Falcon Post-Quantum Signature Scheme Proposal

[Giulio Golinelli]

Hi everyone,

I am to share a technical demonstration and benchmarking project that integrates the Falcon post-quantum signature scheme (Falcon-512) into Bitcoin Core, implemented as a soft-fork within the classic P2WPKH mode. This work aims to provide a practical reference for possible future Falcon adoption, especially as it approaches FIPS standardization.
You can find details at this fork.

Why Falcon?

Falcon is a lattice-based, post-quantum digital signature scheme designed to be secure against quantum attacks. Unlike other PQC candidates such as SPHINCS+ and ML-DSA, Falcon offers significantly smaller signature and public key sizes, as well as efficient signing and verification times. It is implemented in pure C and does not require external dependencies.

Benchmarking & Results
Aspect                           Falcon    ECDSA
Public Key Size (B) 897         33
Signature Size (B) 655         71
Verification Time (μs) 57         120

Verification time is more critical than signature creation time in Bitcoin, since signature creation is performed by clients (wallets), while nodes focus on verification.

Integration

• Falcon was included into the codebase from the original GitHub repository.
• The build system (CMakeLists.txt) was updated to support Falcon.
• Falcon verification has been soft-fork enabled via a new script verification flag.

Next Steps & Reference
This project serves as a practical demonstration of Falcon’s promising performance, highlighting its advantages over currently selected post-quantum signature algorithms such as SPHINCS+ and ML-DSA, which face significant time and space limitations. As Falcon approaches FIPS standardization, this work aims to provide a reference for future adoption and integration in Bitcoin.

Let me know what you think and if this could be of interest for which case I can complement the project by integrating Falcon into all the other spending paths. I also look forward to development/integration corrections.

Best regards,
Giulio

[waxwing/ AdamISZ]

Thanks for the report!

Forgive the rather ignorant question here, but:

Given the obvious that we have a problem with size on-chain (and I'm aware you've focused here specifically on the most plausible scheme that has the least ridiculously large size, and yet it's still 20x larger), has there been comparison of the possibility of batched signing (not batched *verification*, but signing) in different PQ schemes, with a view to a CISA like approach to transactions in a future with much larger keys and sigs? A nice side effect might be a pure economic motivation for much better fungibility (coinjoin becoming much more desirable for the base layer, albeit I think it's in higher layers where we are/will be get(ting) most privacy).

A cursory search tells me that Falcon specifically can't support any kind of batched signing, but I have no idea whether that's correct.

Cheers,

AdamISZ/waxwing

[conduition]

Falcon (FN-DSA) relies on discrete gaussian sampling using constant-time floating point arithmetic for signers, which is very hard to implement quickly and in constant time (securely). Despite being significantly harder to implement than ML-DSA, it only provides a mild (factor of two or so) improvement in signature + pubkey size. This is why we're probably not including FN-DSA in our PQ signature opcode BIP following BIP360.

https://blog.cloudflare.com/nist-post-quantum-surprise/#floating-points-falcons-achilles

While I wouldn't rule out Falcon permanently, I personally feel more research is needed to explore Falcon, its weaknesses, and how flexibly it can be adapted to schemes like CISA, BIP32, and multisignatures. Let it bake a little longer.

If small signatures are your goal, then I'd look into SQIsign, which uses isogeny-based cryptography to produce very small sigs (148b) and pubkeys (65b) using some convoluted mathematical tricks. However, much like Falcon, it is still immature and needs more researchers to optimize its verification, explore its strengths, and attack its weaknesses. 

If you want a PQC scheme that's ready today and also provides small signatures, I'll point you to XMSS, and Jonas Nick's SHRINCS proposal. You can configure an unbalanced XMSS tree to get 272 byte signatures, potentially smaller if you crank up the parameters. The catch is a dependence on statefulness. 

regards,

conduition

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