Abstract
We present a new protocol for efficient distributed computation modulo a shared secret. We further present a protocol to distributively generate a random shared prime or safe prime that is much more efficient than previously known methods. This allows one to distributively compute shared RSA keys, where the modulus is the product of two safe primes, much more efficiently than was previously known.
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A. V. Aho, J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison Wesley, 1974.
J. Algesheimer, J. Camenisch, and V. Shoup. Efficient computation modulo a shared secret with application to the generation of shared safe-prime products. http://www.eprint.iacr.org/2002/029, 2002.
G. Ateniese, J. Camenisch, M. Joye, and G. Tsudik. A practical and provably secure coalition-resistant group signature scheme. In Advances in Cryptology — CRYPTO 2000, vol. 1880 of LNCS, pp. 255–270, 2000.
J. Bar-Ilan and D. Beaver. Non-cryptographic fault-tolerant computing in a constant number of rounds of interaction. In 8th ACM PODC, pp. 201–209, 1989.
M. Ben-Or, S. Goldwasser, and A. Wigderson. Completeness theorems for noncryptographic fault-tolerant distributed computation. In Proc. 20th STOC, pp. 1–10, 1988.
D. Boneh and M. Franklin. Efficient generation of shared RSA keys. In Advances in Cryptology — CRYPTO’ 97, vol. 1296 of LNCS, pp. 425–439, 1997.
J. Camenisch and A. Lysyanskaya. Efficient non-transferable anonymous multishow credential system with optional anonymity revocation. In Advances in Cryptology — EUROCRYPT 2001, vol. 2045 of LNCS, pp. 93–118, 2001.
R. Canetti. Security and composition of multi-party cryptographic protocols. Journal of Cryptology, 13(1):143–202, 2000.
D. Catalano, R. Gennaro, and S. Halevi. Computing inverses over a shared secret modulus. In EUROCRYPT 2000, vol. 1807 of LNCS, pp. 190–206, 2000.
T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, 1992.
R. Cramer and V. Shoup. Signature schemes based on the strong RSA assumption. In Proc. 6th ACM CCS, pp. 46–52. ACM press, nov 1999.
R. Cramer and V. Shoup. Signature schemes based on the strong RSA assumption. ACM Transactions on Information and System Security, 3(3):161–185, 2000.
I. Damgøard and M. Koprowski. Practical threshold RSA signatures without a trusted dealer. In EUROCRYPT 2001, vol. 2045 of LNCS, pp. 152–165, 2001.
U. Feige, A. Fiat, and A. Shamir. Zero-knowledge proofs of identity. Journal of Cryptology, 1:77–94, 1988.
P.-A. Fouque and J. Stern. Fully distributed threshold RSA under standard assumptions. In ASIACRYPT 2001, vol. 2248 of LNCS, pp. 310–330, 2001.
Y. Frankel, P. MacKenzie, and M. Yung. Robust efficient distributed RSA key generation. In Proc. 30th Annual ACM STOC, pp. 663–672, 1998.
M. Franklin and S. Haber. Joint encryption and message-efficient secure computation. In CRYPTO’ 93, vol. 773 of LNCS, pp. 266–277, 1994.
R. Gennaro, S. Halevi, and T. Rabin. Secure hash-and-sign signatures without the random oracle. In EUROCRYPT’ 99, vol. 1592 of LNCS, pp. 123–139, 1999.
R. Gennaro, S. Jarecki, H. Krawczyk, and T. Rabin. Robust and efficient sharing of RSA functions. In Advances in Cryptology — CRYPT0’ 96, vol. 1109 of LNCS, pp. 157–172, 1996.
R. Gennaro, M. O. Rabin, and T. Rabin. Simplified VSS and fast-track multiparty computations with applications to threshold cryptography. In Proc. 17th ACM PODC, 1998.
T. Rabin. A simplified approach to threshold and proactive RSA. In Advances in Cryptology — CRYPTO’ 98, vol. 1642 of LNCS, pp. 89–104, 1998.
A. Shamir. How to share a secret. Communications of the ACM, 22(11):612–613, Nov. 1979.
V. Shoup. Practical threshold signatures. In Advances in Cryptology: EUROCRYPT 2000, vol. 1087 of LNCS, pp. 207–220, 2000.
M. M. T. Wu and D. Boneh. Experimenting with shared generation of RSA keys. In Proceedings of the Internet Society’s 1999 Symposium on Network and Distributed System Security (SNDSS), pp. 43–56, 1999.
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Algesheimer, J., Camenisch, J., Shoup, V. (2002). Efficient Computation Modulo a Shared Secret with Application to the Generation of Shared Safe-Prime Products. In: Yung, M. (eds) Advances in Cryptology — CRYPTO 2002. CRYPTO 2002. Lecture Notes in Computer Science, vol 2442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45708-9_27
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DOI: https://doi.org/10.1007/3-540-45708-9_27
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