Falcon: digital signature based on NTRU

Introduction

NIST’s Post-Quantum standardization process has identified two cryptographic schemes based on lattice theory within digital signatures: CRYSTALS-Dilithium and Falcon.

Within modern cryptographic communication protocols, these solutions will replace the schemes currently used for digital signatures, which are vulnerable to attack by a quantum computer.

While Dilithium has been selected as the primary solution, Falcon may prove more appropriate in particular application scenarios as highlighted by NIST. For example, a more favorable element of Falcon is the ability to transmit a signature in a single IP packet, avoiding fragmentation issues.

On the other hand, Falcon’s design is more complex to understand and implement. The construction is based on three main ingredients: the NTRU mathematical problem, the GPV framework for lattice-based digital hash-and-sign signatures, and the Fast Fourier Sampling signature method.

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The author

Francesco Stocco, a master’s degree in Mathematics from the University of Padua and the Université de Bordeaux attending the Algebra Geometry And Number Theory (ALGANT) program, joined the Telsy Cryptography Research Group in late 2020.