## HASH FUNCTION USING FREE GENERATORS THEOREM OVER THE PROJECTIVE GENERAL LINEAR GROUP

## V. V. Kochamani and P. L. Lilly

** DOI:**

https://doi.org/10.37418/amsj.9.4.59

Abstract

We define the projection mapping from an algebraic structure to quotient structure which gives the images in $GL_{3}(F_{q})$.By using Free Generators Theorem,we obtain the set of pair of matrices with entries in $F_{p}[x]$ which is defined in set $\mathbb{D}$.We work with the elements in $\mathbb{D}$ to construct a Cayley Hash function to protect the local modifications property and the security properties of the corresponding hash functions.We can create an infinite number of Hash functions using the Free Generators Theorem by different values of $p$ and $n$.

**Keywords: **Cryptographic Hash Function, General Linear Group, Projective General Linear Group, Projection mapping, Local Modifications Property.