Advanced Topics in Cryptography - Lattices (Fall 2022) 

​Lattices in complexity theory, cryptography, and quantum computation.

Monday 9:50 - 12:15
Office hour: Monday 13:30 - 14:30

Email: chenyilei@mail.tsinghua.edu.cn
​

TAs: TBD
​

Main ​reference for lattice and complexity theory:
Micciancio and Goldwasser: Complexity of lattice problems: A cryptographic perspective
​

​Websites/Lecture notes/Surveys related to lattices:
Damien Stehle's collection of lattice papers [ site ]
Oded Regev 2004 [ site ]
Vinod Vaikuntanathan 2015 [ site ]
Daniele Micciancio 2016 [ site ]
TAU lattice course 2019 [ site ]
H. Lenstra: Lattices in number theory, algorithm, and applications [ link ]
A. Joux and J. Stern: Lattice reduction, a toolbox for cryptanalyst [ link ]
P. Q. Nguyen and J. Stern: The two faces of lattice in cryptology [ link ]

Main ​reference for cryptography:
A Course in Cryptography,  Rafael Pass & abhi shelat
https://www.cs.cornell.edu/courses/cs4830/2010fa/lecnotes.pdf

A graduate course in applied cryptography,  Dan Boneh & Victor Shoup
Foundations of Cryptography I, II, Oded Goldreich

Tentative Schedule:
Part 1: Introduction: Minkowski's two theorems, all what you want to know about lattices 
Part 2: Algorithms for SVP and CVP: LLL and others
Part 3: Complexity: NP hardness of CVP, SVP (Ajtai, Micciancio, Khot), NP intersect coNP
Part 4: Worst-case to average-case reduction (LWE, SIS, DCP)
Part 5: The cryptographic applications of SIS and LWE: FHE, lattice trapdoor.
Part 6: Quantum and lattices
Part 7: Whatever interesting, if we have time
Last two weeks: Project presentations