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Title: Bivariate polynomial-based secret sharing schemes with secure secret reconstruction
Authors: Ding, Jian
Ke, Pinhui
Lin, Changlu
Wang, Huaxiong
Keywords: Science::Mathematics
Issue Date: 2022
Source: Ding, J., Ke, P., Lin, C. & Wang, H. (2022). Bivariate polynomial-based secret sharing schemes with secure secret reconstruction. Information Sciences, 593, 398-414.
Project: RG12/19
RG21/18 (S)
Journal: Information Sciences
Abstract: A (t,n)-threshold scheme with secure secret reconstruction, or a (t,n)-SSR scheme for short, is a (t,n)-threshold scheme against the outside adversary who has no valid share, but can impersonate a participant to take part in the secret reconstruction phase. We point out that previous bivariate polynomial-based (t,n)-SSR schemes, such as those of Harn et al. (Information Sciences 2020), are insecure, which is because the outside adversary may obtain the secret by solving a system of [Formula presented] linear equations. We revise Harn et al. scheme and get a secure (t,n)-SSR scheme based on a symmetric bivariate polynomial for the first time, where t⩽n⩽2t-1. To increase the range of n for a given t, we construct a secure (t,n)-SSR scheme based on an asymmetric bivariate polynomial for the first time, where n⩾t. We find that the share sizes of our schemes are the same or almost the same as other existing insecure (t,n)-SSR schemes based on bivariate polynomials. Moreover, our asymmetric bivariate polynomial-based (t,n)-SSR scheme is more easy to be constructed compared to the Chinese Remainder Theorem-based (t,n)-SSR scheme with the stringent condition on moduli, and their share sizes are almost the same.
ISSN: 0020-0255
DOI: 10.1016/j.ins.2022.02.005
Rights: © 2022 Elsevier Inc. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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