CO 789: Lattice-Based Cryptography (Fall 2015)

Instructor: David Jao. Office hours: MWF 2:30pm-3:20pm.

Chris Peikert's Lattices in Cryptography course: Fall 2015 (https://web.eecs.umich.edu/~cpeikert/lic15/), Fall 2013 (https://web.eecs.umich.edu/~cpeikert/lic13/)
Oded Regev's Lattices in Computer Science course: Fall 2009 (http://www.cims.nyu.edu/~regev/teaching/lattices_fall_2009/), Fall 2004 (http://www.cims.nyu.edu/~regev/teaching/lattices_fall_2004/)
Daniele Micciancio's Lattices Algorithms and Applications course: Spring 2014 (http://cseweb.ucsd.edu/classes/sp14/cse206A-a/), Winter 2010 (http://www-cse.ucsd.edu/classes/wi10/cse206a), Spring 2007 (http://www-cse.ucsd.edu/classes/sp07/cse206a)
Vinod Vaikuntanathan's Advanced Topics in Cryptography: Lattices course: Fall 2015 (https://people.csail.mit.edu/vinodv/6876-Fall2015/), Fall 2011 (https://people.csail.mit.edu/vinodv/COURSES/CSC2414-F11/)
Shai Halevi's Homomorphic Encryption and Lattices course: Spring 2013 (https://people.csail.mit.edu/shaih/columbia6261/), Spring 2011 (https://people.csail.mit.edu/shaih/lattices-and-HE-class/)

September 14: Lattices -- Definitions, examples, basis, fundamental region
September 16: Existence of bases, Hermite normal form
September 18: Gram-Schmidt orthogonalization, lower bounds for $λ 1$
Sepetmber 21: Minkowski's theorem, upper bounds for $λ 1$
September 23: LLL -- definition and algorithm
September 25: LLL -- proof and applications
September 28: SVP to CVP reduction, NP-hardness of CVP
September 30: Search/decisional CVP equivalence, Babai's nearest plane algorithm
October 2: Ajtai's OWF and CRHF, reduction to SIS
October 5: Discrete Gaussian sampling, SIS to SIVP reduction
October 7: Cyclic lattices and ideals
October 9: SIS to SIVP reduction for cyclic lattices
October 14: LWE and applications
October 16: LWE reductions: Decision to search; self-reducibility
October 19: LWE to BDD reductions
October 21: Quantum LWE to SIVP reduction
October 23: Ring-LWE: definition and applications
October 26: Number fields, algebraic numbers, and the canonical embedding
October 28: Algebraic integers and construction of integral bases
October 30: RLWE cryptosystems; security proofs
November 2: NTRU
November 4: Lattice trapdoors
November 6: IBE and HIBE
November 9: Fully homomorphic encryption
November 11: Attribute-based encryption
November 13: Security proofs for ABE
November 16: Software obfuscation
November 18: Multilinear maps