Abstract
In this paper, we introduce an alternative method to find ordinary cube variables for Keccak-MAC by making full use of the key-independent bit conditions. First, we select some potential candidates for ordinary cube variables by properly adding key-independent bit conditions, which do not multiply with the chosen conditional cube variables in the first two rounds. Then, we carefully determine the ordinary cube variables from the candidates to establish the conditional cube tester. Finally, based on our new method to recover the 128-bit key, the conditional cube attack on 7-round Keccak-MAC-128/256/384 is improved to \(2^{71}\) and 6-round Keccak-MAC-512 can be attacked with at most \(2^{40}\) calls to 6-round Keccak internal permutation. It should be emphasized that our new approach does not require sophisticated modeling. As far as we know, it is the first time to clearly reveal how to utilize the key-independent bit conditions to select ordinary cube variables for Keccak-MAC.
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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). https://doi.org/10.1007/978-3-642-03317-9_1
Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: The Keccak reference (2011). http://keccak.noekeon.org
Bi, W., Dong, X., Li, Z., Zong, R., Wang, X.: MILP-aided cube-attack-like cryptanalysis on Keccak keyed modes. Cryptology ePrint Archive, Report 2018/075 (2018). https://eprint.iacr.org/2018/075
Dinur, I., Dunkelman, O., Shamir, A.: New attacks on Keccak-224 and Keccak-256. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 442–461. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34047-5_25
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. LNCS, vol. 9056, pp. 733–761. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_28
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). https://doi.org/10.1007/978-3-642-01001-9_16
Guo, J., Liu, M., Song, L.: Linear structures: applications to cryptanalysis of round-reduced Keccak. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 249–274. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_9
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. LNCS, vol. 10211, pp. 259–288. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56614-6_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. LNCS, vol. 10624, pp. 99–127. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_4
Qiao, K., Song, L., Liu, M., Guo, J.: New collision attacks on round-reduced Keccak. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10212, pp. 216–243. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56617-7_8
Song, L., Guo, J.: Cube-attack-like cryptanalysis of round-reduced Keccak using MILP. IACR Trans. Symmetric Cryptol. 2018(3), 182–214 (2018)
Song, L., Guo, J., Shi, D., Ling, S.: New MILP modeling: improved conditional cube attacks on Keccak-based constructions. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11273, pp. 65–95. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03329-3_3
Song, L., Liao, G., Guo, J.: Non-full sbox linearization: applications to collision attacks on round-reduced Keccak. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 428–451. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_15
Wang, X., Yin, Y.L., Yu, H.: Finding collisions in the full SHA-1. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 17–36. Springer, Heidelberg (2005). https://doi.org/10.1007/11535218_2
Wang, X., Yu, H.: How to break MD5 and other hash functions. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 19–35. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_2
Acknowledgement
We thank the anonymous reviewers of IWSEC 2019 for their insightful comments and suggestions. Fukang Liu and Zhenfu Cao are supported by National Natural Science Foundation of China (Grant No.61632012, 61672239). Gaoli Wang is supported by the National Natural Science Foundation of China (No. 61572125) and National Cryptography Development Fund (No. MMJJ20180201).
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Liu, F., Cao, Z., Wang, G. (2019). Finding Ordinary Cube Variables for Keccak-MAC with Greedy Algorithm. In: Attrapadung, N., Yagi, T. (eds) Advances in Information and Computer Security. IWSEC 2019. Lecture Notes in Computer Science(), vol 11689. Springer, Cham. https://doi.org/10.1007/978-3-030-26834-3_17
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