Abstract

HENSEL LIFTING: A TOOL FOR FAST DECRYPTION PROCESS IN RSA CRYPTOSYSTEM

1 Mesioye, A.E., 1 Ibharalu, F.T., 1 Onashoga, S.A. and 2Olayiwola, O.M.

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Abstract RSA cryptosystem is known for its effective key exchange management, integrity of data and security. The security strength of RSA cryptosystem lies in the size (length) of the keys, which slows down the operation at the decryption stage of the cryptosystem. Chinese Remainder Theorem (CRT) has been employed in the past to increase the overall performance of the RSA cryptosystem (CRT-RSA) but stills possesses time lag in execution. In this work, a modified CRT (MCRT-RSA) is developed to further improve the speed of RSA at the decryption stage. Algorithms of the classical RSA (RSA), CRT-RSA and MCRT-RSA at the decryption stage were implemented using Visual Studio C- sharp. Analysis of algorithms was carried out by measuring the complexity of each RSA variants through the big-O test with six data characters. The three RSA variants were compared using the parameters of time (t_c) and space (S_c) complexities. Results generated by MCRT-RSA indicated O?(n?^2) and O?(n?^3) for t_c and S_c respectively, while t_c and S_c of CRT-RSA were O?(n?^3) and O?(n?^3) respectively and for RSA, t_c and S_c were O?(n?^4) and O?(n?^4) respectively. Conclusively, MCRT-RSA was found to be more efficient in execution time at the cost of memory usage when compared to RSA and CRT- RSA variants. Keywords? Cryptography; Chinese Remainder; Hensel Lifting; Homomorphic encryption; MultiPower RSA; Classical RSA

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