afast publiclyverifiable secret sharing scheme using non-homogeneous linear recursions

A non-interactive (t; n)-publicly veriable secret sharing scheme (non-interactive (t; n)-pvss scheme) is a (t; n)-secret sharing scheme in which anyone, not only the participants of the scheme, can verify the correctness of the produced shares without interacting with the dealer and participants. the (t; n)-pvss schemes have found a lot of applications in cryptography because they are suitable for real-life scenarios in which an external verier is required to check the correctness of the produced shares without interacting with the dealer and participants. in this paper, we propose a non-interactive (t; n)-pvss scheme using the non-homogeneous linear recursions (nhlrs), and prove its security with a formal method. we compare the computational complexity of our scheme with that of schoenmakers's scheme and show that our non-interactive (t; n)-pvss scheme runs faster than schoenmakers's scheme when n ≥ 5 and n ≥ t ≥ 2n+9/ n . the communicational complexity of our scheme is almost equal to that of schoenmakers's scheme.