-9_20
Funabiki, Y., Todo, Y., Isobe, T., Morii, M.: Improved integral attack on HIGHT. In: Pieprzyk, J., Suriadi, S. (eds.) ACISP 2017. LNCS, vol. 10342, pp. 363–383. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60055-0_19
Knudsen, L., Wagner, D.: Integral cryptanalysis. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 112–127. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45661-9_9
Kölbl, S., Leander, G., Tiessen, T.: Observations on the SIMON block cipher family. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 161–185. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_8
Mouha, N., Preneel, B.: Towards finding optimal differential characteristics for ARX: application to salsa20. Cryptology ePrint Archive, Report 2013/328 (2013)
Sun, L., Wang, W., Liu, R., Wang, M.: MILP-aided bit-based division property for ARX-based block cipher. IACR Cryptology ePrint Archive 2016:1101 (2016)
Sun, L., Wang, W., Wang, M.: MILP-aided bit-based division property for primitives with non-bit-permutation linear layers. IACR Cryptology ePrint Archive 2016:811 (2016)
Sun, L., Wang, W., Wang, M.: Automatic search of bit-based division property for ARX ciphers and word-based division property. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 128–157. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_5
Todo, Y.: Structural evaluation by generalized integral property. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 287–314. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_12
Todo, Y.: Integral cryptanalysis on full MISTY1. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 413–432. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_20
Todo, Y., Isobe, T., Hao, Y., Meier, W.: Cube attacks on non-blackbox polynomials based on division property. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10403, pp. 250–279. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63697-9_9
Todo, Y., Morii, M.: Bit-based division property and application to Simon family. In: Peyrin, T. (ed.) FSE 2016. LNCS, vol. 9783, pp. 357–377. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52993-5_18
Wang, Q., Grassi, L., Rechberger, C.: Zero-sum partitions of PHOTON permutations. IACR Cryptology ePrint Archive 2017:1211 (2017)
Xiang, Z., Zhang, W., Bao, Z., Lin, D.: Applying MILP method to searching integral distinguishers based on division property for 6 lightweight block ciphers. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 648–678. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_24
Yang, G., Zhu, B., Suder, V., Aagaard, M.D., Gong, G.: The Simeck family of lightweight block ciphers. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 307–329. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48324-4_16
Acknowledgement
The authors would like to thank Yosuke Todo for his important comments and suggestions to this paper. This work is supported by National Cryptography Development Fund (MMJJ20170102), National Natural Science Foundation of China (Grant No. 61572293) and Major Scientific and Technological Innovation Projects of Shandong Province, China (2017CXGC0704).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Hu, K., Wang, M. (2019). Automatic Search for a Variant of Division Property Using Three Subsets. In: Matsui, M. (eds) Topics in Cryptology – CT-RSA 2019. CT-RSA 2019. Lecture Notes in Computer Science(), vol 11405. Springer, Cham. https://doi.org/10.1007/978-3-030-12612-4_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-12612-4_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-12611-7
Online ISBN: 978-3-030-12612-4
eBook Packages: Computer ScienceComputer Science (R0)