### DIMACS Theory of Computing Seminar

Title: Optimization of Bootstrapping in Circuits

Speaker: **Fabrice Benhamouda**, IBM Research

Date: Wednesday, April 12, 2017 11:00am-12:00pm

Location: CoRE Bldg, Room 301, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

In 2009, Gentry proposed the first Fully Homomorphic Encryption (FHE) scheme, an extremely powerful cryptographic primitive that enables to perform computations, i.e., to evaluate circuits, on encrypted data without decrypting them first. This has many applications, particularly in cloud computing.

In all currently known FHE schemes, encryptions are associated with
some (non-negative integer) noise level. At each evaluation of an AND gate, this noise
level increases. This increase is problematic because decryption succeeds only if the noise level stays below some maximum level L at every gate of the circuit. To ensure that property, it is possible to perform an operation called bootstrapping to reduce the noise level. Though critical, boostrapping is a time-consuming
operation. This expense motivates a new problem in discrete optimization: minimizing the number of bootstrappings in a circuit while still controlling the noise level.

In this paper, we (1) formally define the bootstrap problem, (2) design a polynomial-time L-approximation algorithm using a novel method of rounding of a linear program, and (3) show a matching hardness result: (L − ε)-inapproximability for any ε > 0.

Joint work with Tancrede Lepoint, Claire Mathieu, and Hang Zhou.

See: http://www.math.rutgers.edu/~sk1233/theory-seminar/S17/