Proceedings of the
The Nineteenth International Conference on Computational Intelligence and Security (CIS 2023)
December 1 – 4, 2023, Haikou, China
Shamir Secret Sharing Scheme Based on Gauss Ring over Finite Fields
1Department of Big Data and Information Engineering, Guizhou Industry Polytechnic College, China.
2School of Cyberspace Security, Hangzhou Dianzi University, China.
ABSTRACT
In this paper, the real and imaginary parts of the Gauss ring are defined on the finite fields with prime order. While the complex reversible prime class is further defined. The complex reversible prime class is the subset of all prime numbers in the form of 4n+3. The sufficient conditions for a Gauss ring over finite fields to become a field are given by using the complex reversible prime class. Finally, the application of the Gauss ring over finite fields to the Shamir secret sharing scheme after it has become a field is presented.
Keywords: Finite fields, Gauss ring, Complex reversible prime class, Gauss field, Shamir secret sharing.
Download PDF
1Department of Big Data and Information Engineering, Guizhou Industry Polytechnic College, China.
2School of Cyberspace Security, Hangzhou Dianzi University, China.
ABSTRACT
In this paper, the real and imaginary parts of the Gauss ring are defined on the finite fields with prime order. While the complex reversible prime class is further defined. The complex reversible prime class is the subset of all prime numbers in the form of 4n+3. The sufficient conditions for a Gauss ring over finite fields to become a field are given by using the complex reversible prime class. Finally, the application of the Gauss ring over finite fields to the Shamir secret sharing scheme after it has become a field is presented.
Keywords: Finite fields, Gauss ring, Complex reversible prime class, Gauss field, Shamir secret sharing.
Download PDF