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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:20240520T025038Z
DTSTART:20220927T200000Z
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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
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