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.
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Bach, E., Peralta, R.: Asymptotic semismoothness probabilities. Math. Comput. 65(216), 1701–1715 (1996)
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)
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)
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)
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)
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)
Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited (preliminary version). In: 30th ACM STOC, pp. 209–218. ACM Press, May 1998
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)
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)
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)
Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. In ACM CCS 99, pp. 46–51. ACM Press, November 1999
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)
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)
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)
Granville, A.: Smooth numbers: computational number theory and beyond. Algorithmic Number Theory 44, 267–323 (2008)
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)
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)
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)
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)
Krawczyk, H., Rabin, T.: Chameleon signatures. In NDSS 2000. The Internet Society, February 2000
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)
Zhu, H.: New digital signature scheme attaining immunity to adaptive chosen-message attack. Chinese Journal of Electronics 10(4), 484–486 (2001)
Zhu, H.: A formal proof of zhus signature scheme. Cryptology ePrint Archive, Report 2003/155, 2003. http://eprint.iacr.org/
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)
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Cash, D., Dowsley, R., Kiltz, E. (2015). Digital Signatures from Strong RSA without Prime Generation. In: Katz, J. (eds) Public-Key Cryptography -- PKC 2015. PKC 2015. Lecture Notes in Computer Science(), vol 9020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46447-2_10
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DOI: https://doi.org/10.1007/978-3-662-46447-2_10
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