## Mathematics in Cryptography II

Toni Bluher

National Security Agency

May 22, 2018

Toni Bluher

National Security Agency

May 22, 2018

Kristin Lauter

Microsoft Research

May 22, 2018

Toni Bluher

National Security Agency

May 21, 2018

Kristin Lauter

Microsoft Research

May 21, 2018

Jill Pipher

Brown University

May 21, 2018

Antti Kupiainen

University of Helsinki

May 15, 2018

Pierre-Francois Rodriguez

University of California

May 11, 2018

Pierre-Francois Rodriguez

University of California

May 10, 2018

Juan Maldacena and Douglas Stanford

May 4, 2018

Ashay Burungale

Universite Paris 13; Member, School of Mathematics

May 1, 2018

Let $E$ be a CM elliptic curve over a totally real number field $F$ and $p$ an odd ordinary prime. If the ${p^{\infty}\mbox{-}\mathrm{Selmer}}$ group of $E$ over $F$ has ${\mathbb{Z}_{p}\mbox{-}\mathrm{corank}}$ one, we show that the analytic rank of $E$ over $F$ is also one (joint with Chris Skinner and Ye Tian). We plan to discuss the setup and strategy.