Short answer: Falcon is a lattice-based signature scheme that NIST selected for standardization as FN-DSA, and FIPS 206 is still in development. Its signing relies on (possibly emulated) floating-point arithmetic, which a 2024 paper says is often regarded as a cause for concern. A 2025 project description proposes implementing Falcon without floating point, as a research goal.
What Falcon is
The Falcon design document describes Falcon, short for Fast-Fourier Lattice-based Compact Signatures over NTRU, as a lattice-based signature scheme. It instantiates the framework of Gentry, Peikert and Vaikuntanathan for hash-and-sign lattice signatures, using NTRU lattices and a trapdoor sampler the authors call fast Fourier sampling. A 2025 project description says Falcon was selected in 2022 by NIST as the future standard FN-DSA after five years of scrutiny, and that it has compact signature sizes and fast verification. FIPS 206 for FN-DSA is still in development.
Where floating point comes in
A 2024 paper from the IACR ePrint archive says Falcon is the most compact of the three post-quantum signature schemes selected by NIST, and offers excellent efficiency and security. It adds that Falcon is based on a complex algorithm for lattice discrete Gaussian sampling which presents a number of implementation challenges. In particular, the paper says, it relies on possibly emulated floating-point arithmetic, which is often regarded as a cause for concern and has been used in side-channel analysis. The design document has a section on floating point in its chapter on implementation and performance.
What the 2024 paper found
The paper says the extent to which Falcon's use of floating-point arithmetic can cause security issues has yet to be thoroughly explored in the literature. It contributes by identifying a way in which Falcon's lattice discrete Gaussian sampler, because of specific design choices, is singularly sensitive to floating-point errors. The authors say small floating-point discrepancies can occur in various ways, including through the use of the two almost but not quite equivalent signing procedures, called dynamic and tree, that the Falcon API exposes. This article does not reproduce the paper's further results, which readers should take from the paper.
The goal of removing floating point
A 2025 project description says Falcon's reliance on floating-point arithmetic presents implementation challenges, particularly for constrained devices, secure hardware implementations, and environments where floating-point support is limited or unavailable. It says the removal of floating-point arithmetic and the adoption of a fully integer-based approach would significantly enhance Falcon's portability, performance and security on various platforms. The project's goal is to implement Falcon without floating-point arithmetic, starting by understanding the existing scheme and identifying where floating point is used, then developing alternative methods using integer arithmetic. This is a plan for research. No result is claimed here.
What this does not tell you
This article summarises one paper's abstract, the Falcon design document and a project description. It says nothing about any product, and it does not claim that Falcon implementations are insecure.
FAQ
What is Falcon?
A lattice-based signature scheme, described in its design document as Fast-Fourier Lattice-based Compact Signatures over NTRU. NIST selected it for standardization as FN-DSA, and FIPS 206 is still in development.
Why is floating point a concern?
A 2024 paper says Falcon relies on possibly emulated floating-point arithmetic, which is often regarded as a cause for concern and has been used in side-channel analysis.
What did the 2024 paper identify?
That Falcon's lattice discrete Gaussian sampler is singularly sensitive to floating-point errors, because of specific design choices.
Why would a constrained device struggle?
A 2025 project description says reliance on floating point creates challenges on constrained devices, secure hardware and environments with limited or no floating-point support.
Has an integer-only Falcon been built?
The 2025 project description sets it as a goal. This article reports no finished result.
All field notes