A Lightweight Variant of Falcon for Efficient Post-Quantum Digital Signature
Kerimbayeva A. Iavich M. Begimbayeva Y. Gnatyuk S. Tynymbayev S. Temirbekova Z. Ussatova O.
July 2025Multidisciplinary Digital Publishing Institute (MDPI)
Information (Switzerland)
2025#16Issue 7
Conventional public-key cryptographic systems are increasingly threatened by advances in quantum computing, accelerating the need for robust post-quantum cryptographic solutions. Among these, Falcon, a compact lattice-based digital signature scheme, has emerged as a leading candidate in the NIST post-quantum standardization process due to its efficiency and theoretical security grounded in hard lattice problems. This work introduces Falcon-M, a modified version of the Falcon algorithm that significantly reduces implementation complexity. It does so by replacing Falcon’s intricate trapdoor-based key-generation mechanism with a simplified approach that utilizes randomized polynomial Gaussian sampling and fast Fourier transform (FFT) operations. Falcon-M incorporates SHA-512 hashing and discrete Gaussian sampling to preserve cryptographic soundness and statistical randomness while maintaining the core structure of Falcon’s signing and verification processes. We formally specify the Falcon-M algorithm, provide an updated pseudocode, and offer a comparative analysis with the original Falcon in terms of algorithmic complexity, security assumptions, and implementation overhead. Additionally, we present formal lemmas and theorems to ensure correctness and define theoretical bounds on forgery resistance. Although Falcon-M does not rely on a formal cryptographic trapdoor, we demonstrate that it achieves strong practical security based on assumptions related to the Short Integer Solution (SIS) problem. Falcon-M is thus well-suited for lightweight post-quantum applications, particularly in resource-constrained environments, such as embedded systems and Internet-of-Things (IoT) platforms.
digital signature , fast Fourier transform , Gaussian distribution , NTRU lattices , post-quantum cryptography
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Department of Cybersecurity, Information Processing and Storage, Satbayev University, 22 Satbayev Str., Almaty, 050013, Kazakhstan
School of Technology, Caucasus University, 1 Paata Saakadze Str., Tbilisi, 0102, Georgia
Institute of Information and Computational Technologies CS MSHE RK, Energo University, 28 Shevchenko Str., Almaty, 050010, Kazakhstan
Faculty of Computer Science and Technology, State University “Kyiv Aviation Institute”, 1 Liubomyra Huzara Ave., Kyiv, 03058, Ukraine
Faculty of Computer Technology and CyberSecurity, International Information Technology University, Manasa Str. 34/1, Almaty, 050040, Kazakhstan
Faculty of Information Technology, Al-Farabi Kazakh National University KazNU, Str. 75/10, Almaty, 050040, Kazakhstan
Department of Cybersecurity
School of Technology
Institute of Information and Computational Technologies CS MSHE RK
Faculty of Computer Science and Technology
Faculty of Computer Technology and CyberSecurity
Faculty of Information Technology
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