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We present a new protocol for efficient distributed computation modulo a shared secret. We further present a protocol to distributively generate a random shared prime or safe prime that is much more efficient than previously known methods. This allows one to distributively compute shared RSA keys, where the modulus is the product of two safe primes, much more efficiently than was previously known.

Efficient Computation Modulo a Shared Secret with Application to the Generation of Shared Safe-Prime Products