An Effective Statistical Test Suite for Pseudorandom number Generators in Digital Signatures and Security Robustness Evaluation including a Wavelet Test for Randomness

The need for random and pseudorandom numbers arises in many cryptographic applications including digital signatures management. For instance, common cryptosystems employ keys that must be generated in a random fashion. Many cryptographic protocols also require random or pseudorandom inputs at various points, e.g., for auxiliary quantities used in generating digital signatures, or for generating challenges in authentication protocols. A suitable set of statistical tests for randomness of message digests (MD5, SHA) and digital signatures DSA algorithms is outlined and evaluated in this paper based mainly on the revisions of National Institute of Standards and Technology (NIST) procedures in detecting deviations of a binary sequence from randomness. Although such an analysis exists for AES standard there is no similar study for message digests or digital signatures. The contribution of this paper lies in the attempt to fill in this gap from an educational point of view, providing relevant plots of the derived sequences, as well as to introduce a novel Discrete Wavelet Transform Test for Randomness.