Generation of Pseudo Random Sequences based on Chaotic Cubic Map and Cyclic Elliptic Curves over GF (28) for Cryptographic Applications

Abstract

Cyclic elliptic curves (CEC) and chaotic sequences are used for cryptographic application from many decades. In this paper, authors propose a hybrid model to generate pseudo random key sequences for symmetric ciphers. Hybrid model is developed using CEC points over GF (28) and a one-dimensional cubic map. In the proposed system first, binary chaotic sequence and CEC points are given to AES SBOX to get two random sequences separately. Byte wise parity is computed for both the sequences. Based on the parity the sequences are either left or right circular shifted by a byte and two sequences are combined using the XOR operation to get the random binary sequence. The randomness of the generated sequences is analysed using various randomness test suites like NIST SP 800-22 Rev.1a and Correlation. It has been observed that all the sequences pass the randomness tests. These sequences are used to encrypt an image using additive stream cipher algorithm. The security analysis of the cipher image is conducted. The results obtained for the proposed system indicates that it is secure against cryptographic attacks.