Using Lattices for Cryptanalysis

Explore the application of lattice-based techniques in cryptanalysis through this comprehensive lecture. Delve into breaking classical cryptography using lattices, solving knapsack problems, and understanding practical lattice reduction methods. Examine lattice attacks on NTRU and gain insights into Coppersmith's method for univariate polynomials. Learn about Coppersmith's Algorithm, including finding solutions modulo divisors and multivariate applications. Discover the concept of approximate common divisors and its relevance in cryptography. This talk, presented by Nadia Heninger from UC San Diego, is part of the Lattices: Algorithms, Complexity, and Cryptography Boot Camp at the Simons Institute.

Intro
Talk outline: Breaking classical crypto with lattices
Warm-up 1: Solving knapsack problems with lattices
Practical note: Current feasible lattice reduction
Warm-up 2: Lattice attacks on NTRU
Coppersmith's method for univariate polynomials
Coppersmith's Algorithm Outline
Coppersmith's method outline
Finding solutions modulo divisors
Multivariate Coppersmith
Application: Approximate common divisors