Practical Signatures from Standard Assumptions

  • Florian Böhl
  • Dennis Hofheinz
  • Tibor Jager
  • Jessica Koch
  • Jae Hong Seo
  • Christoph Striecks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7881)

Abstract

We put forward new techniques for designing signature schemes. As a result, we present practical signature schemes based on the CDH, the RSA, and the SIS assumptions. Our schemes compare favorably with existing schemes based on these assumptions.

Our core idea is the use of tag-based signatures. Concretely, each signatures contains a tag which is uniformly chosen from a suitable tag set. Intuitively, the tag provides a way to embed instances of computational problems. Indeed, carefully choosing these tag spaces provides new ways to partition the set of possible message-tag pairs into “signable” and “unsignable” pairs. In our security proof, we will thus be able to sign all adversarially requested messages, and at the same time use an adversarially generated forgery with suitably large probability.

Keywords

digital signatures CDH assumption pairing-friendly groups RSA assumption SIS assumption 

References

  1. 1.
    Memoirs of the 6th Cryptology Paper Contest, arranged by Korea Communications Commission (2012) Google Scholar
  2. 2.
    Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993, Fairfax, Virginia, USA, November 3-5, pp. 62–73. ACM Press (1993)Google Scholar
  4. 4.
    Boneh, D., Boyen, X.: Short signatures without random oracles. In: Cachin, C., Camenisch, J. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Boneh, D., Boyen, X.: Short signatures without random oracles and the SDH assumption in bilinear groups. Journal of Cryptology 21(2), 149–177 (2008)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Boneh, D., Mironov, I., Shoup, V.: A secure signature scheme from bilinear maps. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 98–110. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Boyen, X.: Lattice mixing and vanishing trapdoors: A framework for fully secure short signatures and more. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 499–517. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Böhl, F., Hofheinz, D., Jager, T., Koch, J., Striecks, C.: Confined guessing: New signatures from standard assumptions. Cryptology ePrint Archive, Report 2013/171 (2013), http://eprint.iacr.org/
  9. 9.
    Cash, D., Kiltz, E., Shoup, V.: The twin diffie-hellman problem and applications. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 127–145. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. 13.
    Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. In: ACM CCS 1999, Kent Ridge Digital Labs., Singapore, November 1-4, pp. 46–51. ACM Press (1999)Google Scholar
  14. 14.
    Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Fischlin, M.: The Cramer-Shoup strong-RSA signature scheme revisited. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 116–129. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Ladner, R.E., Dwork, C. (eds.) 40th ACM STOC, Victoria, British Columbia, Canada, May 17-20, pp. 197–206. ACM Press (2008)Google Scholar
  17. 17.
    Gerbush, M., Lewko, A., O’Neill, A., Waters, B.: Dual form signatures: An approach for proving security from static assumptions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 25–42. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. 18.
    Hofheinz, D., Kiltz, E.: Practical chosen ciphertext secure encryption from factoring. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 313–332. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Hofheinz, D., Kiltz, E.: Programmable hash functions and their applications. Journal of Cryptology 25(3), 484–527 (2012)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    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
  21. 21.
    Hofheinz, D., Jager, T., Knapp, E.: Waters signatures with optimal security reduction. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 66–83. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  22. 22.
    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
  23. 23.
    Hohenberger, S., Waters, B.: Realizing hash-and-sign signatures under standard assumptions. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 333–350. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  24. 24.
    Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: 21st ACM STOC, Seattle, Washington, USA, May 15-17, pp. 44–61. ACM Press (1989)Google Scholar
  25. 25.
    Joye, M.: An efficient on-line/Off-line signature scheme without random oracles. In: Franklin, M.K., Hui, L.C.K., Wong, D.S. (eds.) CANS 2008. LNCS, vol. 5339, pp. 98–107. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  26. 26.
    Krawczyk, H., Rabin, T.: Chameleon signatures. In: NDSS 2000, San Diego, California, USA, February 2-4. The Internet Society (2000)Google Scholar
  27. 27.
    Lu, S., Ostrovsky, R., Sahai, A., Shacham, H., Waters, B.: Sequential aggregate signatures and multisignatures without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 465–485. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  28. 28.
    Döttling, N., Müller-Quade, J., Nascimento, A.C.A.: IND-CCA Secure Cryptography Based on a Variant of the LPN Problem. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 485–503. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  29. 29.
    Rompel, J.: One-way functions are necessary and sufficient for secure signatures. In: 22nd ACM STOC, Baltimore, Maryland, USA, May 14-16, pp. 387–394. ACM Press (1990)Google Scholar
  30. 30.
    Seo, J.H.: Short signature from Diffie-Hellman: Realizing short public key, Cryptology ePrint Archive, Report 2012/480 (2012), http://eprint.iacr.org/2012/480
  31. 31.
    Shamir, A., Tauman, Y.: Improved online/offline signature schemes. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 355–367. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  32. 32.
    Waters, B.: Dual system encryption: Realizing fully secure IBE and HIBE under simple assumptions. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619–636. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  33. 33.
    Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  34. 34.
    Yamada, S., Hanaoka, G., Kunihiro, N.: Space efficient signature schemes from the RSA assumption. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 102–119. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Florian Böhl
    • 1
  • Dennis Hofheinz
    • 1
  • Tibor Jager
    • 2
  • Jessica Koch
    • 1
  • Jae Hong Seo
    • 3
  • Christoph Striecks
    • 1
  1. 1.Karlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Ruhr-Universität BochumBochumGermany
  3. 3.Myongji UniversityYonginRepublic of Korea

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