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Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A course in computational algebraic number theory
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The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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Simplified VSS and fast-track multiparty computations with applications to threshold cryptography
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Signature schemes based on the strong RSA assumption
ACM Transactions on Information and System Security (TISSEC)
Communications of the ACM
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
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AINAW '07 Proceedings of the 21st International Conference on Advanced Information Networking and Applications Workshops - Volume 01
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SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
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EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Computing inverses over a shared secret modulus
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
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Catalano, Gennaro and Halevi (2000) present a protocol for the distributed computation of inverses over a shared secret modulus. The most important application of their protocol is the distributed computation of the private RSA key from the public key. The protocol is attractive, because it requires only two rounds of communication in the case of honest but curious players. The present paper gives a modification of this protocol, which reduces its complexity from O (n 3 (logn )2 + n 2 (logn ) (logN ) + (logN )2) to O (n 3 logn + n 2 logN + (logN )2) bit-operations per player, where n is the number of players and N is the RSA modulus. The number of communication rounds is the same as in the original protocol.