Advanced Topics in Cryptography - Lattices (Fall 2022)
Lattices in complexity theory, cryptography, and quantum computation.
Monday 9:50 - 12:15, 6B201
Office hour: Monday 13:30 - 14:30
Email: chenyilei@mail.tsinghua.edu.cn
TAs: Zewen Fan, Xiaxi Ye
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 SIS and LWE: FHE, lattice trapdoor, IBE, ABE.
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 SIS and LWE: FHE, lattice trapdoor, IBE, ABE.
Part 6: Quantum and lattices
Part 7: Whatever interesting, if we have time
Last two weeks: Project presentations
Tentative Schedule:
09/12 Moon festival
09/19 Introduction, lattice problems
09/26 Minkowski's theorems, NP hardness of CVP, SVP is no harder than CVP
10/03 National holiday, moved to 11/19
10/10 The LLL algorithm
10/17 Short integer solution and learning with errors, q-ary lattices
10/24 Regev's quantum reduction from GapSVP to LWE
10/31 Fully homomorphic encryption, gadget matrices
11/07 Lattice trapdoor and its applications to signature
11/14 Lattice trapdoor II, identity-based encryption,
11/19 The Bonsai technique, signature without random oracle (substitution for 10/03)
11/21 Attribute-based encryption, open problems
11/28 Pseudorandom function and their advanced capabilities
12/05 *Functional encryption, witness encryption, and program obfuscation from lattices
12/12 *Advanced complexity results and algorithms, quantum and lattices
12/19 Presentation I
12/26 Presentation II
09/12 Moon festival
09/19 Introduction, lattice problems
09/26 Minkowski's theorems, NP hardness of CVP, SVP is no harder than CVP
10/03 National holiday, moved to 11/19
10/10 The LLL algorithm
10/17 Short integer solution and learning with errors, q-ary lattices
10/24 Regev's quantum reduction from GapSVP to LWE
10/31 Fully homomorphic encryption, gadget matrices
11/07 Lattice trapdoor and its applications to signature
11/14 Lattice trapdoor II, identity-based encryption,
11/19 The Bonsai technique, signature without random oracle (substitution for 10/03)
11/21 Attribute-based encryption, open problems
11/28 Pseudorandom function and their advanced capabilities
12/05 *Functional encryption, witness encryption, and program obfuscation from lattices
12/12 *Advanced complexity results and algorithms, quantum and lattices
12/19 Presentation I
12/26 Presentation II