scholarly journals Grouped Secret Sharing Schemes Based on Lagrange Interpolation Polynomials and Chinese Remainder Theorem

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Fuyou Miao ◽  
Yue Yu ◽  
Keju Meng ◽  
Yan Xiong ◽  
Chin-Chen Chang
Keyword(s):  
Detailed Analysis ◽  
Secret Sharing ◽  
Lagrange Interpolation ◽  
Chinese Remainder Theorem ◽  
Secret Sharing Schemes ◽  
Access Structure ◽  
Threshold Secret Sharing ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials

In a t , n threshold secret sharing (SS) scheme, whether or not a shareholder set is an authorized set totally depends on the number of shareholders in the set. When the access structure is not threshold, (t,n) threshold SS is not suitable. This paper proposes a new kind of SS named grouped secret sharing (GSS), which is specific multipartite SS. Moreover, in order to implement GSS, we utilize both Lagrange interpolation polynomials and Chinese remainder theorem to design two GSS schemes, respectively. Detailed analysis shows that both GSS schemes are correct and perfect, which means any authorized set can recover the secret while an unauthorized set cannot get any information about the secret.

Publicly Verifiable Secret Sharing Scheme Based on the Chinese Remainder Theorem

2013 ◽  
Vol 278-280 ◽  
pp. 1945-1951
Author(s):  
Xing Xing Jia ◽  
Dao Shun Wang ◽  
Yu Jiang Wu
Keyword(s):  
Secret Sharing ◽  
Lagrange Interpolation ◽  
Chinese Remainder Theorem ◽  
Secret Sharing Schemes ◽  
Secret Sharing Scheme ◽  
Verifiable Secret Sharing ◽  
Sharing Scheme ◽  
Encrypt Data ◽  
Elgamal Cryptosystem ◽  
Secret Reconstruction

Publicly verifiable secret sharing schemes based on Lagrange interpolation utilize public cryptography to encrypt transmitted data and the validity of their shares can be verified by everyone, not only the participants. However, they require O(klog2k) operations during secret reconstruction phase. In order to reduce the computational complexity during the secret reconstruction phase we propose a non-interactive publicly verifiable secret sharing scheme based on the Chinese Remainder Theorem utilizing ElGamal cryptosystem to encrypt data, whonly requires O(k) operations during secret reconstruction phase. Theoretical analysis proves the proposed scheme achieves computation security and is more efficient.

scholarly journals REMARKS ON MULTIVARIATE EXTENSIONS OF POLYNOMIAL BASED SECRET SHARING SCHEMES

2014 ◽  
Vol 6 (2) ◽  
pp. 285-297
Author(s):  
Jakub DERBISZ
Keyword(s):  
Secret Sharing ◽  
Chinese Remainder Theorem ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Secret Sharing Schemes ◽  
Access Structure ◽  
Multivariate Polynomial ◽  
Detailed Exposition ◽  
Theoretical Results ◽  
Threshold Schemes

We introduce methods that use Grobner bases for secure secret sharing schemes. The description is based on polynomials in the ring R = K[X1, . . . , Xl] where identities of the participants and shares of the secret are or are related to ideals in R. Main theoretical results are related to algorithmical reconstruction of a multivariate polynomial from such shares with respect to given access structure, as a generalisation of classical threshold schemes. We apply constructive Chinese remainder theorem in R of Becker and Weispfenning. Introduced ideas find their detailed exposition in our related works

scholarly journals On Lagrange interpolation with equally spaced nodes

2000 ◽  
Vol 62 (3) ◽  
pp. 357-368 ◽  
Author(s):  
Michael Revers
Keyword(s):  
Rate Of Convergence ◽  
Lagrange Interpolation ◽  
End Points ◽  
Quantitative Version ◽  
Equidistant Nodes ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials ◽  
Exact Rate Of Convergence

A well-known result due to S.N. Bernstein is that sequence of Lagrange interpolation polynomials for |x| at equally spaced nodes in [−1, 1] diverges everywhere, except at zero and the end-points. In this paper we present a quantitative version concerning the divergence behaviour of the Lagrange interpolants for |x|3 at equidistant nodes. Furthermore, we present the exact rate of convergence for the interpolatory parabolas at the point zero.

Weighted threshold secret sharing schemes

1999 ◽  
Vol 70 (5) ◽  
pp. 211-216 ◽  
Author(s):  
P. Morillo ◽  
C. Padró ◽  
G. Sáez ◽  
J.L. Villar
Keyword(s):  
Secret Sharing ◽  
Secret Sharing Schemes ◽  
Threshold Secret Sharing
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