Abstract

Introduction: The quest for increasing the security of data in secret-sharing schemes has attracted much attention in the world of cryptography. Several methods have been applied, and the application of the new technique, (n,n)-threshold secretsharing scheme based on equivalence classes, will be a perfect solution. Aims: The aim is to explore and construct strong knowledge in the theory and structure of the secret-sharing scheme on (n,n)- threshold secret-sharing scheme based on equivalence classes; (𝑋) = (𝑦 𝜖 𝑋: (𝑥, 𝑦)𝜖 ℝ) And achieve the following objectives: i. To investigate an (𝑛, 𝑛)-threshold secret-sharing scheme based on the equivalence classes of the prime over ℤ. ii. Investigation of the accuracy of such a scheme. Materials and Methods: The study uses the set of integers modulo a prime and modulo arithmetic on the set of integers. Results: The statistics on the coalition, security analysis, and information-theoretic efficiency are also discussed. Conclusion: The secret sharing scheme on (10,10)-threshold secret-sharing scheme based on equivalence classes of integers modulo a prime is perfect in terms of only qualified coalitions can obtain the secret and it is reliable by means of security. We have used the property of these classes to provide the reconstruction algorithms, and access structures and calculated the number of minimal coalitions of the scheme. This new system is ideal in that the size of the secret is equal to the size of the share.

Keywords: SECRET SHARING, THRESHOLD SECRET SHARING SCHEME, and EQUIVALENCE RELATION