Abstract
In this paper, we study multi-collision probability. For a hash function H:D →R with |R|=n, it has been believed that we can find an s-collision by hashing Q=n ( s − − 1)/ s times. We first show that this probability is at most 1/s! which is very small for large s. We next show that by hashing (s!)1/ s ×Q times, an s-collision is found with probability approximately 0.5 for sufficiently large n. Note that if s=2, it coincides with the usual birthday paradox. Hence it is a generalization of the birthday paradox to multi-collisions.
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References
Bellare, M., Kilian, J., Rogaway, P.: The Security of the Cipher Block Chaining Message Authentication Code. J. Comput. Syst. Sci. 61(3), 362–399 (2000)
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)
Brickell, E., Pointcheval, D., Vaudenay, S., Yung, M.: Design Validations for Discrete Logarithm Based Signature Schemes. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 276–292. Springer, Heidelberg (2000)
Girault, M., Stern, J.: On the Length of Cryptographic Hash-Values Used in Identification Schemes. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 202–215. Springer, Heidelberg (1994)
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)
Rivest, R., Shamir, A.: PayWord and MicroMint: Two Simple Micropayment Schemes. In: Security Protocols Workshop 1996, pp. 69–87 (1996)
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© 2006 Springer-Verlag Berlin Heidelberg
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Suzuki, K., Tonien, D., Kurosawa, K., Toyota, K. (2006). Birthday Paradox for Multi-collisions. In: Rhee, M.S., Lee, B. (eds) Information Security and Cryptology – ICISC 2006. ICISC 2006. Lecture Notes in Computer Science, vol 4296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11927587_5
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DOI: https://doi.org/10.1007/11927587_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49112-5
Online ISBN: 978-3-540-49114-9
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