Advanced Topics in Cryptography - Lattices (Fall 2024)
Lattices in complexity theory, cryptography, and quantum computation.
Friday 9:50 - 12:15, 6B112
Office hour: Friday 13:30-14:30 in my office
Office hour: Friday 13:30-14:30 in my office
Email: [email protected]
TAs: Mengda Bi, Wenjie Li
Main reference for lattice and complexity theory:
Micciancio and Goldwasser: Complexity of lattice problems: A cryptographic perspective
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 ] 2020 [ 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 ]
Damien Stehle's collection of lattice papers [ site ]
Oded Regev 2004 [ site ]
Vinod Vaikuntanathan 2015 [ site ] 2020 [ 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 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
Foundations of Cryptography I, II, Oded Goldreich
Topics:
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 lattice problems: fully homomorphic encryptions, lattice trapdoors, identity and attribute-based encryptions.
Part 6: Quantum and lattices
Part 7: Whatever interesting, if we have time
Last two weeks: Project presentations
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 lattice problems: fully homomorphic encryptions, lattice trapdoors, identity and attribute-based encryptions.
Part 6: Quantum and lattices
Part 7: Whatever interesting, if we have time
Last two weeks: Project presentations
Tentative Schedule:
09/13 Introduction
09/20 Complexity of lattice problems
09/27 Minkowski's theorems, SIS and LWE, q-ary lattices
10/11 Regev's quantum reduction from GapSVP to LWE
10/18 PKE from LWE, the relationship between SIS and LWE
10/25 FHE from LWE
11/01 Lattice trapdoors, Signature
11/08 Signature, project/open problem discussion
11/15 Identity-based encryption, Bonsai technique
11/22 GGH15 technique and witness encryption
11/29 Other classical primitives from lattice: PRF and more
12/06 Quantum and lattice
12/13 Presentation I
12/20 Presentation II
12/27 Presentation III
09/13 Introduction
09/20 Complexity of lattice problems
09/27 Minkowski's theorems, SIS and LWE, q-ary lattices
10/11 Regev's quantum reduction from GapSVP to LWE
10/18 PKE from LWE, the relationship between SIS and LWE
10/25 FHE from LWE
11/01 Lattice trapdoors, Signature
11/08 Signature, project/open problem discussion
11/15 Identity-based encryption, Bonsai technique
11/22 GGH15 technique and witness encryption
11/29 Other classical primitives from lattice: PRF and more
12/06 Quantum and lattice
12/13 Presentation I
12/20 Presentation II
12/27 Presentation III
