Abstract
We describe protocols for three or more parties to jointly generate a composite N=pqr which is the product of three primes. After our protocols terminate N is publicly known, but neither party knows the factorization of N. Our protocols require the design of a new type of distributed primality test for testing that a given number is a product of three primes. We explain the cryptographic motivation and origin of this problem.
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M. Ben-Or, S. Goldwasser, and A. Wigderson. Completeness theorems for noncryptographic fault tolerant distributed computation. In Proceedings of the 20th Annual ACM Symposium on Theory of Computing, pages 1–10. ACM Press, 1988.
D. Boneh and M. Franklin. Efficient generation of shared RSA keys. In Proceedings of Advances in Cryptology: CRYPTO '97, pages 425–439. Lecture Notes in Computer Science, Springer-Verlag, New York, 1998.
M. Blum and S. Goldwasser. An efficient probabilistic public key encryption scheme that hides all partial information. In Proceedings of Advances in Cryptology: CRYPTO '84, pages 289–302. Lecture Notes in Computer Science, Springer-Verlag, New York, 1985.
D. Chaum, C. Crépeau, and I. Damgård. Multiparty unconditionally secure protocols. In Proceedings of the 20th Annual ACM Symposium on Theory of Computing, pages 11–19. ACM Press, 1988.
C. Cocks. Split knowledge generation of RSA parameters. Available from the author (cliff_cocks@cesg. gov.uk).
R. Fagin, M. Naor, and P. Winkler. Comparing information without leaking it. Communications of the ACM, 39(5):77–85, May 1996.
Y. Frankel. A practical protocol for large group oriented networks. In Proceedings of Advances in Cryptology: EUROCRYPT '88, pages 56–61. Lecture Notes in Computer Science, Springer-Verlag, New York, 1990.
Y. Frankel, P. MacKenzie, and M. Yung. Robust efficient distributed RSA key generation. Preprint.
P. Gemmel. An introduction to threshold cryptography. CryptoBytes (a technical newsletter of RSA Laboratories), 2(7), 1997.
J. Grantham. A probable prime test with high confidence. Available online (http://www.clark.net/pub/grantham/pseudo/).
R. Peralta and J. van de Graaf. A simple and secure way to show the validity of your public key. In Proceedings of Advances in Cryptology: CRYPTO '87, pages 128–134. Lecture Notes in Computer Science, Springer-Verlag, New York, 1988.
A. Lenstra and H. W. Lenstra ed. The development of the number field sieve. Lecture Notes in Computer Science 1554, Springer-Verlag, 1994.
H. W. Lenstra. Factoring integers with elliptic curves. Annals of Mathematics, 126:649–673, 1987.
A. Shamir. How to share a secret. Communications of the ACM, 22(11):612–613, November 1979.
M. Wiener. Cryptanalysis of short RSA secret exponents. IEEE Transactions on Information Theory, 36(3):553–558, 1990.
A. Yao. How to generate and exchange secrets. In Proceedings of the 27th Annual ACM Symposium on Theory of Computing, pages 162–167. IEEE Press, 1986.
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Boneh, D., Horwitz, J. (1998). Generating a product of three primes with an unknown factorization. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054866
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DOI: https://doi.org/10.1007/BFb0054866
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