Abstract
We develop a method for generating shared, secret, safe primes applicable to use in threshold RSA signature schemes such as the one developed by Shoup. We would like a scheme usable in practical settings, so our protocol is robust and efficient in asynchronous, hostile environments. We show that the techniques used for robustness need special care when they must be efficient. Specifically, we show optimizations that minimize the number and size of the proofs of knowledge used. We also develop optimizations based on computer arithmetic algorithms, in particular, precomputation and Montgomery modular multiplication.
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Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, p. 207. Springer, Heidelberg (2000)
Algesheimer, J., Camenisch, J.L., Shoup, V.: Efficient computation modulo a shared secret with application to the generation of shared safe-prime products. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 417–432. Springer, Heidelberg (2002)
Fouque, P.-A., Stern, J.: Fully distributed threshold RSA under standard assumptions. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 310–330. Springer, Heidelberg (2001)
Damgård, I.B., Koprowski, M.: Practical Threshold RSA Signatures Without a Trusted Dealer. Technical Report RS-00-30, Basic Research in Computer Science, University of Aarhus (2000)
Malkin, M., Wu, T., Boneh, D.: Experimenting with Shared Generation of RSA keys. In: Symposium on Network and Distributed System Security, pp. 43–56 (1999)
Cramer, R., Shoup, V.: Signature Schemes Based on the Strong RSA Assumption. ACM Transactions on Information and System Security 3, 161–185 (2000)
Catalano, D., Gennaro, R., Halevi, S.: Computing inverses over a shared secret modulus. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 190–207. Springer, Heidelberg (2000)
Boneh, D., Franklin, M.: Efficient generation of shared RSA keys. Journal of the ACM (JACM) 48, 702–722 (2001)
Frankel, Y., MacKenzie, P.D., Yung, M.: Robust Efficient Distributed RSA-Key Generation. In: Annual ACM Symposium on Theory of Computing (1998)
Goldwasser, S., Lindell, Y.: Secure Multi-Party Computation Without Agreement. In: Malkhi, D. (ed.) DISC 2002. LNCS, vol. 2508, pp. 17–32. Springer, Heidelberg (2002)
Shamir, A.: How to share a secret. Communications of the ACM 22 (1979)
Damgård, I., Fujisaki, E.: A Statistically-Hiding Integer Commitment Scheme Based on Groups with Hidden Order. In: ASIACRYPT, pp. 125–142 (2002)
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for noncryptographic fault-tolerant distributed computation. In: Annual ACM Symposium on Theory of Computing, pp. 1–10 (1988)
Mao, W.: Guaranteed correct sharing of integer factorization with off-line shareholders. In: Imai, H., Zheng, Y. (eds.) PKC 1998. LNCS, vol. 1431, pp. 60–71. Springer, Heidelberg (1998)
Montgomery, P.L.: Modular Multiplication Without Trial Division. Mathematics of Computation 44, 519–521 (1985)
Bajard, J.C., Didier, L.S., Kornerup, P.: Modular Multiplication and Base Extensions in Residue Number Systems. In: Proceedings of the 15th IEEE Symposium on Computer Arithmetic, pp. 59–65 (2001)
C¸ .K. Ko¸c, Acar, T.: Fast Software Exponentiation in GF(2k). In: Symposium on Computer Arithmetic, pp. 225–231 (1997)
Bar-Ilan, J., Beaver, D.: Non-Cryptographic Fault-Tolerant Computing in a Constant Number of Rounds of Interaction. In: 8th ACM Symposium on Principles of Distributed Computation, pp. 201–209 (1989)
Frankel, Y., MacKenzie, P., Yung, M.: Adaptively secure distributed public-key systems. Theoretical Computer Science 287, 535–561 (2002)
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Ong, E., Kubiatowicz, J. (2005). Optimizing Robustness While Generating Shared Secret Safe Primes. In: Vaudenay, S. (eds) Public Key Cryptography - PKC 2005. PKC 2005. Lecture Notes in Computer Science, vol 3386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30580-4_9
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DOI: https://doi.org/10.1007/978-3-540-30580-4_9
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