The Learning With Errors Problem and Cryptographic Applications

Explore the Learning With Errors (LWE) problem and its cryptographic applications in this comprehensive lecture by Chris Peikert from the University of Michigan, Ann Arbor. Delve into the foundations of lattice-based cryptography, starting with an introduction to short integer solutions and the LWE problem. Examine the search and decision variants of LWE, and understand the quantum reduction techniques used in lattice-based cryptography. Gain insights into cryptographic applications, including digital signatures and their security aspects. Learn about trapdoors and their role in lattice-based cryptosystems. Participate in an exercise break to reinforce your understanding of the concepts presented. This talk, part of the Lattices: Algorithms, Complexity, and Cryptography Boot Camp at the Simons Institute, offers a deep dive into the theoretical foundations and practical implications of LWE in modern cryptography.