Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Non-cryptographic fault-tolerant computing in constant number of rounds of interaction
Proceedings of the eighth annual ACM Symposium on Principles of distributed computing
Robust efficient distributed RSA-key generation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Signature schemes based on the strong RSA assumption
ACM Transactions on Information and System Security (TISSEC)
Communications of the ACM
Efficient generation of shared RSA keys
Journal of the ACM (JACM)
Adaptively secure distributed public-key systems
Theoretical Computer Science
Secure Computation without Agreement
DISC '02 Proceedings of the 16th International Conference on Distributed Computing
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Fully Distributed Threshold RSA under Standard Assumptions
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A Statistically-Hiding Integer Commitment Scheme Based on Groups with Hidden Order
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Guaranteed Correct Sharing of Integer Factorization with Off-Line Shareholders
PKC '98 Proceedings of the First International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Fast Software Exponentiation in GF(2^k)
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Modular Multiplication and Base Extensions in Residue Number Systems
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Computing inverses over a shared secret modulus
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Practical threshold signatures
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Constant-Round Multiparty Computation for Interval Test, Equality Test, and Comparison
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Multiparty computation for interval, equality, and comparison without bit-decomposition protocol
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Distributed paillier cryptosystem without trusted dealer
WISA'10 Proceedings of the 11th international conference on Information security applications
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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.