Misc - Secret Sharing Schemes

This is about a particular weakness of the Shamir’s secret sharing scheme. During the share reassembly process, Shamir’s secret sharing does not provide a way to verify the correctness of each share being used. Verifiable secret sharing aims to verify that shareholders are honest and not submitting fake shares. The basis of Shamir’s secret sharing is on Lagrange basis polynomials. My solution is based on the computationally efficient approach of the scheme....

This is about Shamir’s secret sharing scheme, where the main idea is based on having sufficient points to fully define a polynomial curve. A polynomial of degree $t - 1$ can only be constructed if $t$ points (shares) are known. In this challenge, only the first share is known, so it seems like we do not have any way of retrieving the value. However, we can observe two points: The coefficient $c_i$ is generated by calculating the SHA-256 hash of the previous coefficient $c_{i - 1}$....