Abstract
At Crypto’97 Boneh and Franklin proposed a protocol to eciently generate shared RSA keys. In the case of two parties, the drawback of their scheme is the need of an independent third party. Furthermore, the security is guaranteed only if the three players follow the protocol. In this paper, we propose a protocol that enables two parties to evaluate any algebraic expression, including an RSA modulus, along the same lines as in the Boneh-Franklin protocol. Our solution does not need the help of a third party and the only assumption we make is the existence of an oblivious transfer protocol. Furthermore, it remains robust even if one of the two players deviates from the protocol.
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M. Bellare and S. Micali. Non-Interactive Oblivious Transfer and Application. In Crypto’ 89, LNCS 435, pages 547–557. Springer-Verlag, 1990.
M. Ben-Or, S. Goldwasser, and A. Wigderson. Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation. In Proc. of the 20th STOC, pages 1–10. ACM Press, 1988.
C.H. Bennett, G. Brassard, C. Crépeau, and M.-H. Skubiszewska. Practical Quantum Oblivious Transfer. In Crypto’ 91, LNCS 576, pages 351–366. Springer-Verlag, 1992.
S. Blackburn, S. Blake-Wilson, M. Burmester, and S. Galbraith. Shared Generation of Shared RSA Keys. Technical Report CORR 98-19, University of Waterloo, 1998. Available at http://www.cacr.math.uwaterloo.ca.
D. Boneh and M. Franklin. Efficient Generation of Shared RSA Keys. In Crypto’ 97, LNCS 1294, pages 425–439. Springer-Verlag, 1997.
G. Brassard, C. Crépeau, and J-M. Robert. Information Theoretic Reductions among Disclosure Problems. In Proc. of the 21th FOCS, pages 168–173. IEEE, 1986.
G. Brassard, C. Crépeau, and J-M. Robert. All-or Nothing Disclosure of Secrets. In Crypto’ 86, LNCS 263, pages 234–238. Springer-Verlag, 1987.
D. Ohaum, O. Orépeau, and I. Damgård. Multiparty Unconditionally Secure Protocols. In Proc. of the 20th STOC, pages 11–19. ACM Ptess, 1988.
B. Chot and E. Kushilevitz. A Zeto-One Law for Boolean Privacy. In Proc. of the 21st STOC, pages 62–72. ACM Press, 1989.
C. Cocks. Split Knowledge Generation of RSA Parameters. In Cryptography and Coding; Proceedings of 6th IMA Conference, LNCS 1355, pages 89–95. Springer-Verlag, 1997.
C. Cocks. Split Generation of RSA Parameters with Multiple Participants. Technical report, 1998. Available at http://ww.cesg.gov.uk.
C. Crépeau and J. Kilian. Achieving Oblivious Transfer Using Weakened Security Assumptions. In Proc. of the 29th FOCS, pages 42–52. IEEE, 1988.
C. Crépeau, J. van de Graaf, and A. Tapp. Commited Oblivious Transfer and Private Multy-Party Computation. In Crypto’ 95, LNCS 963, pages 110–123. Springer-Verlag, 1995.
S. Even, O. Goldreich, and A. Lempel. A Randomized Protocol for Signing Contracts. Communications of the ACM, 28:637–647, 1985.
Y. Frankel, P. MacKenzie, and M. Yung. Robust Efficient Distributed RSA-Key Generation. In Proc. of the 30th STOC. ACM Press, 1998.
O. Goldreich, S. Micali, and A. Wigderson. How to Play any Mental Game. In Proc. of the 19th STOC, pages 218–229. ACM Press, 1987.
S. Goldwasser, S. Micali, and C. Rackoff. The Knowledge Complexity of Interactive Proof Systems. SIAM journal of computing, 18(1):186–208, february 1989.
J. Kilian. Founding Cryptography on Oblivious Transfer. In Proc. of the 20th STOC, pages 20–31. ACM Press, 1988.
D. Naccache and J. Stern. A New Public Key Cryptosystem Based on Higher Residues. In Proc. of the 5th CCCS. ACM press, 1998.
D. Pointcheval and J. Stern. Security Proofs for Signature Schemes. In Eurocrypt’ 96, LNCS 1070, pages 387–398. Springer-Verlag, 1996.
M. Rabin. How to exchange secrets by oblivious transfer. Technical Report TR-81, Harvard Aiken Computation Laboratory, 1981.
J.N. Rosser and L. Schoenfeld. Approximate Formulas for some Functions of Prime Numbers. Illinois Journal of Mathematics, 6(l):64–94, march 1962.
K. Sakurai and H. Shizuya. A Structural Comparison of the Computational Difficulty of Breaking Discrete Log Cryptosystems. Journal of Cryptology, 11(l):29–43, 1998.
S. Spalding and R. Wright. Experimental Performance of Shared RSA Modulus Generation. In proc. of Algorithms and Experiments 93, pages 34–43, 1998.
J.P. Stern. A New and Efficient All-Or-Nothing Disclosure of Secrets Protocol. In Asiacrypt’ 98, LNCS. Springer-Verlag, 1998.
A. C. Yao. How to Generate and Exchange Secrets. In Proc. of the 27th FOCS, pages 162–167. IEEE, 1986.
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Poupard, G., Stern, J. (1998). Generation of Shared RSA Keys by Two Parties. In: Ohta, K., Pei, D. (eds) Advances in Cryptology — ASIACRYPT’98. ASIACRYPT 1998. Lecture Notes in Computer Science, vol 1514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49649-1_2
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