Kamara Lectures 6 + 7 : Zero - Leakage Solutions

In the first lecture we covered—at a high level—several ways to search on encrypted data. We also mentioned that for all solutions, there is a tradeoff between efficiency, security and expressiveness. Here we will cover one extreme of the solution space: the zero-leakage or leakage-free solutions. Note that by zero-leakage we do not mean that nothing is leaked. Rather, what we mean is that what is leaked can be derived efficiently from the security parameter. We can build zero-leakage solutions from a primitive called oblivious RAM (ORAM). There are several ways to design ORAMs. The first is based fully-homomorphic encryption (FHE) and the second is based only on symmetric-key encryption (SKE). SKE-based ORAMs have received a lot of attention and there are many different constructions that achieve different levels of efficiency. In these notes we will discuss the FHE-based ORAM construction and the first and simplest SKE-based ORAM called the square-root solution. Then we will see how to use ORAM for encrypted search.