On the Security of Secret Sharing Over a Ring and the Fast Implementation

Secret sharing is the method to share secrets among a group of shares, and the secret can be reconstructed if one obtains a predefined number of shares. The polynomial secret sharing is usually constructed over a field. In this letter, a novel polynomial secret sharing over a ring is proposed. In particular, by choosing a certain ring, the fast Fourier transform can be applied on the encoding of secret sharing. The analysis shows that the...