Sharp interpolation of rational points and post-quantum cryptography

Abstract: For curves, it is more or less conjectured that the Chabauty method with the Mordell–Weil sieve will give a polynomial-time algorithm for finding the sets of rational points over number fields. Whether this is true for arbitrary varieties is unclear. Over finite fields the situation is different. This is the MQ problem, which is NP-complete. This problem is the essence of multivariate cryptography and forms the basis of most post-quantum signature schemes. The aim of this talk is to give an overview of the interpolation of rational subvarieties and discuss where this fits in with modern cryptography.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html