In the field of Cryptography, public key algorithms satisfy all the four requirements of security: Confidentiality, Integrity, Non -repudiation, Authentication as compared to the conventional Crypto system. . RSA and RSA-based digital signature algorithms are some of the most popularly used public-key infrastructure cryptographic algorithms with their roots in the modular arithmetic. Public key Cryptography is widely known to be slower than symmetric key alternatives for massive computations of modular arithmetic. The modular arithmetic and modular exponentiation makes RSA computationally expensive when compared to symmetric algorithms. Therefore, to make a more efficient, secure and faster implementation of RSA Algorithms is publicly concerned. With the development of the OpenMP , more computing problems are solved by using the CPU(Central Processing Unit) based implementation.