Date of Award

Fall 1-2026

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Cyber Operations (PhDCO)

First Advisor

Jihene Kaabi EP Harrath

Second Advisor

Austin O’Brien

Third Advisor

Youssef Harrath

Abstract

Although essential, cryptographic security practice often relies on assumptions and abstractions that are difficult to audit under emerging quantum resource models. This creates an unnecessary barrier between the algorithms that govern the connected and the people cryptography protects. Modern cryptography relies on the assumption that computational complexity guarantees security. As algorithms become increasingly complex, their resistance to attack is presumed to increase. Practical constraints suggest that this relationship is neither linear nor indefinite. Resource limitations, algorithmic structure, and pressures from quantum computing introduce points at which added complexity ceases to improve and may instead degrade cryptographic robustness. This dissertation asks whether added algorithmic complexity inherently diminishes cryptographic security. To answer it, we propose and prove a law-like theory of cryptographic feasibility: security resides in finite adversarial feasibility windows, governed by chintropy-based curvature laws, and these windows inevitably collapse—across schemes and parameters—under realistic quantum resource improvements, providing a feasibility engine that complements the Turing and complexity models of computation. We formalize this inherent, fine-grained, and mathematically measurable complexity–security law and introduce a framework that both drastically reduces the effort required for provably optimal parameter selection and, to our knowledge, is the first mathematical language to enable cross-scheme cryptographic security analyses. The work culminates in a holistic formula for cryptographic resilience that replaces binary security assessments with quantitatively grounded feasibility bounds. Regardless of the asymptotic complexity of the underlying problem, operational security is governed by finite feasibility windows that shift under adversarial optimization and hardware improvement. The results therefore complement traditional complexity classes by focusing on secure deployability under bounded budgets and evolving adversarial cost.

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