TITLE: How to Use a Short Basis: Trapdoors for Lattices and New Cryptographic Construction

ABSTRACT: Cryptographic schemes based on *lattices* are attractive for several reasons: their computations are simple and easily parallelized, they have thus far resisted attacks by quantum algorithms, and their security can be based on *worst-case* hardness assumptions. To date, such schemes have unfortunately been limited mainly to collision-resistant hash functions and public-key encryption.

This talk will describe how to securely exploit innate "trapdoors" in lattices. The cryptographic applications include new kinds of trapdoor functions, simple "hash-and-sign" digital signature schemes, and identity-based encryption -- all based on standard worst-case lattice assumptions. The talk will be self-contained, and no prior knowledge of lattices will be assumed.

Joint work with Craig Gentry and Vinod Vaikuntanathan.