Fast Three-Party Shared Generation of RSA Keys Without Distributed Primality Tests

Distributed primality tests for the purpose of testing the factors of the jointly generated RSA modulus were always considered as a nightmare due to the large amount of time required for this test to succeed. Enormous number of trials must be performed before a suitable RSA modulus is established. In this paper we propose a protocol to allow three parties to share the generation of a RSA modulus N and to share the secret key d. The protocol enjoys the following properties which do not exist in previous protocols: • The protocol does not need any distributed primality tests. The three parties are able to find a suitable modulus from the first trial without any additional tests. • The protocol can generate a RSA modulus which is a composite of safe primes. • The protocol is less vulnerable to the RSA attacks in [26, 27].

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