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Friday, August 14, 2020 — 3:30 PM EDT
Title: Constructing broken SIDH parameters: a tale of De Feo, Jao, and Plut's serendipity.
| Speaker: | Chloe Martindale |
| Affiliation: | University of Bristol |
| Zoom: | Please email Emma Watson. |
Abstract:
This talk is motivated by analyzing the security of the cryptographic key exchange protocol SIDH (Supersingular Isogeny Diffie-Hellman), introduced by 2011 by De Feo, Jao, and Plut. We will first recall some mathematical background as well as the protocol itself. The 'keys' in this protocol are elliptic curves, which are typically described by equations in x and y of the form y^2 = x^3 + ax + b. Of importance in this talk will be 'endomorphisms' associated to elliptic curves: these are functions that map an elliptic curve to itself which also satisfy some nice properties.
Friday, August 21, 2020 — 3:30 PM EDT
Title: An Algorithmic Reduction Theory for Binary Codes: LLL and more
Joint work with Thomas Debris-Alazard and Wessel van Woerden
| Speaker: | Léo Ducas |
| Affiliation: | Centrum Wiskunde & Informatica (CWI) |
| Zoom: | Please email Emma Watson |
Abstract:
Lattice reduction is the task of finding a basis of short and somewhat orthogonal vectors of a given lattice. In 1985 Lenstra, Lenstra and Lovasz proposed a polynomial time algorithm for this task, with an application to factoring rational polynomials. Since then, the LLL algorithm has found countless application in algorithmic number theory and in cryptanalysis.