This article analyzes the profound impact of quantum computing on modern cryptographic systems. It explores the computational complexity theory framework to assess the vulnerability of current cryptographic mechanisms, which rely on complex mathematical problems. The analysis confirms that symmetric cryptography and hash functions remain relatively secure against quantum attacks, primarily threatened by Grover's algorithm. In contrast, widely used public-key cryptosystems are critically vulnerable to Shor's algorithm. The study concludes by examining the transition to post-quantum cryptography, highlighting the challenges of efficiency, trust, and usability that must be overcome before these new algorithms can be widely deployed.

Cryptography, Quantum Computing, Shor’s Algorithm

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