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|Title:||Bivariate polynomial-based secret sharing schemes with secure secret reconstruction||Authors:||Ding, Jian
|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. https://dx.doi.org/10.1016/j.ins.2022.02.005||Project:||RG12/19
|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.||URI:||https://hdl.handle.net/10356/163882||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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