Key Sequences based on Cyclic Elliptic Curves over GF(2⁸) with Logistic Map for Cryptographic Applications

Abstract

The chaotic functions and cyclic elliptic curves (CEC) has attracted many researchers, especially cryptographers, since decades. As CEC and chaotic functions meet the requirements of the cryptography, they are widely used either in key sequence generation or encryption/decryption process. Since in symmetric key encryption, stream ciphers need a large key sequence to encrypt/decrypt the information, authors propose a hybrid model to generate pseudo random sequence using CEC and logistic map. The hybrid model is developed using CEC points over GF(2 8 ) and an one-dimensional logistic map. In the proposed system, binary chaotic sequence and CEC points are given to AES S-box to get two random sequences separately. Byte wise parity is computed for both the sequences. Based on the parity of both the bytes, one of the byte is left shifted and the other is right shifted by two positions in a circular manner. Later, both the bytes are combined using the XOR operation to get the random binary sequence. The generated sequences are analysed for randomness using various test suites like NIST, Correlation, FIPS, and TestU01. It has been observed that all the sequences pass the randomness tests. Using additive stream cipher, image encryption is implemented by considering the generated sequence as key sequence. The performance evaluation and security analysis of the encryption process is conducted. The results obtained for the proposed system indicate that the system is robust to withstand many cryptanalytic attacks.