This paper proposes a novel hash algorithm whose security is based on the multivariate nonlinear polynomial equations of NP-hard problem over a finite field and combines with HAIFA iterative framework. Over the current widely used hash algorithms, the new algorithm has the following advantages: its security is based on a recognized difficult mathematical problem; the hash length can be changed freely; its design can be automated such that users may construct specific hash function meeting the actual needs. Furthermore, we discuss the security, efficiency and performance of the new algorithm. Under some related difficult mathematical assumptions and theoretical analysis, the new algorithm is proven practical by the experiment results, and capable of achieving security of an ideal hash function by choosing suitable parameters. In addition, it can also be used as a pseudo-random number generator for the good randomness of its output. This paper proposes a novel hash algorithm whose security is based on the multivariate nonlinear polynomial equations of NP-hard problem over a finite field and combines with HAIFA iterative framework. The new widely has has the following advantages: its the design of the security is based on a recognized difficult mathematical problem; the hash length can be changed freely; its design may be automated such that users may construct specific hash function meeting the actual needs Under some related difficult mathematical assumptions and theoretical analysis, the new algorithm is proven practical by the experiment results, and capable of achieving security an ideal hash function by choosing suitable parameters. In addition, it can also be used as a pseudo-random number generator for the good randomness of its output.