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.