Hypercubes and Private Information Retrieval

In geometry, a hypercube is a regular polytype - a generalisation of a 3-dimensional cube to lambda-dimensions, with mutually perpendicular sides of equal lengths. For lambda = 0, 1, 2, 3, and 4, a hypercube is a point, a straight line segment, a square, a cube and a tesseract respectively. In this paper, we apply the concept of hypercubes in computationally private information retrieval (CPIR) based on additively homomorphic cryptosystems and optimise it further at the cost of a measurable privacy loss.