Abstract
Preneel et al. (Crypto 1993) assessed 64 possible ways to construct a compression functions out of a blockcipher. They conjectured that 12 out of these 64 so-called PGV constructions achieve optimal security bounds for collision resistance and preimage resistance. This was proven by Black et al. (Journal of Cryptology, 2010), if one assumes that the blockcipher is ideal. This result, however, does not apply to “non-ideal” blockciphers such as AES. To alleviate this problem, we revisit the PGV constructions in light of the recently proposed idea of random-oracle reducibility (Baecher and Fischlin, Crypto 2011). We say that the blockcipher in one of the 12 secure PGV constructions reduces to the one in another construction, if any secure instantiation of the cipher, ideal or not, for one construction also makes the other secure. This notion allows us to relate the underlying assumptions on blockciphers in different constructions, and show that the requirements on the blockcipher for one case are not more demanding than those for the other. It turns out that this approach divides the 12 secure constructions into two groups of equal size, where within each group a blockcipher making one construction secure also makes all others secure. Across the groups this is provably not the case, showing that the sets of “good” blockciphers for each group are qualitatively distinct. We also relate the ideal ciphers in the PGV constructions with those in double-block-length hash functions such as Tandem-DM, Abreast-DM, and Hirose-DM. Here, our results show that, besides achieving better bounds, the double-block-length hash functions rely on weaker assumptions on the blockciphers to achieve collision and everywhere preimage resistance.
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References
Andreeva, E., Neven, G., Preneel, B., Shrimpton, T.: Seven-property-preserving iterated hashing: ROX. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 130–146. Springer, Heidelberg (2007)
Armknecht, F., Fleischmann, E., Krause, M., Lee, J., Stam, M., Steinberger, J.: The preimage security of double-block-length compression functions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 233–251. Springer, Heidelberg (2011)
Baecher, P., Brzuska, C., Fischlin, M.: Notions of black-box reductions, revisited. Cryptology ePrint Archive, Report 2013/101 (2013), http://eprint.iacr.org/
Baecher, P., Fischlin, M.: Random oracle reducibility. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 21–38. Springer, Heidelberg (2011)
Bellare, M., Kohno, T.: Hash function balance and its impact on birthday attacks. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 401–418. Springer, Heidelberg (2004)
Bellare, M., Rogaway, P.: The security of triple encryption and a framework for code-based game-playing proofs. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 409–426. Springer, Heidelberg (2006)
Biryukov, A., Khovratovich, D.: Related-key cryptanalysis of the full AES-192 and AES-256. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 1–18. Springer, Heidelberg (2009)
Biryukov, A., Khovratovich, D., Nikolić, I.: Distinguisher and related-key attack on the full AES-256. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 231–249. Springer, Heidelberg (2009)
Black, J.A., Rogaway, P., Shrimpton, T.: Black-box analysis of the block-cipher-based hash-function constructions from PGV. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 320–335. Springer, Heidelberg (2002)
Black, J., Rogaway, P., Shrimpton, T., Stam, M.: An analysis of the blockcipher-based hash functions from PGV. Journal of Cryptology 23(4), 519–545 (2010)
Coron, J.-S., Dodis, Y., Malinaud, C., Puniya, P.: Merkle-damgård revisited: How to construct a hash function. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 430–448. Springer, Heidelberg (2005)
Dodis, Y., Ristenpart, T., Shrimpton, T.: Salvaging merkle-damgård for practical applications. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 371–388. Springer, Heidelberg (2009)
Ferguson, N., Lucks, S., Schneier, B., Whiting, D., Bellare, M., Kohno, T., Callas, J., Walker, J.: The skein hash function family (2008)
Fleischmann, E., Gorski, M., Lucks, S.: On the security of tandem-DM. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 84–103. Springer, Heidelberg (2009)
Gauravaram, P., Knudsen, L.R., Matusiewicz, K., Mendel, F., Rechberger, C., Schläfffer, M., Thomsen, S.S.: Grøstl — a SHA-3 candidate (2011)
Harnik, D., Kilian, J., Naor, M., Reingold, O., Rosen, A.: On robust combiners for oblivious transfer and other primitives. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 96–113. Springer, Heidelberg (2005)
Herzberg, A.: On tolerant cryptographic constructions. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 172–190. Springer, Heidelberg (2005)
Hirose, S.: Provably secure double-block-length hash functions in a black-box model. In: Park, C.-S., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 330–342. Springer, Heidelberg (2005)
Hirose, S.: Some plausible constructions of double-block-length hash functions. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 210–225. Springer, Heidelberg (2006)
Khovratovich, D.: New Approaches to the Cryptanalysis of Symmetric Primitives. Ph.D. thesis, University of Luxembourg (2010)
Kuwakado, H., Morii, M.: Indifferentiability of single-block-length and rate-1 compression functions. IEICE Transactions 90-A(10), 2301–2308 (2007)
Lai, X., Massey, J.L.: Hash functions based on block ciphers. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 55–70. Springer, Heidelberg (1993)
Lee, J., Kwon, D.: The security of abreast-dm in the ideal cipher model. IEICE Transactions 94-A(1), 104–109 (2011)
Lee, J., Stam, M., Steinberger, J.: The collision security of tandem-DM in the ideal cipher model. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 561–577. Springer, Heidelberg (2011)
Maurer, U.M., Renner, R.S., Holenstein, C.: Indifferentiability, impossibility results on reductions, and applications to the random oracle methodology. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 21–39. Springer, Heidelberg (2004)
Pietrzak, K.: Compression from collisions, or why CRHF combiners have a long output. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 413–432. Springer, Heidelberg (2008)
Preneel, B., Govaerts, R., Vandewalle, J.: Hash functions based on block ciphers: A synthetic approach. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 368–378. Springer, Heidelberg (1994)
Reingold, O., Trevisan, L., Vadhan, S.P.: Notions of reducibility between cryptographic primitives. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 1–20. Springer, Heidelberg (2004)
Rogaway, P.: Formalizing human ignorance. In: Nguyen, P.Q. (ed.) VIETCRYPT 2006. LNCS, vol. 4341, pp. 211–228. Springer, Heidelberg (2006)
Rogaway, P., Shrimpton, T.: Cryptographic hash-function basics: Definitions, implications, and separations for preimage resistance, second-preimage resistance, and collision resistance. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 371–388. Springer, Heidelberg (2004)
Simon, D.R.: Findings collisions on a one-way street: Can secure hash functions be based on general assumptions? In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 334–345. Springer, Heidelberg (1998)
Stam, M.: Blockcipher-based hashing revisited. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 67–83. Springer, Heidelberg (2009)
Wei, L., Peyrin, T., Sokołowski, P., Ling, S., Pieprzyk, J., Wang, H.: On the (In)Security of IDEA in various hashing modes. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 163–179. Springer, Heidelberg (2012)
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Baecher, P., Farshim, P., Fischlin, M., Stam, M. (2013). Ideal-Cipher (Ir)reducibility for Blockcipher-Based Hash Functions. In: Johansson, T., Nguyen, P.Q. (eds) Advances in Cryptology – EUROCRYPT 2013. EUROCRYPT 2013. Lecture Notes in Computer Science, vol 7881. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38348-9_26
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