A Novel RSA Attack Leveraging Christoffel and Stern-Brocot Tree Properties

A Novel RSA Attack Leveraging Christoffel and Stern-Brocot Tree Properties | 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 Novel RSA Attack Leveraging Christoffel and Stern-Brocot Tree Properties Abhishek Krishnamoorthy, Robinson Thamburaj This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4680852/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This research paper explores the properties of ChristoffelWords, which are formed using a binary alphabet. These words have been extensively studied by Jean Berstel, Christophe Reutenauer, and others, due to their intriguing combinatorial and geometrical characteristics. We have established specific combinatorial properties of the Christoffel and Stern-Brocot trees, which in certain cases can be effectively utilized to compute the modulo multiplicative inverse of a natural number and have also presented a novel algorithm to attack the RSA cryptosystem using this application. Christoffel words Christoffel Tree Stern-Brocot Tree continued fractions modulo multiplicative inverse RSA cryptosystems Full Text Additional Declarations The authors declare no competing interests. Supplementary Files arvindRSA.aux arvindRSA.log arvindRSA.out arvindRSA.synctex.gz arvindRSA.tex empty.eps snjnl.cls Cite Share Download PDF Status: Posted Version 1 posted 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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