Abstract

Abstract. We propose a threshold RSA scheme which is as efficient as the fastest previous threshold RSA scheme (by Shoup), but where two assumptions needed in Shoup’s and in previous schemes can be dropped, namely that the modulus must be a product of safe primes and that a trusted dealer generates the keys. The robustness (but not the unforgeability) of our scheme depends on a new intractability assumption, in addition to security of the underlying standard RSA scheme. 1

Citations

331	Security and Composition of Multiparty Cryptographic Protocols - Canetti - 2000
240	Approximate formulas for some functions of prime numbers - Rosser, Schoenfeld - 1962
173	Practical threshold signatures - Shoup - 2000
162	A Threshold Cryptosystem without a Trusted Party - Pedersen - 1991
112	Efficient generation of shared rsa keys - Boneh, Franklin
107	Secure distributed key generation for discrete-log based cryptosystems - Gennaro, Jarecki, et al. - 1999
66	Robust and efficient sharing of RSA functions - Gennaro, Jarecki, et al.
25	A Unified Framework for Analyzing Security of Protocols - Canetti
19	E#cient generation of shared RSA keys - Boneh, Franklin - 1997
12	Robust ecient distributed RSA-key generation - Frankel, MacKenzie, et al. - 1998
10	Robust and ecient sharing of RSA functions - Gennaro, Jarecki, et al. - 1996
8	Sharing Decryption in the Context of Voting or - Fouque, Poupard, et al. - 2000
3	and Moti Yung Robust Efficient Distributed RSA-Key Generation - Frankel, MacKenzie
2	Practical Threshold Signatures, Proceedings of EuroCrypt 2000, Springer Verlag LNCS series nr. 1807. BRICS Report Series Publications RS-00-30 Ivan B. Damg˚ard and Maciej Koprowski. Practical Threshold RSA Signatures Without a Trusted Dealer - Shoup - 2000
1	Jurik: A Generalization and some Applications of Paillier’s Probabilistic Public-key System - Damg˚ard
1	and Moti Yung Optimal-Resilience Proactive Public-Key Cryptosystems - Frankel, Gemmell, et al.
1	Kouichi Sakurai and Moti Yung On Threshold RSA-Signing with no Dealer - Miyazaki