Post-Quantum Cryptography: What It Is and How to Learn It

The threat: why Shor's algorithm breaks current encryption

RSA and elliptic curve cryptography (ECC) -- the public-key systems securing most internet traffic, financial transactions, and government communications -- rely on mathematical problems that are computationally hard for classical computers. RSA's security rests on the difficulty of factoring large integers. ECC relies on the discrete logarithm problem over elliptic curves. These problems have no known classical algorithms that scale efficiently.

Shor's algorithm, published in 1994, solves both integer factoring and discrete logarithms in polynomial time on a quantum computer. A quantum computer running Shor's algorithm on a sufficiently large number of qubits could break RSA-2048 and ECC-256 in hours, compared to the billions of years required by the best known classical algorithms. This means that once large fault-tolerant quantum computers exist, all current public-key infrastructure is vulnerable.

The threat is not only future -- it is already present. "Harvest now, decrypt later" (HNDL) attacks are being conducted today: adversaries record encrypted data now and plan to decrypt it retroactively when quantum computers mature. Communications that must remain confidential for 10-20 years are already at risk. See the Shor's algorithm guide for a detailed technical explanation.

The NIST PQC standards (2024)

After a multi-year evaluation process involving submissions from cryptographers worldwide, NIST finalized its first post-quantum cryptography standards in 2024. These are the algorithms governments and companies are migrating to now.

PQC vs QKD: two very different approaches

Two quantum-safe security technologies are often confused: post-quantum cryptography (PQC) and quantum key distribution (QKD). They solve related problems through completely different means.

For most organizations, PQC is the relevant technology. QKD is a niche solution for high-value, high-budget scenarios where classical channels cannot be trusted at all.

Who needs to learn PQC

Post-quantum cryptography is no longer a purely academic concern. Three groups have concrete, immediate reasons to understand it:

• Security engineers. Implementing PQC in TLS, SSH, certificate infrastructure, and application-layer protocols is becoming a job requirement. Understanding which algorithms to use, how hybrid classical-PQC schemes work during the transition period, and how to integrate PQC libraries into existing systems is practical, deployable knowledge.
• Policy and governance professionals. Regulatory mandates (NIST, NSA, EU NIS2) are driving PQC migration requirements across critical infrastructure. Security leaders need to understand PQC well enough to assess their organization's exposure, build a migration roadmap, and communicate risk to boards and regulators.
• Quantum computing learners. Understanding Shor's algorithm and its cryptographic implications is an important part of understanding why quantum computing matters. The connection between quantum algorithms and real-world security infrastructure is one of the field's most compelling stories.