A new collision resistant hash function based on optimum dimensionality reduction using Walsh-Hadamard transform

Hash functions play the most important role in various cryptologic applications, ranging from data integrity checking to digital signatures. Our goal is to introduce a new hash function using Walsh-Hadamard transform for achieving dimensionality reduction (compression) with a regular and one-way distribution. Merkle-Damgard (MD) transform is applied to this compression function in order to turn it into a hash function. Our algorithm has a flexible framework in which some parameters and steps could be changed according to different needs for more security or less computation time. Our emphasis is on its resistance against some variations of birthday attack. We evaluate collision resistant behavior of this algorithm for some configurations by calculating the balance factor. As we will see our balance factor is very close to SHA-1 ´s. We present some experimental results to determine the balance factor of this algorithm for several output lengths. The experiment is done first, by converting the hash function to a similar one with a lower range size for an exact evaluation. Moreover, for larger range size, we use some bits of the output with a fraction of possible inputs, randomly chosen, to obtain another approximation of its balance factor. We also analyze avalanche effect of our proposed function which is another common measurement for cryptographic hash functions.