This thesis investigates the use of Goldbach partitions for secure communication protocols and for finding large prime numbers that are fundamental to these protocols. It is proposed that multiple third parties be employed in TLS/SSL and secure communication protocols to distribute the trust and eliminate dependency on a single third party, which decreases the probability of forging a digital certificate and enhances the overall security of the system. Two methods are presented in which the secret key is not compromised until all third parties involved in the process are compromised. A new scheme to distribute secret shares using two third parties in the piggy bank cryptographic paradigm is proposed. Conditions under which Goldbach partitions are efficient in finding large prime numbers are presented. A method is also devised to sieve prime numbers which uses less number of operations as compared to the Sieve of Eratosthenes.