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Developing a multiple secret sharing scheme by residue number system

N. I. Chervyakov (*)
M. G. Babenko (*)
Alassane BA (**)
M. A. Deryabin (*)
M. N. Shabalina (*)

(*) Department of Applied Mathematics and Mathematical modeling, North Caucasian federal University, Stavropol, Russia
Addrees: 1,Pushkin Street, Stavropol, 355009
(**) Laboratory of Computer, Network and Telecommunications, Cheikh Anta Diop University of Dakar, Dakar, Senegal
Address: Avenue Cheikh Anta Diop, Dakar BP 5005 Dakar-Fann

Mathematics Subject Classification: (MSC 2010) 13A02, 13A05, 13A15,13A30, 13E10, 13F15,13F20, 13J07,13M10
Key words: multiple secret sharing schemes, Residue number system, Tridiagonal Toeplitz matrix, Chinese remainder theorem


The process of multiple secret sharing scheme construction is the method of distributing $m$ arbitrary linked secrets MATH among $n$ participants. Research in this area aims at reduction of the algorithmic complexity and at the same time, the increasing of their speed. In this paper, a multiple secret sharing scheme based on use of residue number system RNS and Toeplitz matrix is proposed. Tests show high performance of secret sharing and recovery schemes when compared to some frequently used secret sharing models.
The paper is organized as follows: after introduction in section 1, section 2 gives methods and algorithms used. Work in section 3 concern secret sharing scheme using the Toeplitz matrix. In section 4 we have model and analysis of the computational complexity. Paper concludes in section 5.

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