A Fast Method for Finding Separable Goppa Polynomials Used in Post-Quantum McEliece-Based Cryptography

A Fast Method for Finding Separable Goppa Polynomials Used in Post-Quantum McEliece-Based Cryptography | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Fast Method for Finding Separable Goppa Polynomials Used in Post-Quantum McEliece-Based Cryptography Mariano López-García, Enrique Cantó-Navarro This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6511517/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Oct, 2025 Read the published version in EURASIP Journal on Information Security → Version 1 posted 10 You are reading this latest preprint version Abstract This paper introduces a simple and efficient method for generating Goppa polynomials used in post-quantum cryptography based on any variant of the McEliece algorithm. The approach demonstrates that such polynomials can be constructed more rapidly by multiplying several low-degree polynomials that satisfy specific properties. It is also proven that employing these polynomials does not compromise the code's error-correcting capability or overall security. The proposed method is especially advantageous when high-order Goppa polynomials are required. As a proof of concept, we present an application for user identification that combines cryptography and iris biometrics. In this system, encrypted versions of iris templates are securely stored. Using the homomorphic property of McEliece, recognition can be performed within the encrypted domain, ensuring that biometric data remains confidential throughout the entire process. Post-Quantum cryptography McEliece biometrics iris recognition Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 24 Oct, 2025 Read the published version in EURASIP Journal on Information Security → Version 1 posted Editorial decision: Revision requested 31 Jul, 2025 Reviews received at journal 18 Jun, 2025 Reviewers agreed at journal 30 May, 2025 Reviewers agreed at journal 29 May, 2025 Reviews received at journal 26 May, 2025 Reviewers agreed at journal 26 May, 2025 Reviewers invited by journal 22 May, 2025 Editor assigned by journal 21 May, 2025 Submission checks completed at journal 25 Apr, 2025 First submitted to journal 23 Apr, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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