A Verifiable and Detectable Secret Sharing Scheme by Using a New Geometric Approach

Secret sharing schemes are methods for distributing a secret among n participants in such a way that any qualified subsets of participants can recover the secret, and unqualified participants can not. In 1979, secret sharing schemes were first independently introduced by Blakley and Shamir. In 1987, Feldman proposed a verifiable secret sharing scheme based on Shamir’s Scheme, that every participant can verify their share is true or not. Wu and He proposed a geometric approach for sharing secrets by using a hyperspherical polynomial in 1995. The secret can hide in any one of the coefficients of a hyperspherical polynomial. This paper propose a new geometric approach for sharing secrets based on a hyperelliptic function that is efficient than Wu and He’s Scheme. Moreover, we modify it to be a practical scheme that can verify the shares and detect the cheater, which is more efficient than Feldman’s scheme.