What is Post-Quantum Cryptography?

Post-quantum cryptography (PQC) refers to cryptographic algorithms designed to resist attacks from both classical and quantum computers. Today’s widely deployed public-key algorithms – RSA, ECDSA, and Diffie-Hellman – rely on mathematical problems that quantum computers can solve efficiently. PQC replaces them with algorithms grounded in problems believed to remain hard even for large-scale quantum machines.

Why Quantum Computers Threaten Current Cryptography

Shor’s Algorithm Breaks Public-Key Cryptography

In 1994, Peter Shor showed that a sufficiently large quantum computer can factor integers and compute discrete logarithms in polynomial time. This directly breaks:

A quantum computer with roughly 4,000 error-corrected logical qubits could break RSA-2048 in hours. Classical computers would need billions of years for the same task.

Grover’s Algorithm Weakens Symmetric Cryptography

Grover’s algorithm provides a quadratic speedup for searching unstructured databases. Applied to cryptography, it effectively halves the security level of symmetric keys and hash functions:

Algorithm Classical Security Post-Quantum Security
AES-128 128 bits ~64 bits
AES-256 256 bits ~128 bits
SHA-256 256-bit preimage ~128-bit preimage

The practical impact is straightforward: AES-256 remains safe, but AES-128 would need to be upgraded.

Timeline: “Harvest Now, Decrypt Later”

Estimates for when a cryptographically relevant quantum computer (CRQC) will exist vary widely – anywhere from the early 2030s to beyond 2040. However, the “harvest now, decrypt later” threat is real today: adversaries can record encrypted network traffic now and store it until a quantum computer becomes available to decrypt it. Data with long confidentiality requirements (government secrets, medical records, financial data) is already at risk.

NIST PQC Standardization

The U.S. National Institute of Standards and Technology (NIST) began its Post-Quantum Cryptography Standardization process in 2016. After multiple rounds of evaluation, the following standards have been published:

FIPS 203: ML-KEM (Module-Lattice Key Encapsulation)

FIPS 204: ML-DSA (Module-Lattice Digital Signature Algorithm)

FIPS 205: SLH-DSA (Stateless Hash-Based Digital Signature Algorithm)

Falcon (FN-DSA, Pending FIPS 206)

Korean PQC (KPQC) Standards

South Korea has conducted a parallel post-quantum standardization effort through the Korean Post-Quantum Cryptography (KPQC) competition, organized by the Korean Cryptographic Research Association. This process evaluated algorithms specifically suitable for Korean government and industry use cases.

Selected algorithms include:

These algorithms address both domestic Korean compliance requirements and provide additional diversity beyond the NIST selections.

Mathematical Foundations

Post-quantum algorithms draw security from several families of hard mathematical problems:

Lattice Problems (LWE, SIS)

The Learning With Errors (LWE) and Short Integer Solution (SIS) problems involve finding short vectors in high-dimensional lattices. No known quantum algorithm provides a significant speedup for these problems. ML-KEM, ML-DSA, Falcon, and NTRU all rely on lattice hardness.

Hash-Based Security

Hash-based signatures (SLH-DSA) rely only on the security of the underlying hash function. If the hash function is collision-resistant and preimage-resistant, the signature scheme is secure. This is the most conservative approach – it makes the fewest assumptions.

Code-Based Cryptography

Schemes like Classic McEliece use error-correcting codes (Goppa codes). Security relies on the difficulty of the syndrome decoding problem. Code-based cryptography has been studied since 1978 (McEliece cryptosystem) with no known quantum speedup.

MPC-in-the-Head

Algorithms like AIMer construct digital signatures by converting a multi-party computation (MPC) protocol into a non-interactive zero-knowledge proof. Security derives from the underlying symmetric primitives used in the MPC protocol.

How MetaMUI Implements PQC

MetaMUI Crypto Primitives provides 48 cryptographic algorithms across 10 platforms (C, Rust, Go, Python, Java, Kotlin, C#, Swift, TypeScript/WASM, Dart), covering both NIST and KPQC standards. Key design principles:

For guidance on which algorithm to use, see the Algorithm Selector. To understand how cross-platform verification works, see Cross-Language Interoperability.