cryptographic hash function is a deterministic procedure that compresses an arbitrary block of numerical data and returns a fixed-size bit string. There exist many hash functions: MD5, HAVAL, SHA, … It was reported that these hash functions are not longer secure. Our work is focused in the construction of a new hash function based on composition of functions. The construction used the NP-completeness of Three-dimensional contingency tables and the relaxation of the constraint that a hash function should also be a compression function.