Perfect verification of modular scheme

  • Gennadii V. Matveev Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus
  • Vladislav V. Matulis Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

Abstract

Secret sharing schemes are used to distribute a secret value among a group of users so that only authorized set of them can reconstruct the original secret correctly. The modular secret sharing scheme (MSSS) we are studying is based on the Chinese Remainder Theorem. In this scheme the secrets s(x), S(x), s1(x),…, sk(x) are defined as follows s(x) = S(x) = mod m(x), si(x) = S(x) mod mi(x), i = 1, 2, …, k. All the secrets and moduli are chosen from polynomial ring Fp[x], and the reconstruction of secret s(x) is carried out by applying the above-mentioned Chinese Remainder Theorem. The verification of any secret sharing scheme is understood as the protocol of verification by the participants of their partial secrets and (or) the protocol for verifying the legitimacy of the actions of the dealer. In this paper, we introduce a perfect verification protocol of MSSS. It means that none information leaks under distribution and verification. Two verification protocols are introduced in this paper. The first one is simpler and it depends on assumption about dealer honesty. If there is no such assumption verification is more complex. Both protocols are based on one work by J. Benalo and generalize the protocol proposed earlier by M. Vaskovsky and G. Matveev in two ways. First, the general, not only the threshold access structure is verified, and secondly, the dealer is not necessarily honest. Earlier, N. Shenets found the perfection condition of MSSS. Thus, if these conditions аre met, both the MSSS and its verification protocol are perfect.

Author Biographies

Gennadii V. Matveev, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

associate professor at the department of higher mathematics, faculty of applied mathematics and informatics

Vladislav V. Matulis, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

master’s degree student at the department of higher mathematics, fa culty of applied mathematics and informatics

References

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Published
2018-11-07
Keywords: polynomial modular scheme, secret sharing, verification, secret, partial secret, finite field
How to Cite
Matveev, G. V., & Matulis, V. V. (2018). Perfect verification of modular scheme. Journal of the Belarusian State University. Mathematics and Informatics, 2, 4-9. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/778
Issue
No 2 (2018): Journal of the Belarusian State University. Mathematics and Informatics
Section
Mathematical Logic, Algebra and Number Theory

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