Seminar, InfoSec Seminar: Finding twin smooth integers for isogeny-based cryptography

Speaker: Craig Costello

Date/Time: 11-Feb-2021, 16:00 UTC

Venue: Virtual Seminar


Abstract: This talk will discuss the problem of finding two consecutive integers that are as smooth as possible. Like many examples of good problems in computational number theory, this one is easy to state but non-trivial to address. The talk will discuss a number of attempts to solve the problem and the current state-of-the-art.


The motivation for finding twin smooth integers in in their application to post-quantum cryptography. Recent proposals for compact isogeny-based key exchange and digital signatures both require large primes p that lie between two smooth composites. This can be seen as a special case of the twin smooth problem in which the sum of the twins also happens to be prime.


This is joint work with Michael Naehrig and Michael Meyer.


Bio: Craig Costello is a Principal Researcher at Microsoft in the USA whose interests are in computational number theory and cryptography. In recent years his research has aimed to develop efficient, compact and secure post-quantum cryptography using supersingular isogenies.

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