The nature of the RSA public modulus N as a composite of at least two secret large primes was always considered as a major obstacle facing the RSA function sharing without the help of a trusted dealer. The incorporated parties must agree on a suitable RSA modulus with no information revealed to them about its prime factors. Enormous number of trials must be performed before a suitable modulus is established. According to the number theory, for two L-bit primes modulus, the number of trials is in the order. Efforts have been made to reduce the quadratic slowdown in the generation process, however, most of these protocols allow the joint generation of a multi-prime RSA modulus which is a drift from standard.