Abstract
In a digital signature scheme with message recovery, rather than transmitting the message m and its signature σ, a single enhanced signature τ is transmitted. The verifier is able to recover m from τ and at the same time verify its authenticity. The two most important parameters of such a scheme are its security and overhead |τ| − |m|. A simple argument shows that for any scheme with “n bits security” |τ| − |m| ≥ n, i.e., the overhead is lower bounded by the security parameter n. Currently, the best known constructions in the random oracle model are far from this lower bound requiring an overhead of n + logq h , where q h is the number of queries to the random oracle. In this paper we give a construction which basically matches the n bit lower bound. We propose a simple digital signature scheme with n + o(logq h ) bits overhead, where q h denotes the number of random oracle queries.
Our construction works in two steps. First, we propose a signature scheme with message recovery having optimal overhead in a new ideal model, the random invertible function model. Second, we show that a four-round Feistel network with random oracles as round functions is tightly “public-indifferentiable” from a random invertible function. At the core of our indifferentiability proof is an almost tight upper bound for the expected number of edges of the densest “small” subgraph of a random Cayley graph, which may be of independent interest.
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Abe, M., Kiltz, E., Okamoto, T.: Chosen ciphertext security with optimal ciphertext overhead. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 355–371. Springer, Heidelberg (2008)
Alon, N., Kaufman, T., Krivelevich, M., Ron, D.: Testing triangle-freeness in general graphs. SIAM J. Discrete Math. 22(2), 786–819 (2008)
Bellare, M., Ristenpart, T.: Simulation without the artificial abort: Simplified proof and improved concrete security for waters’ IBE scheme. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 407–424. Springer, Heidelberg (2009)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993, pp. 62–73. ACM Press (November 1993)
Bellare, M., Rogaway, P.: The exact security of digital signatures: How to sign with RSA and Rabin. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996)
Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)
Cachin, C., Micali, S., Stadler, M.A.: Computationally private information retrieval with polylogarithmic communication. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 402–414. Springer, Heidelberg (1999)
Chevallier-Mames, B., Phan, D.H., Pointcheval, D.: Optimal asymmetric encryption and signature paddings. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 254–268. Springer, Heidelberg (2005)
Coron, J.-S.: On the exact security of full domain hash. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 229–235. Springer, Heidelberg (2000)
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)
Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM Journal on Computing 17(2), 281–308 (1988)
Green, B.: Counting sets with small sumset, and the clique number of random cayley graphs. Combinatorica, 307–326 (2005)
Holenstein, T., Künzler, R., Tessaro, S.: The equivalence of the random oracle model and the ideal cipher model, revisited. In: Fortnow, L., Vadhan, S.P. (eds.) ACM STOC, pp. 89–98. ACM Press (June 2011)
Kakvi, S.A., Kiltz, E.: Optimal security proofs for full domain hash, revisited. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 537–553. Springer, Heidelberg (2012)
Katz, J., Wang, N.: Efficiency improvements for signature schemes with tight security reductions. In: Jajodia, S., Atluri, V., Jaeger, T. (eds.) ACM CCS 2003, pp. 155–164. ACM Press (October 2003)
Kiltz, E., Pietrzak, K., Szegedy, M.: Digital signatures with minimal overhead. Cryptology ePrint Archive, Report 2012/658 (2012), http://eprint.iacr.org/
Mandal, A., Patarin, J., Seurin, Y.: On the public indifferentiability and correlation intractability of the 6-round feistel construction. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 285–302. Springer, Heidelberg (2012)
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)
Naor, A., Verstraëte, J.: A note on bipartite graphs without 2k-cycles. Comb. Probab. Comput. 14(5-6), 845–849 (2005)
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Ladner, R.E., Dwork, C. (eds.) ACM STOC, pp. 187–196. ACM Press (May 2008)
Yoneyama, K., Miyagawa, S., Ohta, K.: Leaky random oracle. IEICE Transactions 92-A(8), 1795–1807 (2009)
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Kiltz, E., Pietrzak, K., Szegedy, M. (2013). Digital Signatures with Minimal Overhead from Indifferentiable Random Invertible Functions. In: Canetti, R., Garay, J.A. (eds) Advances in Cryptology – CRYPTO 2013. CRYPTO 2013. Lecture Notes in Computer Science, vol 8042. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40041-4_31
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