2009/2010 Summer Session Research Scholarship Project

Supervisor: Luke McAven

Title: An Investigation of the Cycle Structure of Short Digest Cryptographic

Hash Functions.

Project Description:

Hash functions are widely used in cryptography as a means of producing a small message dependent digest. Hash chains involve the repeated action of the hash function on the output from the hash function, with the action being many-to-one and the chains necessary eventually resulting in cycles. In this research the cycle structure of hash functions with short message digests will be investigated, experimentally and theoretically. By restricting our attention to short hash functions we can reasonably carry out experiments. Hash functions of length 32 would be probably be prohibitively long for the experimental aspects of this research. We expect the computational experiments to form a basis for a theoretical analysis of the possible cycle structures.

Expected Outcome:

One outcome should be code functionality capable of appropriately describing the cycle structure of a linked-in hash function. Experimental results regarding the application of this to certain reduced hash functions are expected as illustrations. On the theoretical side we expect a report on the possible cycle structures of hash functions. This is leading in the direction of identifying useful cycle structures for hash functions to have, and possibly as a means for identifying subsets of hash families of short hash functions that could be used in distributed calculations of longer hash functions.