Verification of modular secret sharing

  • Maksim M. Vaskouski Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus
  • Gennadii V. Matveev Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

Abstract

In the present paper new scheme of secret verification are constructed. Verification with trusted party participation is conducted with help of an external device, which takes an arbitrary polynomial S(x), input element x0 ∈ Fpn and returns a value ξS(x0), where ξ is an Fpn – valued uniformly distributed random variable. It is shown that using of such device allows any user to verify his secret. Polynomial verification scheme is based on verification of divisibility g(x)|f(x) in the ring Z[x]. Only a value of polynomial S(x) in unknown point x = l is disclosed at the proposed verification method. Benaloh’s verification of the modular scheme allows any shareholder to ensure in consistency of all partial secrets, i. e. any legal group of shareholders can restore the secret S(x) correctly. None information about the secret S(x), excepting a prior information, is disclosed. The proposed protocols can be used safely for schemes over arbitrary finite fields without additional restrictions on a size of a filed. 

Author Biographies

Maksim M. Vaskouski, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

PhD (physics and mathematics), docent; associate professor at the department of higher mathematics, faculty of applied mathematics and computer sciences

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

PhD (physics and mathematics), docent; associate professor at the department of higher mathematics, faculty of applied mathematics and computer sciences

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Published
2018-01-24
Keywords: polynomial modular scheme, secret, partial secret, finite field
How to Cite
Vaskouski, M. M., & Matveev, G. V. (2018). Verification of modular secret sharing. Journal of the Belarusian State University. Mathematics and Informatics, 2, 17-22. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/744
Issue
No 2 (2017): Journal of the Belarusian State University. Mathematics and Informatics
Section
Mathematical Logic, Algebra and Number Theory

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