Digital Signatures from Strong RSA without Prime Generation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9020)

Abstract

We construct a signature scheme that is proved secure, without random oracles, under the strong RSA assumption. Unlike other efficient strong-RSA based schemes, the new scheme does not generate large prime numbers during signing. The public key size and signature size are competitive with other strong RSA schemes, but verification is less efficient. The new scheme adapts the prefix signing technique of Hohenberger and Waters (CRYPTO 2009) to work without generating primes.

Keywords

Digital signatures Strong RSA 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bach, E., Peralta, R.: Asymptotic semismoothness probabilities. Math. Comput. 65(216), 1701–1715 (1996)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Barić, N., Pfitzmann, B.: Collision-free accumulators and fail-stop signature schemes without trees. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 480–494. Springer, Heidelberg (1997) CrossRefGoogle Scholar
  3. 3.
    Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 93, pp. 62–73. ACM Press, Nov. (1993)CrossRefGoogle Scholar
  4. 4.
    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) CrossRefGoogle Scholar
  5. 5.
    Böhl, F., Hofheinz, D., Jager, T., Koch, J., Seo, J.H., Striecks, C.: Practical signatures from standard assumptions. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 461–485. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  6. 6.
    Camenisch, J.L., Lysyanskaya, A.: Signature schemes and anonymous credentials from bilinear maps. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 56–72. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  7. 7.
    Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited (preliminary version). In: 30th ACM STOC, pp. 209–218. ACM Press, May 1998Google Scholar
  8. 8.
    Catalano, D., Fiore, D., Warinschi, B.: Adaptive pseudo-free groups and applications. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 207–223. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  9. 9.
    Coron, J.-S., Handschuh, H., Naccache, D.: ECC: Do We Need to Count? In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 122–134. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  10. 10.
    Coron, J.-S., Naccache, D.: Security Analysis of the Gennaro-Halevi-Rabin Signature Scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, p. 91. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  11. 11.
    Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. In ACM CCS 99, pp. 46–51. ACM Press, November 1999Google Scholar
  12. 12.
    Dodis, Y., Oliveira, R., Pietrzak, K.: On the generic insecurity of the full domain hash. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 449–466. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  13. 13.
    Fischlin, M.: The Cramer-Shoup strong-RSA signature scheme revisited. In: Desmedt, Y. (ed.) PKC 2003, volume of. LNCS, vol. 2567, pp. 116–129. Springer, Heidelberg (2003)Google Scholar
  14. 14.
    Gennaro, R., Halevi, S., Rabin, T.: Secure Hash-and-Sign Signatures without the Random Oracle. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, p. 123. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  15. 15.
    Granville, A.: Smooth numbers: computational number theory and beyond. Algorithmic Number Theory 44, 267–323 (2008)MathSciNetGoogle Scholar
  16. 16.
    Guillou, L.C., Quisquater, J.-J.: A Practical Zero-Knowledge Protocol Fitted to Security Microprocessor Minimizing Both Transmission and Memory. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 123–128. Springer, Heidelberg (1988) CrossRefGoogle Scholar
  17. 17.
    Hofheinz, D., Jager, T., Kiltz, E.: Short Signatures from Weaker Assumptions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 647–666. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  18. 18.
    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) CrossRefGoogle Scholar
  19. 19.
    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) CrossRefGoogle Scholar
  20. 20.
    Krawczyk, H., Rabin, T.: Chameleon signatures. In NDSS 2000. The Internet Society, February 2000Google Scholar
  21. 21.
    Kurosawa, K., Schmidt-Samoa, K.: New online/offline signature schemes without random oracles. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 330–346. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  22. 22.
    Zhu, H.: New digital signature scheme attaining immunity to adaptive chosen-message attack. Chinese Journal of Electronics 10(4), 484–486 (2001)Google Scholar
  23. 23.
    Zhu, H.: A formal proof of zhus signature scheme. Cryptology ePrint Archive, Report 2003/155, 2003. http://eprint.iacr.org/
  24. 24.
    Fujisaki, E., Okamoto, T.: Statistical zero knowledge protocols to prove modular polynomial relations. In: Kaliski Jr, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 16–30. Springer, Heidelberg (1997) CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceRutgers UniversityNew BrunswickUSA
  2. 2.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyKarlsruheGermany
  3. 3.Horst Görtz Institute for IT-SecurityRuhr-Universität BochumBochumGermany

Personalised recommendations