Chaotic Complex Hashing: A simple chaotic keyed hash function based on complex quadratic map

Abstract

In the last two decades, the use of chaotic iterative maps in cryptographic systems, especially chaotic hash functions, has been expanding. Sensitivity to small changes in initial conditions and control parameters in chaotic systems is the best feature for designing a chaotic hash function. This paper introduces a new generalized chaotic map based on a complex quadratic map, which in addition to the chaotic behavior in the real and imaginary parts, also has a high key length, which can guarantee the security of a cryptographic system. Various analyses of dynamical systems, such as the bifurcation diagram and the Lyapunov exponent, show that the proposed chaotic map has the characteristics of a chaotic dynamical system. The foundation of a secure and efficient algorithm for designing and developing a new hash function lies in how to use this new chaotic map. Also, statistical analysis, collision analysis, key space analysis, and speed analysis use to prove the security and efficiency of the proposed method. The results of these analyses and their comparison with similar methods show that the proposed method can be a reliable and efficient method for practical applications in information technology.