The Quantum Challenge to Cryptography: from Threat to Catalyst

The security of the modern Internet depends on a small set of mathematical problems that classical computers cannot solve efficiently. In 1994, Shor's algorithm disrupted the foundation of these mathematical problems, rendering RSA, Diffie-Hellman, and elliptic curve cryptography theoretically broken. No quantum computer capable of this has been built, yet the prospect alone has set off the largest coordinated transition in the history of applied cryptography. This thesis looks at that challenge from a specific angle: quantum computing has not only endangered cryptography, but it has also catalyzed the most rigorous and systematic restructuring of cryptographic practice in the internet era. The work is a literature review based on NIST post-quantum standards, foundational quantum algorithm papers, and resource estimation research. The analysis shows that the harvest now, decrypt later (HNDL) threat makes the migration to post-quantum cryptography necessary even before a cryptographically relevant quantum computer becomes available. The FIPS 203, 204, and 205 standards, the hybrid key exchange already active in major browsers, and the crypto agility as a design principle are concrete outcomes of this pressure, confirming the central thesis.