{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:50:00Z","timestamp":1787028600851,"version":"3.56.0"},"reference-count":27,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T00:00:00Z","timestamp":1751328000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Satbayev University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>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\u2019s 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\u2019s 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.<\/jats:p>","DOI":"10.3390\/info16070564","type":"journal-article","created":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T09:29:01Z","timestamp":1751362141000},"page":"564","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Lightweight Variant of Falcon for Efficient Post-Quantum Digital Signature"],"prefix":"10.3390","volume":"16","author":[{"given":"Aigerim","family":"Kerimbayeva","sequence":"first","affiliation":[{"name":"Department of Cybersecurity, Information Processing and Storage, Satbayev University, 22 Satbayev Str., Almaty 050013, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3109-7971","authenticated-orcid":false,"given":"Maksim","family":"Iavich","sequence":"additional","affiliation":[{"name":"School of Technology, Caucasus University, 1 Paata Saakadze Str., Tbilisi 0102, Georgia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yenlik","family":"Begimbayeva","sequence":"additional","affiliation":[{"name":"Institute of Information and Computational Technologies CS MSHE RK, Energo University, 28 Shevchenko Str., Almaty 050010, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4992-0564","authenticated-orcid":false,"given":"Sergiy","family":"Gnatyuk","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science and Technology, State University \u201cKyiv Aviation Institute\u201d, 1 Liubomyra Huzara Ave., 03058 Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sakhybay","family":"Tynymbayev","sequence":"additional","affiliation":[{"name":"Faculty of Computer Technology and CyberSecurity, International Information Technology University, Manasa Str. 34\/1, Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhanerke","family":"Temirbekova","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Al-Farabi Kazakh National University KazNU, Str. 75\/10, Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olga","family":"Ussatova","sequence":"additional","affiliation":[{"name":"Institute of Information and Computational Technologies CS MSHE RK, Energo University, 28 Shevchenko Str., Almaty 050010, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1145\/359340.359342","article-title":"A Method for Obtaining Digital Signatures and Public-Key Cryptosystems","volume":"21","author":"Rivest","year":"1978","journal-title":"Commun. 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