Abstract

The advent of large-scale quantum computing poses a fundamental threat to classical public-key cryptographic systems underpinning modern digital infrastructure. Widely deployed schemes such as RSA and elliptic curve cryptography rely on computational hardness assumptions—integer factorization and discrete logarithms—that are vulnerable to quantum algorithms such as Shor's algorithm. As critical infrastructure systems increasingly depend on secure communication, authentication, and data integrity mechanisms, the transition to quantum-resistant cryptography has become an urgent national and global priority. This paper examines the mathematical foundations of post-quantum cryptography (PQC) and their application to data protection in critical infrastructure environments, analyzes core hardness assumptions underlying leading PQC families, proposes a quantum-readiness framework for critical infrastructure sectors, and presents empirical benchmarking results across energy, healthcare, financial, and transportation systems. By integrating rigorous mathematical analysis with experimental performance data, this work provides a structured roadmap for transitioning mission-critical systems toward quantum-resilient data protection architectures.

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