A Robust Hash Function Using Cross-Coupled Chaotic Maps with Absolute-Valued Sinusoidal Nonlinearity

This paper presents a compact and effective chaosbased keyed hash function implemented by a cross-coupled topology of chaotic maps, which employs absolute-value of sinusoidal nonlinearity, and offers robust chaotic regions over broad parameter spaces with high degree of randomness through chaoticity measurements using the Lyapunov exponent. Hash function operations involve an initial stage when the chaotic map accepts initial conditions and a hashing stage that accepts input messages and generates the alterable-length hash values. Hashing performances are evaluated in terms of original message condition changes, statistical analyses, and collision analyses. The results of hashing performances show that the mean changed probabilities are very close to 50%, and the mean number of bit changes is also close to a half of hash value lengths. The collision tests reveal the mean absolute difference of each character values for the hash values of 128, 160 and 256 bits are close to the ideal value of 85.43. The proposed keyed hash function enhances the collision resistance, comparing to MD5 and SHA1, and the other complicated chaos-based approaches. An implementation of hash function Android application is demonstrated. Keywords—Hash Function; Cross-Coupled Chaotic Map; Sinusoidal Nonlinearity; Information security; Authentication