3 research outputs found
Near Optimal Rate Homomorphic Encryption for Branching Programs
We initiate the study of good rate homomorphic encryption schemes.
Based on previous work on securely evaluating (binary I/O) branching programs, we propose a leveled homomorphic encryption scheme
for {\em large-output} polynomial-size branching programs (which we call ) that possesses near optimal-rate. The rate analysis of the new scheme is intricate: the best rate is achieved if a certain parameter is set equal to the only positive root of a degree- polynomial, where is the length of the branching program. We employ the Newton-Puiseux algorithm to find a Puiseux series for this parameter, and based on this, propose a -time algorithm to find an integer approximation to .
We also describe a rate-optimal 1-out-of- CPIR based on rate-optimal homomorphic encryption. In concrete terms, when applied to say, a movie database with elements of -bits, the client can privately download a movie with a communication rate of almost , hence sacrificing only about of bandwidth for privacy.
We also analyze the optimality of the rate efficiency of our scheme in a novel model that may be of independent interest. Our -out-of- CPIR has rate , while we show that no black-box construction surpasses in terms of rate, where is the length of the database elements and the security parameter