Post-Quantum Cryptography (PQC)
Next-generation cryptographic algorithms designed around mathematical problems that remain hard even for quantum computers.
I. Overview
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flowchart LR
A["Existing\npublic-key cryptography"] -- "Hard problems such as lattice-based math" --> B["Resistance to\nquantum computers"]
style A fill:#f9f9f9,stroke:#333,stroke-width:3px
style B fill:#e1f5fe,stroke:#01579b,stroke-width:3px
Definition: Next-generation cryptographic algorithms designed around complex mathematical problems that remain difficult to solve even with the immense computing power of a quantum computer.
Necessity:
( Responding to the Quantum Threat ) Preparing for the collapse of existing cryptographic systems due to the immense computing power of quantum computers
( Achieving Crypto-Agility ) A flexible cryptographic architecture is required so that new security threats can be responded to quickly
( Long-Term Security ) Proactively strengthens security for critical national infrastructure — public, financial, and defense sectors — in preparation for a future Q-Day
II. Mechanism & Components
A. Fundamental Principles and Transition Architecture
flowchart LR
A["Existing crypto\nRSA / ECC"] -->|"Quantum attack\n(Shor's algorithm)"| B["Q-Day\ndecryption threat"]
B --> C{"Transition method"}
C -->|"Transitional period"| D["Hybrid approach\nexisting + PQC in parallel"]
C -->|"Full transition"| E["PQC-only operation\n(NIST standard algorithms)"]
D --> F["Crypto-Agility\nachieved"]
E --> F
Key point: A “hybrid” approach — running existing cryptography alongside post-quantum cryptography — is emerging as the leading transitional strategy.
B. Major Algorithm Families by Mathematical Foundation
| Category | Mathematical Basis & Features | Representative Algorithms |
|---|---|---|
| Lattice-based | Uses the shortest vector problem (SVP) within a lattice structure; the most efficient and widely used approach | Kyber, Dilithium |
| Code-based | Uses the difficulty of decoding error-correcting codes; long track record of security validation, but larger key sizes | McEliece |
| Multivariate (MV) | Uses the difficulty of solving multivariate quadratic polynomial systems; fast signing speed | Rainbow |
| Hash-based | Uses the security of one-way hash functions; very strong quantum resistance | SPHINCS+ |
III. Outlook & Future Direction
| Algorithm Family | Mathematical Basis | Standardization Status |
|---|---|---|
| Lattice-based | Shortest vector problem (SVP) | NIST-selected (Kyber, Dilithium); most efficient, most widely adopted |
| Code-based | Error-correcting code decoding | Long security track record; larger key sizes limit adoption |
| Multivariate | Multivariate quadratic polynomial systems | Fast signing; narrower deployment |
| Hash-based | One-way hash function security | Very strong quantum resistance (SPHINCS+) |
The realistic transition path is hybrid, not a single cutover date — running existing RSA/ECC alongside PQC during the migration window protects against both a flawed new algorithm and the quantum threat itself, which is why “hybrid” already leads as the transitional strategy rather than serving as a mere stopgap. For any organization holding long-lived sensitive data, “harvest now, decrypt later” is a today problem, not a future one, since data encrypted with classical algorithms now can be stored and broken once a cryptographically relevant quantum computer exists.
Domestic initiatives such as K-PQC that prioritize rollout in the public and financial sectors ahead of a global mandate are a sensible hedge, not overcaution — the sectors holding the most sensitive long-lived data have the least room to wait for full NIST-track maturity.
Last updated 18 Aug 2026, 00:00 UTC.