BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN PRODID:iCalendar-Ruby BEGIN:VEVENT CATEGORIES:Lectures & Presentations DESCRIPTION:The Mathematics Department Algebra Seminar features Francisco J avier Lobillo Borrero\, Universidad de Granada\, Spain\, discussing "Skew d ifferential Goppa codes and their application to McEliece cryptosystem" on Tuesday\, Sept. 27\, from 4-5 p.m. via Zoom. \n\nZoom information:\n\nhttps ://us06web.zoom.us/j/97235712165?pwd=OHFSL2lXVnVUWU9pdUxRQlhkRG1oUT09Meetin g ID: 972 3571 2165Passcode: 8nuxSQ \n\nAbstract: Code-based cryptography proposals still alive after the Round 4 for the NIST Post-Quantum Cryptogr aphy competition. The strength of these technologies rests upon the hardne ss of the decoding problem for a general linear code. Of course\, an effici ent decoding algorithm is required in practice. So\, what is already needed is a family of codes with some conveniently masked properties that allow their efficient decoding. The original McEliece criptosystem took advantage of such features enjoined by classic Goppa binary codes.\n\n \n\nOne way to introduce Goppa codes is the following. Let \(F \subseteq L\) be a field extension and let \(g \in L[x]\) be a polynomial. A subset of group of uni ts in \(L[x]/\langle g \rangle\) represented by linear polynomials is selec ted\, and their inverses allow to build a parity check matrix of the Goppa code. The arithmetic in \(L[x]\) is a main tool in the design of efficient decoding algorithms for Goppa codes.\n\n \n\nFrom an algebraic point of vie w\, our proposal replaces\, in the simplest case\, the cyclic group of unit s of \(L[x]/\langle g \rangle\) by a general linear group\, whose mathemati cal structure is more complex. In order to design an efficient decoding alg orithm\, this non-commutative group is presented as the group of units of O re polynomials in \(L[x\;\sigma\,\partial]\) modulo a suitable invariant po lynomial \(g\). The arithmetic of this non-commutative polynomial ring is u sed to design efficient decoding algorithms. Classic Goppa codes are instan ces of our construction. Therefore\, the security of our cryptosystem is ex pected to be as strong as the original one. DTEND:20220927T210000Z DTSTAMP:20241123T214705Z DTSTART:20220927T200000Z LOCATION: SEQUENCE:0 SUMMARY:Algebra Seminar | Skew differential Goppa codes and their applicati on to McEliece cryptosystem\, Sept. 27 UID:tag:localist.com\,2008:EventInstance_40994546665018 URL:https://calendar.ohio.edu/event/algebra_seminar_sept_27 END:VEVENT END:VCALENDAR