Conference Agenda

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Authors
 
Session Overview
Session
MS145, part 1: Isogenies in Cryptography
Time:
Wednesday, 10/Jul/2019:
10:00am - 12:00pm

 Location: Unitobler, F-123
52 seats, 100m^2

Presentations
10:00am - 12:00pm

Isogenies in Cryptography

Chair(s): Tanja Lange (Eindhoven University of Technology, Netherlands, The), Chloe Martindale (Eindhoven University of Technology, Netherlands, The), Lorenz Panny (Eindhoven University of Technology, Netherlands, The)

The isogeny graph of elliptic curves over finite fields has long been a subject of study in algebraic geometry and number theory. During the past 10 years several authors have shown multiple applications in cryptology. One interesting feature is that systems built on isogenies seem to resist attacks by quantum computers, making them the most recent family of cryptosystems studied in post-quantum cryptography.

This mini-symposium brings together presentations on cryptosystems built on top of isogenies, their use in applications, and different approaches to the cryptanalysis, including quantum cryptanalysis.

 

(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)

 

Overview of isogenies in cryptography (Part I)

Chloe Martindale1, Lorenz Panny2
1Eindhoven University of Techonology, 2Eindhoven University of Technology

We will give an introductory overview of the current landscape in isogeny-based cryptography, including SIDH/SIKE and CSIDH. We will then summarise the latest developments and present some open problems.

 

Overview of isogenies in cryptography (Part II)

Lorenz Panny, Chloe Martindale
Eindhoven University of Technology

We will give an introductory overview of the current landscape in isogeny-based cryptography, including SIDH/SIKE and CSIDH. We will then summarise the latest developments and present some open problems.

 

Quantum attacks against isogenies

Daniel J. Bernstein
University of Illinois at Chicago

Childs, Jao, and Soukharev introduced a subexponential quantum attack against the original isogeny-based cryptosystem from Couveignes, Rostovtsev, and Stolbunov. The attack uses a subexponential quantum algorithm introduced by Kuperberg to find hidden shifts. This talk will (1) introduce the hidden-shift problem and the isogeny problem, (2) survey the attack algorithms, and (3) summarize the latest analyses of the costs of attacking CSIDH. This includes joint work with Lange, Martindale, and Panny (https://quantum.isogenies.org).

 

Pre- and post-quantum Diffie-Hellman

Benjamin Smith
INRIA & LIX - Ecole Polytechnique

From a mathematical and algorithmic point of view, one of the nice features of commutative isogeny-based cryptosystems (such as CSIDH) is that they are governed by particularly simple algebraic structures, namely commutative groups acting on sets. On a strictly formal level, this allows us to draw strong analogies with classical Diffie-Hellman and discrete-logarithm-based cryptosystems, problems, and algorithms. In this talk we will explore these analogies and their limitations, and consider the relationships between the "hard" problems underlying commutative isogeny-based cryptosystems in both the pre- and post-quantum settings.