Abstract
The purpose of secure multi-party computation is to enable protocol participants to compute a public function of their private inputs while keeping their inputs secret, without resorting to any trusted third party. However, opening the public output of such computations inevitably reveals some information about the private inputs. We propose a measure generalizing both Renyi entropy and $g$ -entropy so as to quantify this information leakage. In order to control and restrain such information flows, we introduce the notion of function substitution, which replaces the computation of a function that reveals sensitive information with that of an approximate function. We exhibit theoretical bounds for the privacy gains that this approach provides and experimentally show that this enhances the confidentiality of the inputs while controlling the distortion of computed output values. Finally, we investigate the inherent compromise between accuracy of computation and privacy of inputs and we demonstrate how to realize such optimal trade-offs.
Highlights
W E STUDY the setting of functions f that map n integral inputs x1, . . . , xn into one integral output
Secure Multi-party Computation (SMC) is a domain of cryptography that can implement such a black-box functionality: it enables protocol participants to compute a public function of their private inputs, such that no trusted third party is required, and that the confidentiality of the inputs is protected [1]–[6]
In [15], we introduced a model of deceitful adversaries which enabled us to reason about the acceptable leakage, and to quantify, based on Shannon entropy, the information that such attackers can deduce from public outputs and their own private inputs
Summary
W E STUDY the setting of functions f that map n integral inputs x1, . . . , xn into one integral output. W E STUDY the setting of functions f that map n integral inputs x1, . The computation of function f is secure if its evaluation protects the privacy of the inputs, so that agent j cannot learn more from this computation about the other values xi than what agent j is able to infer from knowledge of her own input x j and the publicly observable output f Secure Multi-party Computation (SMC) is a domain of cryptography that can implement such a black-box functionality: it enables protocol participants to compute a public function of their private inputs, such that no trusted third party is required, and that the confidentiality of the inputs is protected [1]–[6]. Let (D) be the set of all probability distributions whose support is contained in D. The set of positive integers will be denoted by N>0 while R≥0 and R>0 will denote the set of non-negative and positive real numbers respectively
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