Lattice-Based: Uses hard problems in high-dimensional lattices; strong candidates like CRYSTALS-Dilithium (signatures) and CRYSTALS-Kyber (key exchange) are NIST standards.
Hash-Based: Relies on hash functions (e.g., SHA-3), offering simple, fast, but often stateful signatures (e.g., SPHINCS+).
Code-Based: Based on error-correcting codes, known for large keys but robust security (e.g., McEliece).
Multivariate: Uses complex systems of polynomial equations (e.g., Rainbow, though weakened).
Implementation Strategies for Blockchains
Replace Digital Signatures: Substitute current signatures (ECDSA) with PQC alternatives for new transactions and key generation.
Hybrid Systems: Combine classical and PQC signatures during transition for backward compatibility.
Signature Aggregation: Combine multiple signatures into one to reduce blockchain bloat.
State Proofs: Securely attest to past ledger states, as pioneered by Algorand with FALCON.
Hash Functions: Upgrade hash functions to be quantum-resistant (e.g., SHA-3).
Challenges & Considerations
Larger Keys/Signatures: PQC schemes often result in bigger data, impacting storage and bandwidth.
Performance Trade-offs: Larger sizes can slow down transaction processing and consensus.
Protocol Redesign: Requires significant changes to consensus mechanisms and data structures.
Examples in Use
Algorand: Uses FALCON for State Proofs to secure ledger history.
Other Projects: Exploring Dilithium, SPHINCS+, and hybrid approaches for quantum readiness.
