Isogenies and Lattices in Cryptography - Session 12

Explore the intersection of isogenies and lattices in cryptography through this comprehensive lecture. Delve into topics such as twin smooth integers, polynomials, and delayed encryption. Examine the applications of these concepts in sealed bid auctions and encryption algorithms. Investigate lattice-based cryptography, including the Reverse Minkowski Theorem and new lattice sampling techniques. Learn about the Hidden Number Problem, ideal lattices, and arithmetic curves. Gain insights into the current state of the art in isogeny-based and lattice-based cryptography, and understand their potential implications for future cryptographic systems.

Introduction
Motivation
Finding twin smooth integers
Polynomials
Example
Contributions
Questions
Delayed delayed encryption
Sealed bid auctions
Encryption
Lattices
Algorithm
Reverse Minkowski Theorem
New Lattice TwoStage Sampling
New Lattice Function Class
Current State of Art
Contribution
Next talk
Hidden Number Problem
Literature
Lattice Barrier
Summary
Ideal Lattice
Arithmetic Curve
Prime Ramification
Prime Ideal SVPE