On distributed cryptographic protocols for threshold RSA signing and decrypting with no dealer

We consider methods for threshold RSA decryption among distributed agencies without any dealer or trusted party. The first solution is a combination o f two techniques by [9] and [7]. It demonstrates the feasibility of combini ng the distributed key generation and the RSA secure function application. The second solution is another approach making the distributed key distribu tion simpler and alleviating a burden of each shareholder in comparison wit h the first scheme. The latter scheme is newly developed technique based on [9] and further inspired by Simmons' protocol-failure of RSA (we believe t hat it is very interesting that a "protocol failure attack" be turned into a constructive method). Our comparison between these two schemes indicates a new measure of the performance of a distributed cryptographic protocol th at consists of multiple stages.