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

Abstract

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

Private Liquidity Matching Using MPC

“…MPC was also used for privacy-preserving financial data analysis, such as [7] to conduct statistics over the performance of companies throughout the year or to compute the systemic risk between financial institutions such as in [2] and [25]. Also, [30] and [19] used MPC for detecting fraud between financial institutions, and [11] used MPC for privacy-preserving federated learning for financial applications.…”