A cryptographic model based on logistic map and a 3-D matrix

Abstract

A new data encryption scheme is proposed based on the position substitution, shuffling and a diffusion process. The algorithm searches for the position of a text symbol in randomly generated 3-D matrix and subsequently replaces the symbol. The positions in matrix are shuffled in a retraceable manner depending upon the encryption key. Further, the substituted positions are diffused so that all the cipher text get affected even if a single symbol is changed. The system uses a Logistic map for matrix generation and position shuffling. The algorithm also checks the integrity of cipher text by including its parity in encrypted form. As the system includes substitution, permutation and diffusion, high level of cryptographic complexity is achieved in cipher text. The proposed method is key sensitive output cipher text is random in nature and has avalanche effect. The key length chosen is sufficient to resist a brute force attack. The cryptographic model as a whole demonstrate remarkable resistance to statistical attacks which is a key feature. Detailed runtime comparison with different known cryptographic systems is given.