Gentry-Peikert-Vaikuntanathan that improves the modulus q in the SIS reduction.Lattice attacks against LWE (Lindner-Peikert): Lecture 3.The original BKW paper (with an algorithm for LPN):. Chris Peikert's course at Michigan/Georgia Tech.Oded Regev's course at Tel-Aviv University.A precursor of this course at MIT: Fall 2015 and Fall 2017 and Fall 2018.Ideal Lattices and Ring Learning with Errors. The GGH15 Multilinear Map and Applications. The key equation and applications to attribute-based encryption, fully homomorphic signatures and constrained pseudorandom functions. Identity-based Encryption and Hierarchical IBE.įully Homomorphic Encryption. Lattice Trapdoors and Discrete Gaussian Sampling. Pseudorandom Functions and Learning with Rounding. Reductions for LWE (Worst-to-average case, Search-to-decision) Worst-case to Average-case Reduction for SIS. Basic properties and cryptographic applications: public and private-key encryption and collision-resistant hashing.Īlgorithms for LWE. Schedule (tentative and subject to change) Lecture Lecture notes for the class are here (all in one file).Starting March 15, we are moving the class online.The first class is on Monday Jan 27, 2020.References listed below, as well as instructor's notes.īased on (a) class participation (come to class attend a talk of your choice in each of the three workshops, and write a short email to the instructor with a review of the talk, including a summary, what you liked/disliked and any ideas you got from watching it) and (b) a final project (either come up with a new result - talk to the instructor for project ideas - or write a short survey on a topic that will be useful to future researchers). Instead, we will use lecture notes and papers from the M 5pm - 7:30pm (with a break in between), Mathematical maturity and comfort with linear algebraic notions is the most important pre-requisite, followed by courses in the theory of computation (CS 172 or equivalent) and cryptography (CS 171 or CS 276). This is an advanced course, intended for beginning graduate students and upper level undergraduates in CS and Math. In particular, to get more out of the course, the students are encouraged to attend the bootcamp and the workshops of the program. The course is intended to complement the Spring'20 Simons Institute program on Lattices. This course explores the various facets of lattices, the LWE problem and their applications in cryptography. In the last two decades, the Learning with Errors (LWE) Problem, whose hardness is closely related to lattice problems, has revolutionized modern cryptography by giving us (a) a basis for "post-quantum" cryptography, (b) a dizzying variety of cryptographic primitives such as fully homomorphic encryption and signatures, attribute-based and functional encryption, a rich set of pseudorandom functions, various types of program obfuscation and much more and finally, (c) a unique source of computational hardness with worst-case to average-case connections. In the 80s and the early 90s, lattices served as a destructive force, giving the cryptanalysts some of their most potent attack tools. The role of lattices in cryptography has been revolutionary and dramatic. The study of integer lattices, discrete additive subgroups of R n, serves as a bridge between number theory and geometry and has for centuries received the attention of illustrious mathematicians including Lagrange, Gauss, Dirichlet, Hermite and Minkowski.
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