Lectures 4 + 5 : The ( In ) Security of Encrypted Search

data types. An abstract data type is a collection of objects together with a set of operations defined on those objects. Examples include sets, dictionaries (also known as key-value stores or associative arrays) and graphs. The operations associated with a data type fall into one of two categories: query operations, which return information about the objects; and update operations, which modify the objects. If the data type supports only query operations it is static, otherwise it is dynamic. For simplicity we define data types as having a single operation but note that the definitions can be extended to capture multiple operations in the natural way. Data structures. A data structure for type a T is a concrete representation of type-T objects in some computational model. For us, the underlying model will always the random access machine (RAM) model of computation. The structure used to represent a type-T object is usually optimized to support the queries associated with T as efficiently as possible; that is, one designs the structure in such a way that there is an efficient algorithm to evaluate these queries. For data types that support multiple queries, the structure is usually designed to efficiently support as many of T ’s queries as possible. As a concrete example, the dictionary data type can be represented using various data structures depending on which queries one wants to support efficiently: hash tables support Get and Put in expected O(1) time whereas balanced binary search trees support both operations in worst-case log(n) time. We model a type-T data structure as a collection of three ensembles S = {Sk}k∈N, Q = {Qk}k∈N and A = {Ak}k∈N. If a type-T structure DS supports only a single query, we often write DS(q) to denote the answer a ∈ Ak that results from querying DS on q ∈ Qk.