Abstract
This paper explains how to design fully secure RSA-type cryptosystems from schemes only secure against passive attacks, in the standard model. We rely on instance-independence assumptions, which, roughly speaking, conjecture that for certain problems, an interactive access to a solver for another problem does not help the challenger. Previously, instance-independence assumptions were used in a “negative” way, to prove that certain schemes proven in the random oracle model were not provable in the standard model.
Our paradigm applies virtually to all (weakly secure) RSA-type encryption schemes for which public-key RSA exponent can be arbitrarily chosen. As an illustration, we present a chosen-ciphertext secure variant of the Naccache-Stern encryption scheme.
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References
Abe, M., Cui, Y., Imai, H., Kiltz, E.: Efficient hybrid encryption from ID-based encryption. In: Designs, Codes and Cryptography (to appear)
Bellare, M., Namprempre, C., Pointcheval, D., Semanko, M.: The one-more-RSA-inversion problems and the security of Chaum’s blind signature scheme. Journal of Cryptology 16(3), 185–215 (2003)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: CCS 1993, pp. 62–73. ACM Press, New York (1993)
Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)
Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM Journal on Computing 36(5), 915–942 (2006)
Boneh, D., Katz, J.: Improved efficiency for CCA-secure cryptosystems built using identity- based encryption. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 87–103. Springer, Heidelberg (2005)
Brassard, G., Chaum, D., Crépeau, C.: Minimum disclosure proofs of knowledge. Journal of Computer and System Sciences 37(2), 156–189 (1988)
Camenisch, J., Stadler, M.: Efficient group signature schemes for large groups (extended abstract). In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 410–424. Springer, Heidelberg (1997)
Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 207–222. Springer, Heidelberg (2004)
Catalano, D., Gennaro, R., Howgrave-Graham, N., Nguyen, P.Q.: Paillier’s cryptosystem revisited. In: CCS 2001, pp. 206–214. ACM Press, New York (2001)
Chevallier-Mames, B., Joye, M.: Chosen-ciphertext secure RSA-type cryptosystems. In: Full version of this paper, available from Cryptology ePrint Archive, http://eprint.iacr.org/2009/377
Chevallier-Mames, B., Naccache, D., Stern, J.: Linear bandwidth Naccache-Stern encryption. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 327–339. Springer, Heidelberg (2008)
Coppersmith, D.: Small solutions to polynomial equations, and low exponent RSA vulnerabilities. Journal of Cryptology 10(4), 233–260 (1997)
Coron, J.-S., Naccache, D.: Security analysis of the Gennaro-Halevi-Rabin signature scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 91–101. Springer, Heidelberg (2000)
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)
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)
Dent, A.W.: A brief history of provably secure public-key encryption. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 357–370. Springer, Heidelberg (2008)
Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. SIAM Journal on Computing 30(2), 391–437 (2000)
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)
Fujisaki, E., Okamoto, T.: How to enhance the security of public-key encryption at minimum cost. IEICE Transaction of Fundamentals of Electronic Communications and Computer Science E83-A(1), 24–32 (2000)
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)
Girault, M.: An identity-based identification scheme based on discrete logarithms modulo a composite number. In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 481–486. Springer, Heidelberg (1991)
Gjøsteen, K.: A new security proof for Damgård’s ElGamal. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 150–158. Springer, Heidelberg (2006)
Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28(2), 270–299 (1984)
Kiltz, E.: Chosen-ciphertext security from tag-based encryption. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 581–600. Springer, Heidelberg (2006)
Krawczyk, H., Rabin, T.: Chameleon signatures. In: Network and Distributed System Security Symposium (NDSS 2000), pp. 143–154. Internet Society (2000)
Kurosawa, K., Desmedt, Y.: A new paradigm of hybrid encryption scheme. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 426–442. Springer, Heidelberg (2004)
Lipmaa, H.: On CCA1-security of ElGamal and Damgård’s ElGamal. Cryptology ePrint Archive. In: Report 2008/234 (2008)
Micali, S., Schnorr, C.-P.: Efficient, perfect polynomial random number generators. Journal of Cryptology 3(3), 157–172 (1991)
Miller, G.L.: Riemann’s hypothesis and tests for primality. Journal of Computer and System Sciences 13(3), 300–317 (1976)
Naccache, D., Stern, J.: A new public-key cryptosystem. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 27–36. Springer, Heidelberg (1997)
Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: 22nd ACM STOC, pp. 427–437. ACM Press, New York (1990)
Paillier, P.: Impossibility proofs for RSA signatures in the standard model. In: Abe, M. (ed.) CT-RSA 2007. LNCS, vol. 4377, pp. 31–48. Springer, Heidelberg (2007)
Paillier, P., Villar, J.L.: Trading one-wayness against chosen-ciphertext security in factoring-based encryption. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 252–266. Springer, Heidelberg (2006)
Pandey, O., Pass, R., Vaikuntanathan, V.: Adaptive one-way functions and applications. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 57–74. Springer, Heidelberg (2008)
Phan, D.H., Pointcheval, D.: Chosen-ciphertext security without redundancy. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 1–18. Springer, Heidelberg (2003)
Pointcheval, D.: New public key cryptosystems based on the dependent-RSA problems. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 239–254. Springer, Heidelberg (1999)
Poupard, G., Stern, J.: Security analysis of a practical “on the fly” authentication and signature generation. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 422–436. Springer, Heidelberg (1998)
Rackoff, C., Simon, D.R.: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 433–444. Springer, Heidelberg (1992)
Shoup, V.: Why chosen ciphertext security matters. Technical Report RZ 3076, IBM Research (November 1998)
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Chevallier-Mames, B., Joye, M. (2009). Chosen-Ciphertext Secure RSA-Type Cryptosystems. In: Pieprzyk, J., Zhang, F. (eds) Provable Security. ProvSec 2009. Lecture Notes in Computer Science, vol 5848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04642-1_5
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