Secure Fast Evaluation of Iterative Methods: With an Application to Secure PageRank

Iterative methods are a standard technique in many areas of scientific computing. The key idea is that function applied repeatedly until the resulting sequence converges to correct answer. When applying such secure computation methodology (for example using MPC, FHE, or SGX) one either needs perform enough steps ensure convergence irrespective input data, test within algorithm, and this itself leads leakage data. Using Banach Fixed Point theorem, its extensions, we show data-leakage can be quantified. We then apply (via MPC) implementation PageRank methodology. For allowing small amount produces much more efficient implementation, for underlying graphs ‘leakage’ already known any attacker.