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Encryption and Decryption schemes based on applications of Laplace Transforms are unable to provide more security to communicate the information. Rivest, Shemir, Adleman (RSA) Cryptosystem is popular public-key algorithm. This paper provides the conditions that give rise to the RSA Cryptosystem based on the Laplace Transform techniques. The modified RSA cryptosystem is explained with an algorithm. The proposed algorithm is implemented using a high level program and time complexity of the proposed algorithm is tested with RSA cryptosystem algorithms. The comparison reveals that the proposed algorithm enhances the data security as compare with RSA cryptosystem algorithms and application of Laplace Transform for cryptosystem scheme. The statistical analysis for the proposed and existing algorithms is provided

ElGamal algorithm is public key cryptosystem and a signature scheme in the speed of the procedures for generating and verifying signatures. An implementation of ElGamal scheme for Laplace Transform Cryptosystem is proposed and it is executed using a .NET program. The time analysis is, compared with existing algorithms. The comparison reveals that the proposed cryptosystem enhances the data security and password security. The statistical tools are use for the planned scheme and accessible algorithms. They are, analyzed graphically.