Quadratic Secret Sharing and Conditional Disclosure of Secrets

被引:0
|
作者
Beimel, Amos [1 ]
Othman, Hussien [1 ]
Peter, Naty [2 ]
机构
[1] Ben Gurion Univ Negev, Dept Comp Sci, IL-84105 Beer Sheva, Israel
[2] Georgetown Univ, Dept Comp Sci, Washington, DC 20057 USA
基金
以色列科学基金会; 欧洲研究理事会;
关键词
Protocols; Servers; Cryptography; Upper bound; Boolean functions; Transforms; Task analysis; Secret sharing; share size; polynomial secret sharing; PRIVATE INFORMATION-RETRIEVAL; EXPONENTIAL LOWER BOUNDS; COMPLEXITY; SIZE;
D O I
10.1109/TIT.2023.3296588
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
There is a huge gap between the upper and lower bounds on the share size of secret-sharing schemes for n-party access structures; consistent with our current knowledge the optimal share size can be anywhere between polynomial and exponential in n. For linear secret-sharing schemes, the share size for almost all n-party access structures is exponential in n. We would like to study larger classes of secret-sharing schemes with two goals: 1) prove lower bounds for larger classes of secret-sharing schemes; and 2) construct efficient secret-sharing schemes. Given this motivation, Paskin-Cherniavsky and Radune (ITC'20) introduced a new class of secret-sharing schemes in which the shares are generated by applying degree-d polyno-mials to the secret and some random field elements. We define and study two additional classes of polynomial secret-sharing schemes: 1) schemes in which the reconstruction of the secret is done using polynomials; and 2) schemes in which both sharing and reconstruction are done by polynomials. Our main result is a construction of secret-sharing schemes and conditional disclosure of secrets protocols with quadratic sharing and reconstruction that are more efficient than linear secret-sharing schemes. To complement our results, we prove lower bounds on the share size for schemes with polynomial reconstruction. Finally, we give an evidence that schemes with polynomial sharing are probably stronger than schemes with polynomial reconstruction.
引用
收藏
页码:7295 / 7316
页数:22
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