Algorithmic Number Theory University of Bordeaux
In this course we will discuss several aspects of algorithmic numbertheory closely related to cryptography.
> Applicants should: - Have completed, with good results, a Bachelor of science degree inMathematics or equivalent. - Have thorough proficiency in written and spoken English.
Exams take place in December.
> The course will be organized as follows: - In the first part we will discuss classical algorithms forprimality and factorisation. - The second part will be an introduction to quantum algorithms, inview of a discussion of Shor quantum algorithm for factorization anddiscrete log problem, which are of (quantum) polynomial complexity. - In the third part, we will discuss Euclidean lattices, and theirrecent applications to cryptography that (conjecturally) resistquantum algorithms.> The course will be illustrated by programming sessions using SAGE.> Bibliography: - J. von zur Gathen and J. Gerhard: Modern computer algebra,Cambridge University Press, New York,1999. - A. M. Childs and W. van Dam: Quantum algorithms foralgebraicproblems, Reviews of Modern Physics, 2010 - C. Peikert: A Decade of Lattice Cryptography[https://web.eecs.umich.edu/~cpeikert/pubs/lattice-survey.pdf], 2016.
> Lectures and practical work: - 48 course hours. - 120 hours of personal study.
Online Course Requirement
- This course is part of the ALGANT Joint Master Program. - For further information on the program structure, partnerinstitutions, scholarship opportunities, etc., please visit: ALGANTErasmus Mundus. [http://algant.eu/]Duration: 12 weeks (Fall Semester)Language of instruction: EnglishMode of delivery: Face-to-face teaching
Site for Inquiry
Please inquire about the courses at the address below.
Contact person: Xavier Carusoxavier.firstname.lastname@example.orgJean-Marc Couveignesjeanemail@example.comGilles Zemorgilles.firstname.lastname@example.org