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Generalized First Pre-image Tractable Random Oracle Model and Signature Schemes

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Information Security and Privacy (ACISP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7372))

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Abstract

Weakened Random Oracle Models (WROMs) are variants of the Random Oracle Model (ROM) under some weakened collision resistance assumptions. Cryptographic schemes proven secure in WROMs can ensure security even when the underlying random oracles are susceptible to certain extent of collision attacks, second pre-image attacks, or first pre-image attacks. In this paper, we show that a WROM variant called FPT-ROM (First Pre-Image Tractable ROM) can further be weakened to a Generalized FPT-ROM which can capture more practical attacks, for example, the chosen prefix collision attack by Stevens et al. (CRYPTO 2009). This type of attacks has never been captured by any existing WROMs. Achieving security against FPT-ROM has been known as one of the most challenging problems in constructing cryptographic schemes in WROMs. In the second part of this paper, we propose a generic transformation which converts a large class of signature schemes secure in ROM to a class of variants, which can be proven secure in all the WROMs, including our newly proposed Generalized FPT-ROM. The transformation does not increase the signature size, and it can apply to many practical and highly efficient signature schemes such as the Full-Domain Hash signature, Schnorr signature, and many others.

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References

  1. Bellare, M., Micali, S.: How to sign given any trapdoor permutation. Journal of the ACM 39(1), 214–233 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Denning, D.E., Pyle, R., Ganesan, R., Sandhu, R.S., Ashby, V. (eds.) CCS 1993, pp. 62–73. ACM Press, New York (1993)

    Chapter  Google Scholar 

  3. 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)

    Google Scholar 

  4. Bellare, M., Rogaway, P.: Collision-Resistant Hashing: Towards Making UOWHFs Practical. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 470–484. Springer, Heidelberg (1997)

    Google Scholar 

  5. MacKenzie, P.D., Yang, K.: On Simulation-Sound Trapdoor Commitments. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 382–400. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  6. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. Journal of Cryptology 17(4), 297–319 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. De Cannière, C., Rechberger, C.: Preimages for Reduced SHA-0 and SHA-1. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 179–202. Springer, Heidelberg (2008)

    Google Scholar 

  8. 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)

    Chapter  Google Scholar 

  9. Coron, J.-S.: Optimal Security Proofs for PSS and Other Signature Schemes. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 272–287. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. ACM Transactions on Information and System Security 3(3), 161–185 (2000)

    Article  Google Scholar 

  11. Dwork, C., Naor, M.: An Efficient Existentially Unforgeable Signature Scheme and Its Applications. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 234–246. Springer, Heidelberg (1994)

    Google Scholar 

  12. Fiat, A., Shamir, A.: How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)

    Google Scholar 

  13. Gennaro, R., Halevi, S., Rabin, T.: Secure Hash-and-Sign Signatures without the Random Oracle. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 123–139. Springer, Heidelberg (1999)

    Google Scholar 

  14. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Dwork, C. (ed.) STOC 2008, pp. 197–206. ACM Press, New York (2008)

    Chapter  Google Scholar 

  15. Goldwasser, S., Micali, S., Rivest, R.: A digital signature scheme secure against adaptive chosen message attacks. SIAM Journal on Computing 17(2), 281–308 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  16. Halevi, S., Krawczyk, H.: Strengthening Digital Signatures Via Randomized Hashing. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 41–59. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Hess, F.: Efficient Identity Based Signature Schemes Based on Pairings. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 310–324. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  18. Hofheinz, D., Jager, T., Kiltz, E.: Short signatures from weaker assumptions (2011), http://eprint.iacr.org/2011/296.pdf

  19. Hofheinz, D., Kiltz, E.: Programmable Hash Functions and Their Applications. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 21–38. Springer, Heidelberg (2008)

    Google Scholar 

  20. Hohenberger, S., Waters, B.: Short and Stateless Signatures from the RSA Assumption. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 654–670. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Kawachi, A., Numayama, A., Tanaka, K., Xagawa, K.: Security of Encryption Schemes in Weakened Random Oracle Models (Extended Abstract). In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 403–419. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  22. Leurent, G.: MD4 is Not One-Way. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 412–428. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Liskov, M.: Constructing an Ideal Hash Function from Weak Ideal Compression Functions. In: Biham, E., Youssef, A.M. (eds.) SAC 2006. LNCS, vol. 4356, pp. 358–375. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  24. Mironov, I.: Collision-Resistant No More: Hash-and-Sign Paradigm Revisited. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 140–156. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  25. Naito, Y., Wang, L., Ohta, K.: How to construct cryptosystems and hash functions in weakened random oracle models. Cryptology ePrint Archive, Report 2009/550 (2009)

    Google Scholar 

  26. Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: Johnson, D.S. (ed.) STOC 1989, pp. 33–43. ACM Press, New York (1989)

    Chapter  Google Scholar 

  27. Numayama, A., Isshiki, T., Tanaka, K.: Security of Digital Signature Schemes in Weakened Random Oracle Models. In: Cramer, R. (ed.) PKC 2008. LNCS, vol. 4939, pp. 268–287. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  28. Pasini, S., Vaudenay, S.: Hash-and-Sign with Weak Hashing Made Secure. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds.) ACISP 2007. LNCS, vol. 4586, pp. 338–354. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  29. Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 21(2), 120–126 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  30. Rompel, J.: One-way functions are necessary and sufficient for secure signatures. In: Ortiz, H. (ed.) STOC 1990, pp. 387–394. ACM Press, New York (1990)

    Chapter  Google Scholar 

  31. Schnorr, C.P.: Efficient signature generation by smart cards. Journal of Cryptology 4(3), 161–174 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  32. Stevens, M., Lenstra, A.K., de Weger, B.: Chosen-Prefix Collisions for MD5 and Colliding X.509 Certificates for Different Identities. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 1–22. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  33. Stevens, M., Sotirov, A., Appelbaum, J., Lenstra, A., Molnar, D., Osvik, D.A., de Weger, B.: Short Chosen-Prefix Collisions for MD5 and the Creation of a Rogue CA Certificate. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 55–69. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  34. Wang, X., Yin, Y.L., Yu, H.: Finding Collisions in the Full SHA-1. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 17–36. Springer, Heidelberg (2005)

    Google Scholar 

  35. Wang, X., Yu, H.: How to Break MD5 and Other Hash Functions. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 19–35. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  36. Waters, B.: Efficient Identity-Based Encryption Without Random Oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Hong Kong

    Xiao Tan & Duncan S. Wong

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  1. Xiao Tan
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  2. Duncan S. Wong
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Editors and Affiliations

  1. School of Computer Science and Software Engineering, University of Wollongong, Northfields Avenue, NSW, 2522, Wollongong, Australia

    Willy Susilo

  2. School of Computer Science and Software Engineering, University of Wollongong, Northfields Avenue, 2522, Wollongong, NSW, Australia

    Yi Mu

  3. School of Computer Science and Software Engineering, University of Wollongong, Northfields Avenue, 2522, Wollongong, NSW, Australia

    Jennifer Seberry

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Tan, X., Wong, D.S. (2012). Generalized First Pre-image Tractable Random Oracle Model and Signature Schemes. In: Susilo, W., Mu, Y., Seberry, J. (eds) Information Security and Privacy. ACISP 2012. Lecture Notes in Computer Science, vol 7372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31448-3_19

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  • DOI: https://doi.org/10.1007/978-3-642-31448-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31447-6

  • Online ISBN: 978-3-642-31448-3

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