Abstract
Troika is a recently proposed sponge-based hash function for IOTA’s ternary architecture and platform, which is developed by CYBERCRYPT. In this paper, we introduce the preimage attack on 2 and 3 rounds of Troika with a divide-and-conquer approach. Instead of directly matching a given hash value, we propose equivalent conditions to determine whether a message is the preimage before computing the complete hash value. As a result, for the two-round hash value that can be generated with one block, we can search the preimage only in a valid space and efficiently enumerate the messages which can satisfy most of the equivalent conditions with a guess-and-determine technique. For the three-round preimage attack, an MILP-based method is applied to separate the one-block message space into two parts in order to obtain the best advantage over brute force. Our experiments show that the time complexity of the preimage attack on 2 (out of 24) rounds of Troika can be improved to \(3^{79}\), which is \(3^{164}\) times faster than the brute force. For the preimage attack on 3 (out of 24) rounds of Troika, we can obtain an advantage of \(3^{25.7}\) over brute force. In addition, how to construct the second preimage for two-round Troika in seconds is presented as well. Our attacks do not threaten the security of Troika.
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References
Cybercrypt. https://www.cyber-crypt.com/troika-challenge/
Gurobi. https://www.gurobi.com/
Troika: a ternary hash function (2018). https://www.cyber-crypt.com/wp-content/uploads/2018/12/20181221.iota_.troika-reference.v1.0.1.pdf
Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: The Keccak reference (2011). http://keccak.noekeon.org
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
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
Li, T., Sun, Y., Liao, M., Wang, D.: Preimage attacks on the round-reduced Keccak with cross-linear structures. IACR Trans. Symmetric Cryptol. 2017(4), 39–57 (2017)
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). https://doi.org/10.1007/978-3-642-34704-7_5
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., 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
Acknowledgement
We thank the anonymous reviewers of IWSEC 2019 for their insightful comments and suggestions. We also thank the Troika Group for the discussion. Fukang Liu is supported by Invitation Programs for Foreigner-based Researchers of the National Institute of Information and Communications Technology (NICT). Takanori Isobe is supported by Grant-in-Aid for Scientific Research (B) (KAKENHI 19H02141) for Japan Society for the Promotion of Science.
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Liu, F., Isobe, T. (2019). Preimage Attacks on Reduced Troika with Divide-and-Conquer Methods. 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_18
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DOI: https://doi.org/10.1007/978-3-030-26834-3_18
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