Abstract
We show that the Winternitz one-time signature scheme is existentially unforgeable under adaptive chosen message attacks when instantiated with a family of pseudo random functions. Compared to previous results, which require a collision resistant hash function, our result provides significantly smaller signatures at the same security level. We also consider security in the strong sense and show that the Winternitz one-time signature scheme is strongly unforgeable assuming additional properties of the pseudo random function. In this context we formally define several key-based security notions for function families and investigate their relation to pseudorandomness. All our reductions are exact and in the standard model and can directly be used to estimate the output length of the hash function required to meet a certain security level.
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References
Bellare, M.: New proofs for nmac and hmac: Security without collision-resistance. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 602–619. Springer, Heidelberg (2006)
Bellare, M., Kilian, J., Rogaway, P.: The security of the cipher block chaining message authentication code. Journal of Computer and System Sciences 61(3), 362–399 (2000)
Bleichenbacher, D., Maurer, U.M.: Directed acyclic graphs, one-way functions and digital signatures. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 75–82. Springer, Heidelberg (1994)
Buchmann, J., Dahmen, E., Ereth, S., Hülsing, A., Rückert, M.: On the security of the winternitz one-time signature scheme. Cryptology ePrint Archive, Report 2011/191 (2011), http://eprint.iacr.org/
Buchmann, J., Dahmen, E., Klintsevich, E., Okeya, K., Vuillaume, C.: Merkle signatures with virtually unlimited signature capacity. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 31–45. Springer, Heidelberg (2007)
Canetti, R., Micciancio, D., Reingold, O.: Perfectly one-way probabilistic hash functions (preliminary version). In: STOC, pp. 131–140 (1998)
Coronado García, L.C.: On the security and the efficiency of the merkle signature scheme. Technical Report 2005/192, Cryptology ePrint Archive (2005), Available at http://eprint.iacr.org/2005/192/
Dahmen, E., Okeya, K., Takagi, T., Vuillaume, C.: Digital signatures out of second-preimage resistant hash functions. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 109–123. Springer, Heidelberg (2008)
Dods, C., Smart, N., Stam, M.: Hash based digital signature schemes. In: Smart, N.P. (ed.) Cryptography and Coding 2005. LNCS, vol. 3796, pp. 96–115. Springer, Heidelberg (2005)
Fischlin, M.: Pseudorandom function tribe ensembles based on one-way permutations: Improvements and applications. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 432–445. Springer, Heidelberg (1999)
Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM 33(4), 792–807 (1986)
Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual Symposium on the Theory of Computing, pp. 212–219. ACM Press, New York (1996)
Hevia, A., Micciancio, D.: The provable security of graph-based one-time signatures and extensions to algebraic signature schemes. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 379–396. Springer, Heidelberg (2002)
Lamport, L.: Constructing digital signatures from a one way function. Technical Report SRI-CSL-98, SRI International Computer Science Laboratory (1979)
Levin, L.: One way functions and pseudorandom generators. Combinatorica 7, 357–363 (1987)
Luk, M., Perrig, A., Whillock, B.: Seven cardinal properties of sensor network broadcast authentication. In: ACM Workshop on Security of Ad Hoc and Sensor Networks, SASN (2006)
Merkle, R.C.: A certified digital signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 218–238. Springer, Heidelberg (1990)
Perrig, A.: The biba one-time signature and broadcast authentication protocol. In: ACM Conference on Computer and Communications Security, pp. 28–37 (2001)
Perrig, A., Canetti, R., Tygar, J.D., Song, D.: Efficient authentication and signing of multicast streams over lossy channels. In: IEEE Symposium on Security and Privacy, pp. 56–73 (2000)
Reyzin, L., Reyzin, N.: Better than biBa: Short one-time signatures with fast signing and verifying. In: Batten, L.M., Seberry, J. (eds.) ACISP 2002. LNCS, vol. 2384, pp. 1–47. Springer, Heidelberg (2002)
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)
Rompel, J.: One-way functions are necessary and sufficient for secure signatures. In: STOC 1990: Proceedings of the twenty-second annual ACM symposium on Theory of computing, pp. 387–394. ACM Press, New York (1990)
Shor, P.W.: Algorithms for quantum computation: Discrete logarithms and factoring. In: Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science (FOCS 1994), pp. 124–134. IEEE Computer Society Press, Los Alamitos (1994)
Yao, A.C.: Theory and application of trapdoor functions. Annual IEEE Symposium on Foundations of Computer Science 0, 80–91 (1982)
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Buchmann, J., Dahmen, E., Ereth, S., Hülsing, A., Rückert, M. (2011). On the Security of the Winternitz One-Time Signature Scheme. In: Nitaj, A., Pointcheval, D. (eds) Progress in Cryptology – AFRICACRYPT 2011. AFRICACRYPT 2011. Lecture Notes in Computer Science, vol 6737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21969-6_23
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