Modified Form of Cayley Hash Function

In 1994 (AT CRYPTO94) introduced the celebrated Zemor-Tillich hash function over SL2(F2n) is mathematically very efficient and simple method but now finally it was broken by Grassl et al., 2011. Yet with a new choice of generators Zemor-Tillich constructions still remains of interest and a lot of construction was based on this type of hash function was created. One of our new construction is the devised Hash Function as follows: to an arbitrary text of {0, 1} *, associate the string of {A, B} obtained by substituting 0 for A and 1 for B, then assign to A and B values of adequately chosen matrices of Heis(Z). Now, in this paper we suggest a new version of a Cayley hash function using a discrete Heisenberg group. The Hashed value is the computed product. We improved the security Properties of the Cayley Hash Function. Here we hold a different concept to form a Factorisation Problem harder. We hold an efficient way to impose limits on the type of factorisations for attacking H.