Cryptology ePrint Archive: Report 2021/207

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

Daniele Cozzo and Nigel P. Smart and Younes Talibi Alaoui

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.

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Date: received 25 Feb 2021

Contact author: daniele cozzo at kuleuven be, nigel smart@kuleuven be, younes talibialaoui@kuleuven be

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Version: 20210301:171347 (All versions of this report)

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