Statistical Analysis of Hybrid AES using Cryptographically Secure Pseudorandom Bit Generator

Abstract

The perpetual evolution of cryptanalytic techniques necessitates continuous reinforcement of established cryptographic standards. The Advanced Encryption Standard (AES) is a cornerstone of modern information security, yet its theoretical susceptibility to attacks, particularly when implemented with predictable or non-random components, remains a subject of academic enquiry. This paper investigates a hybrid cryptographic approach to enhance the statistical randomness of AES-generated ciphertext. The primary objective is to evaluate whether integrating cryptographically secure pseudorandom number generator (CSPRNG) at the pre-encryption stage can produce ciphertext with superior statistical properties. We encrypt a large plaintext, over 150,000 characters, using three distinct methodologies: original AES, AES hybridized with GF7 PRNG (AESGF7) and AES hybridized with the Blum-Blum-Shub (BBS) generator (AESBBS). Each method is executed with 300 unique cryptographic keys to generate a robust sample set of ciphertext. The statistical quality of the resulting binary sequences is rigorously assessed using the complete 15-test suite from the National Institute of Standards and Technology (NIST) Statistical Test Suite (STS). The findings, based on analyses of pass proportions and p-value distributions, reveal a complex relationship between hybridization and randomness. While both hybrid models generally improve the passing rates over original AES, the AESBBS variant introduces significant non-uniformity in its p-value distributions for several tests, a subtle statistical flaw. In contrast, the AESGF7 model not only enhances passing rates but also maintains uniform p-value distribution across all tests. This research concludes that the GF7-based hybrid approach offers a more balanced and statistically sound improvement, effectively strengthening resilience against statistical attacks without introducing new, undesirable artifacts.