Attacks on multilinear maps

Abstract

In this thesis, I explore the current multilinear map candidates and attacks against them. This involves analyzing the three proposals for multilinear maps which are based on ideal lattices, integers, and standard lattices. The attacks exploit the geometry of the lattices and linearity of the integers to break security. I also compare the applications of these schemes with what is required for attacks. Key agreement seems to need certain features of multilinear maps which expose vulnerabilities while other applications like indistinguishability obfuscation. I analyze the attacks against these maps and show why they are not able to break the program obfuscation application of multilinear maps.