Welcome to the resource topic for 2013/503
Title:
On secret sharing with nonlinear product reconstruction
Authors: Ignacio Cascudo, Ronald Cramer, Diego Mirandola, Carles Padro, Chaoping Xing
Abstract:Multiplicative linear secret sharing is a fundamental notion in the area of secure multi-party computation (MPC) and, since recently, in the area of two-party cryptography as well. In a nutshell, this notion guarantees that the product of two secrets is obtained as a linear function of the vector consisting of the coordinate-wise product of two respective share-vectors''. This paper focuses on the following foundational question, which is novel to the best of our knowledge. Suppose we {\em abandon the latter linearity condition} and instead require that this product is obtained by {\em some}, not-necessarily-linear product reconstruction function’'. {\em Is the resulting notion equivalent to multiplicative linear secret sharing?} We show the (perhaps somewhat counter-intuitive) result that this relaxed notion is strictly {\em more general}. Concretely, fix a finite field \FF_q as the base field over which linear secret sharing is considered. Then we show there exists an (exotic) linear secret sharing scheme with an unbounded number of players n such that it has t-privacy with t = \Omega(n) and such that it does admit a product reconstruction function, yet this function is {\em necessarily} nonlinear. In addition, we determine the minimum number of players for which those exotic schemes exist. Our proof is based on combinatorial arguments involving quadratic forms. It extends to similar separation results for important variations, such as strongly multiplicative secret sharing.
ePrint: https://eprint.iacr.org/2013/503
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .