ADVANCED ANALYSIS OF ONE-WAY FUNCTIONS AND THEIR IMPLICATIONS FOR MODERN CRYPTOGRAPHY
Abstract
This thesis investigates the theoretical foundations, mathematical properties, and practical applications of one-way functions in modern cryptography and information security. One-way functions are characterized by their asymmetry, whereby forward computation is computationally efficient while inversion remains computationally infeasible in the absence of additional secret knowledge. The security of numerous cryptographic primitives, including public-key encryption, digital signature algorithms, authentication mechanisms, and cryptographic hash functions, is fundamentally based on the computational complexity of such functions. The paper presents a comprehensive analysis of prominent one-way function paradigms, including modular exponentiation, integer factorization, discrete logarithm problems, and hash-based constructions. Furthermore, the role of one-way functions in post-quantum cryptography and the design of secure communication systems is critically evaluated. The results demonstrate that one-way functions remain foundational elements for ensuring security, trust, and resilience in contemporary digital infrastructures.
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