Cohomology-Based Quantum Obfuscation of Group Periods: Using Galois Cohomology and Non-Split Extensions to Subvert Quantum Period-Finding Algorithms

Quantum Fourier Transform (QFT)-based attacks such as Shor’s algorithm rely critically on detecting algebraic periodicity in abelian groups. These structures, however, become non-trivial to analyze under group extensions that introduce obfuscating cohomological noise. This paper proposes a novel cryptographic framework wherein classical periodic group structures are camouflaged using Galois cohomology via non-split exact sequences, thus nullifying the effectiveness of QFT-based period detection. We define and construct cohomological extensions over group actions where the second cohomology group H ² (G, A) encodes obfuscating twistings, producing pseudo-periodicities imperceptible to standard quantum techniques. We prove that under these conditions, group elements cannot be harmonically decomposed due to ambiguity in orbit lifting and cocycle resolutions. Furthermore, we demonstrate via simulated quantum interference experiments (in .NET Core) that Fourier peaks vanish under these twisted extensions, effectively impeding any constructive period recovery. Our contributions include a full mathematical construction of such group cohomology models, a cryptographic embedding protocol, and a simulation engine that visualizes and quantifies the decay in periodic signal under Shor-style quantum attacks. We conclude by outlining future cryptosystems based on non-split extensions and the role of higher-degree cohomology in cryptographic hardening.