Abstract
The first part of this paper considers the diamond structures which were first introduced and applied in the herding attack by Kelsey and Kohno [7]. We present a new method for the construction of a diamond structure with 2d chaining values the message complexity of which is \(\mathrm{O}(2^{\frac{n+d}{2}})\). Here n is the length of the compression function used. The aforementioned complexity was (with intuitive reasoning) suggested to be true in [7] and later disputed by Blackburn et al. in [3]. In the second part of our paper we give new, efficient variants for the two types of Trojan message attacks against Merkle-Damgård hash functions presented by Andreeva et al. [1] The message complexities of the Collision Trojan Attack and the stronger Herding Trojan Attack in [1] are \(\mathrm{O}(2^{\frac{n}{2}+r})\) and \(\mathrm{O}(2^{\frac{2n}{3}}+2^{\frac{n}{2}+r})\), respectively. Our variants of the above two attack types are the Weak Trojan Attack and the Strong Trojan Attack having the complexities \(\mathrm{O}(2^{\frac{n+r}{2}})\) and \(\mathrm{O}(2^{\frac{2n-s}{3}}+2^{\frac{n+r}{2}})\), respectively. Here 2r is the cardinality of the prefix set and 2s is the length of the Trojan message in the Strong Trojan Attack.
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Andreeva, E., Bouillaguet, C., Dunkelman, O., Kelsey, J.: Herding, Second Preimage and Trojan Message Attacks beyond Merkle-Damgård. In: Jacobson Jr., M.J., Rijmen, V., Safavi-Naini, R. (eds.) SAC 2009. LNCS, vol. 5867, pp. 393–414. Springer, Heidelberg (2009)
Andreeva, E., Bouillaguet, C., Fouque, P.-A., Hoch, J.J., Kelsey, J., Shamir, A., Zimmer, S.: Second Preimage Attacks on Dithered Hash Functions. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 270–288. Springer, Heidelberg (2008)
Blackburn, S., Stinson, D., Upadhyay, J.: On the Complexity of the Herding Attack and Some Related Attacks on Hash Functions. Cryptology ePrint Archive, Report 2010/030 (2010), http://eprint.iacr.org/2010/030
Damgård, I.: A Design Principle for Hash Functions. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 416–427. Springer, Heidelberg (1990)
Hoch, J., Shamir, A.: Breaking the ICE - Finding Multicollisions in Iterated Concatenated and Expanded (ICE) Hash Functions. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 179–194. Springer, Heidelberg (2006)
Joux, A.: Multicollisions in Iterated Hash Functions. Application to Cascaded Constructions. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 306–316. Springer, Heidelberg (2004)
Kelsey, J., Kohno, T.: Herding Hash Functions and the Nostradamus Attack. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 183–200. Springer, Heidelberg (2006)
Kelsey, J., Schneier, B.: Second Preimages on n-Bit Hash Functions for Much Less than 2n Work. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 474–490. Springer, Heidelberg (2005)
Kortelainen, J., Halunen, K., Kortelainen, T.: Multicollision attacks and generalized iterated hash functions. Journal of Mathematical Cryptology 4, 239–270 (2010)
Kortelainen, J., Kortelainen, T., Vesanen, A.: Unavoidable Regularities in Long Words with Bounded Number of Symbol Occurrences. In: Fu, B., Du, D.-Z. (eds.) COCOON 2011. LNCS, vol. 6842, pp. 519–530. Springer, Heidelberg (2011)
Kortelainen, T., Vesanen, A., Kortelainen, J.: Generalized Iterated Hash Functions Revisited: New Complexity Bounds for Multicollision Attacks. In: Galbraith, S., Nandi, M. (eds.) INDOCRYPT 2012. LNCS, vol. 7668, pp. 172–190. Springer, Heidelberg (2012)
Menezes, A.J., van Oorschot, P.C., Vanstone, S.A. (eds.): Handbook of Applied Cryptology, pp. 321–376 (1996)
Merkle, R.: A Certified Digital Signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 218–238. Springer, Heidelberg (1990)
Nandi, M., Stinson, D.: Multicollision attacks on some generalized sequential hash functions. IEEE Transactions on Information Theory 53(2), 759–767 (2007)
Suzuki, K., Tonien, D., Kurosawa, K., Toyota, K.: Birthday paradox for multicollisions. IEICE Transactions 91A(1), 39–45 (2008)
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Kortelainen, T., Kortelainen, J. (2013). On Diamond Structures and Trojan Message Attacks. In: Sako, K., Sarkar, P. (eds) Advances in Cryptology - ASIACRYPT 2013. ASIACRYPT 2013. Lecture Notes in Computer Science, vol 8270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-42045-0_27
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