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Towards Bidirectional Ratcheted Key Exchange Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Improved Division Property Based Cube Attacks Exploiting Algebraic Properties of Superpoly

Authors : Qingju Wang, Yonglin Hao, Yosuke Todo, Chaoyun Li, Takanori Isobe, Willi Meier

Published in: Advances in Cryptology – CRYPTO 2018

Publisher: Springer International Publishing

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Abstract

The cube attack is an important technique for the cryptanalysis of symmetric key primitives, especially for stream ciphers. Aiming at recovering some secret key bits, the adversary reconstructs a superpoly with the secret key bits involved, by summing over a set of the plaintexts/IV which is called a cube. Traditional cube attack only exploits linear/quadratic superpolies. Moreover, for a long time after its proposal, the size of the cubes has been largely confined to an experimental range, e.g., typically 40. These limits were first overcome by the division property based cube attacks proposed by Todo et al. at CRYPTO 2017. Based on MILP modelled division property, for a cube (index set) I, they identify the small (index) subset J of the secret key bits involved in the resultant superpoly. During the precomputation phase which dominates the complexity of the cube attacks, \(2^{|I|+|J|}\) encryptions are required to recover the superpoly. Therefore, their attacks can only be available when the restriction \(|I|+|J|<n\) is met.
In this paper, we introduced several techniques to improve the division property based cube attacks by exploiting various algebraic properties of the superpoly.
1.
We propose the “flag” technique to enhance the preciseness of MILP models so that the proper non-cube IV assignments can be identified to obtain a non-constant superpoly.
 
2.
A degree evaluation algorithm is presented to upper bound the degree of the superpoly. With the knowledge of its degree, the superpoly can be recovered without constructing its whole truth table. This enables us to explore larger cubes I’s even if \(|I|+|J|\ge n\).
 
3.
We provide a term enumeration algorithm for finding the monomials of the superpoly, so that the complexity of many attacks can be further reduced.
 
As an illustration, we apply our techniques to attack the initialization of several ciphers. To be specific, our key recovery attacks have mounted to 839-round Trivium, 891-round Kreyvium, 184-round Grain-128a and 750-round Acornrespectively.

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previous chapter Cryptanalysis via Algebraic Spans
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Footnotes
1
Integral attacks also require to traverse some active plaintext bits and check whether the summation of the corresponding ciphertext bits have zero-sum property, which equals to check whether the superpoly has \(p(\varvec{x}, \varvec{v})\equiv 0\).
 
2
While this paper was under submission, Fu et al. released a paper on ePrint [24] and claimed that 855 rounds initialization of Trivium can be attacked.
 
3
Because of the page limitation, we put part of detailed applications about Kreyvium, Grain-128a and Acornin the full version [25].
 
