We consider methods for threshold RSA decryption among distributed agencies without any dealer or trusted party. We present two methods: One is based on the previous two techniques by [FMY98] and [FGMY97]. It demonstrates the feasibility of combining the distributed key generation and the RSA secure function application. The other method [MS99] is newly developed technique based on [FMY98] and further inspired by Simmons’ protocol-failure of RSA (we believe that it is very interesting that a “protocol failure attack” be turned into a constructive method!). The latter requires less “distributed computation” as the key is being set up and it can be more smoothly incorporated into the existing distributed key generation techniques.