We propose a hash function based on arithmetic coding and public-key cryptography. The resistance of the hash function to second preimage attack, collision and differential cryptanalysis is based on the properties of arithmetic coding as a non-linear dynamical system. The resistance of the hash function to first preimage attack is based on the public-key cryptography. The new hash function uses the strength of HMAC with the difference that it didn't need a secret key for calculating the hash (in this step, it uses one, two or three public -keys) and in the classical attack, an adversary need to break the public key algorithm or to have all the secret keys to perform his attack.