Literature
1.
Dinur, I., Shamir, A.: Cube attacks on tweakable black box polynomials. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 278–299. Springer, Heidelberg (2009)CrossRef
2.
Aumasson, J.-P., Dinur, I., Meier, W., Shamir, A.: Cube testers and key recovery attacks on reduced-round MD6 and Trivium. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 1–22. Springer, Heidelberg (2009)CrossRef
3.
Dinur, I., Shamir, A.: Breaking Grain-128 with dynamic cube attacks. In: Joux, A. (ed.) FSE 2011. LNCS, vol. 6733, pp. 167–187. Springer, Heidelberg (2011)CrossRef
4.
Fouque, P.-A., Vannet, T.: Improving key recovery to 784 and 799 rounds of Trivium using optimized cube attacks. In: Moriai, S. (ed.) FSE 2013. LNCS, vol. 8424, pp. 502–517. Springer, Heidelberg (2014)
5.
Salam, M.I., Bartlett, H., Dawson, E., Pieprzyk, J., Simpson, L., Wong, K.K.-H.: Investigating cube attacks on the authenticated encryption stream cipher ACORN. In: Batten, L., Li, G. (eds.) ATIS 2016. CCIS, vol. 651, pp. 15–26. Springer, Singapore (2016)
6.
Liu, M., Yang, J., Wang, W., Lin, D.: Correlation cube attacks: from weak-key distinguisher to key recovery. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part II. LNCS, vol. 10821, pp. 715–744. Springer, Cham (2018)CrossRef
7.
Dinur, I., Morawiecki, P., Pieprzyk, J., Srebrny, M., Straus, M.: Cube attacks and cube-attack-like cryptanalysis on the round-reduced Keccak sponge function. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part I. LNCS, vol. 9056, pp. 733–761. Springer, Heidelberg (2015)
8.
Huang, S., Wang, X., Xu, G., Wang, M., Zhao, J.: Conditional cube attack on reduced-round Keccak sponge function. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part II. LNCS, vol. 10211, pp. 259–288. Springer, Cham (2017)CrossRef
9.
Li, Z., Bi, W., Dong, X., Wang, X.: Improved conditional cube attacks on Keccak keyed modes with MILP method. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part I. LNCS, vol. 10624, pp. 99–127. Springer, Cham (2017)CrossRef
10.
Li, Z., Dong, X., Wang, X.: Conditional cube attack on round-reduced ASCON. IACR Trans. Symmetric Cryptol. 2017(1), 175–202 (2017)
11.
Dong, X., Li, Z., Wang, X., Qin, L.: Cube-like attack on round-reduced initialization of Ketje Sr. IACR Trans. Symmetric Cryptol. 2017(1), 259–280 (2017)
12.
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, Part III. LNCS, vol. 10403, pp. 250–279. Springer, Cham (2017)CrossRef
13.
Todo, Y.: Structural evaluation by generalized integral property. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part I. LNCS, vol. 9056, pp. 287–314. Springer, Heidelberg (2015)
14.
Todo, Y.: Integral cryptanalysis on full MISTY1. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part I. LNCS, vol. 9215, pp. 413–432. Springer, Heidelberg (2015)CrossRef
15.
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)CrossRef
16.
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, Part I. LNCS, vol. 10031, pp. 648–678. Springer, Heidelberg (2016)CrossRef
17.
18.
19.
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, Part I. LNCS, vol. 10624, pp. 128–157. Springer, Cham (2017)CrossRef
20.
Funabiki, Y., Todo, Y., Isobe, T., Morii, M.: Improved integral attack on HIGHT. In: Pieprzyk, J., Suriadi, S. (eds.) ACISP 2017, Part I. LNCS, vol. 10342, pp. 363–383. Springer, Cham (2017)CrossRef
21.
Wang, Q., Grassi, L., Rechberger, C.: Zero-sum partitions of PHOTON permutations. In: Smart, N.P. (ed.) CT-RSA 2018. LNCS, vol. 10808, pp. 279–299. Springer, Cham (2018)CrossRef
22.
23.
Liu, M.: Degree evaluation of NFSR-based cryptosystems. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part III. LNCS, vol. 10403, pp. 227–249. Springer, Cham (2017)CrossRef
24.
25.
Wang, Q., Hao, Y., Todo, Y., Li, C., Isobe, T., Meier, W.: Improved division property based cube attacks exploiting algebraic properties of superpoly (full version). Cryptology ePrint Archive, Report 2017/1063 (2017). https://​eprint.​iacr.​org/​2017/​1063
26.
Todo, Y., Isobe, T., Meier, W., Aoki, K., Zhang, B.: Fast correlation attack revisited-cryptanalysis on full Grain-128a, Grain-128, and Grain-v1. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10991, pp. 129–159. Springer, Cham (2018)
27.
Lehmann, M., Meier, W.: Conditional differential cryptanalysis of Grain-128a. In: Pieprzyk, J., Sadeghi, A.-R., Manulis, M. (eds.) CANS 2012. LNCS, vol. 7712, pp. 1–11. Springer, Heidelberg (2012)CrossRef
28.
Mouha, N., Wang, Q., Gu, D., Preneel, B.: Differential and linear cryptanalysis using mixed-integer linear programming. In: Wu, C.-K., Yung, M., Lin, D. (eds.) Inscrypt 2011. LNCS, vol. 7537, pp. 57–76. Springer, Heidelberg (2012)CrossRef
29.
Sun, S., Hu, L., Wang, P., Qiao, K., Ma, X., Song, L.: Automatic security evaluation and (related-key) differential characteristic search: application to SIMON, PRESENT, LBlock, DES(L) and other bit-oriented block ciphers. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part I. LNCS, vol. 8873, pp. 158–178. Springer, Heidelberg (2014)
30.
Sun, S., Hu, L., Wang, M., Wang, P., Qiao, K., Ma, X., Shi, D., Song, L., Fu, K.: Towards finding the best characteristics of some bit-oriented block ciphers and automatic enumeration of (related-key) differential and linear characteristics with predefined properties. Cryptology ePrint Archive, Report 2014/747 (2014). https://​eprint.​iacr.​org/​2014/​747
31.
32.
Sasaki, Y., Todo, Y.: New impossible differential search tool from design and cryptanalysis aspects. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part III. LNCS, vol. 10212, pp. 185–215. Springer, Cham (2017)CrossRef
33.
Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications, vol. 290. Macmillan, London (1976)CrossRef
Metadata
Title
Improved Division Property Based Cube Attacks Exploiting Algebraic Properties of Superpoly
Authors
Qingju Wang
Yonglin Hao
Yosuke Todo
Chaoyun Li
Takanori Isobe
Willi Meier
Copyright Year
2018
Book
Advances in Cryptology – CRYPTO 2018

Print ISBN: 978-3-319-96883-4

Electronic ISBN: 978-3-319-96884-1

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-96884-1_10

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