Attacks and Defenses for Single-Stage Residue Number System PRNGs

This paper explores the security of a single-stage residue number system (RNS) pseudorandom generator (PRNG), which has previously been shown to provide extremely high-quality outputs when evaluated through available RNG statistical test suites or in using Shannon and Kolmogorov entropy metrics. In contrast, rather than blindly performing analyses on RNS PRNG, this provides both white box black that facilitate reverse engineering underlying generation algorithm obtain residues, equivalently key, algorithm. We develop demonstrate conditional analysis permits extraction key given priori knowledge state transitions as well PRNG parameters (but not key) problems where multiplicative characteristic is too large transitions. then discuss multiple defenses perturbations for fool original attack algorithm, including deliberate noise injection code hopping. present modification accounts noise, but rapidly increases search space complexity. Lastly, we memory requirements time required attacker defender maintain these defenses.