New Circular Security Counterexamples from Decision Linear and Learning with Errors

We investigate new constructions of n-circular counterexamples with a focus on the case of n = 2. We have a particular interest in what qualities a cryptosystem must have to be able to separate such circular security from IND-CPA or IND-CCA security. To start, we ask whether there is something special about the asymmetry in bilinear groups that is inherent in the works of [1] and [17] or whether it is actually the bilinearity that matters. As a further question, we explore whether such counterexamples are derivable from other assumptions such as the Learning with Errors (LWE) problem. If it were difficult to find such counterexamples, this might bolster our confidence in using 2-circular encryption as a method of bootstrapping Fully Homomorphic Encryption systems that are based on lattice assumptions. The results of this paper broadly expand the class of assumptions under which we can build 2circular counterexamples. We first show for any constant k ≥ 2 how to build counterexampl...

• Type: Journal
• Year: 2015
• Where: ASIACRYPT
• Authors: Allison Bishop, Susan Hohenberger, Brent Waters
• Keywords: ASIACRYPT 2015, Cryptology