Assessing mathematically the effectiveness of a data encryption model

The most popular RSA cryptography produced long ciphertext, decelerated the encryption and decryption time and was unsuitable for encrypting the credit and debit card data. Some studies by combining prime factorization method and discrete logarithm proposed hybrid encryption systems, however, they failed to indicate if these systems could create small ciphertext, accelerate the encryption and decryption time and were suitable for encrypting data embedded within the small devices. Developing countries encountered encryption problems because they lacked researches in finding an efficient encryption model which would support the encryption of the credit and debit card data. This problem could be addressed by generating a data encryption model and comparing its efficiency with the RSA in terms of the ciphertext sizes and the encryption and decryption computation time. The purpose of this experimental study was to compare between the ciphertext sizes, encryption and decryption times when the mathematical operations of the data encryption model a ≡ b(xy)modq modp were used to encrypt and decrypt the customer verification values (CVV) and the ciphertext sizes, encryption and decryption times when the RSA cryptography was applied to encrypt and decrypt the same CVVs. The independent variable in the research was the data encryption model and the dependent variables were the ciphertext sizes, encryption and decryption computation times. The researcher encrypted randomly generated thirty-five CVV numbers and decrypted a single CVV with 354 iterations by using Mathematica 9 and Maple 17. The researcher conducted t-tests for the paired differences between the means for testing the null hypotheses. The t-statistics values were -2.963, -29.107 and -14.666 and their corresponding p-values were .041, 0.000008, and 0.000126. The null hypotheses were rejected at the 95% level of significance and the alternative hypotheses were accepted. The research revealed that the data encryption model produced smaller ciphertext and faster encryption and decryption times than the RSA. Future researches were recommended for exploring the effectiveness of the data encryption model in encrypting the alphabets, its security level, its implementation cost and whether the model would produce smaller cipher text and accelerate the encryption and decryption time than the symmetric key cryptography.