LUC Cryptosystem is a public key cryptosystem based on Lucas Function. It is first discussed by Smith and Lennon in 1993. They proposed a new public key system using Lucas Function instead of using exponentiation based as found in RSA. Lucas Function is the second order linear recurrence relation. The computation of LUC Cryptosystem is based on the computation of Lucas Function. Many of the existing computation algorithms for Lucas Function are suitable for one processor and there is no problem to design a computation algorithm for one processor as the Lucas Function can be implemented directly into programming codes. In this paper, the Binary Numbers will be used as a technique for parallel computation algorithm. The encryption process using Ve(P,1)(mod N) to get ciphertext, C from plaintext, P. While the decryption used Vd(C,1)(mod N) to get P from C. Meanwhile N is the product of two relatively primes p and q. In this case, the public key e (usually in decimal numbers) will be converted to the Binary Numbers. Then, this number will be use in manipulating the Lucas Functions properties such as V2n, V2n+1 and V2n-1 to find the fast computation techniques for Lucas Functions. Both processes run on special distributed memory multiprocessors machine known as Sun Fire V1280. The proposed techniques can reduce a computation time for LUC Cryptosystem computation compare to the computation algorithm for one processor. As a comparison, the computation time for one processor and several numbers of processors are also included.