How Can Bitcoin Resist Quantum Computers? A Comparative Analysis of Three Lattice-Based Signature Schemes
This report from Blockstream Research analyzes three lattice-based signature schemes as quantum-resistant candidates for Bitcoin, focusing on Dilithium, Falcon, and the now-withdrawn Hawk. Core evaluation criteria include on-chain costs (combined size of public key and signature), implementation complexity, deployment risks, and potential for integration with Bitcoin's existing infrastructure like BIP-32 hierarchical deterministic wallets.
Key Findings:
* **Dilithium** is praised for its design simplicity, using only integer operations, making secure implementation easier. However, it has the largest size (5,261 bytes for security level 3).
* **Falcon** offers the most compact signatures and the fastest verification. Its main drawback—platform-dependent floating-point operations in signing—can be mitigated with a slower, deterministic integer-based implementation. The report recommends **Falcon-1024** (security level 5) for its safety margin.
* **Hawk**, which aimed for a better balance, was withdrawn after a cryptographic attack revealed a structural flaw that halved its estimated security.
The report concludes that Falcon-1024 is the most suitable lattice-based choice for Bitcoin, pending the finalization of its NIST FN-DSA standard. In the short term, it still recommends hash-based signatures (like SPHINCS+) as a lower-risk transitional solution, with future hybrid deployments as a possibility.
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