  In this paper we present an improved version of HF-hash, viz., GB-hash : Hash
Functions Using Groebner Basis. In case of HF-hash, the compression function
consists of 32 polynomials with 64 variables which were taken from the first 32
polynomials of hidden field equations challenge-1 by forcing last 16 variables
as 0. In GB-hash we have designed the compression function in such way that
these 32 polynomials with 64 variables form a minimal Groebner basis of the
ideal generated by them with respect to graded lexicographical (grlex) ordering
as well as with respect to graded reverse lexicographical (grevlex) ordering.
In this paper we will prove that GB-hash is more secure than HF-hash as well as
more secure than SHA-256. We have also compared the efficiency of our GB-hash
with SHA-256 and HF-hash.
