Generalized Mignotte's Sequences Over Polynomial Rings

This paper introduces the generalization of Mignotte modular secret sharing over the polynomial rings. Mignotte proposed threshold secret sharing over the ring of integers. We extend his method for the ring of polynomials which is Euclidean as well and therefore allowing to use the Chinese Remainder Theorem. In particular, we prove that any access structure can be realized within this modular approach. Further, we put the bounds on the number of participants of such secret sharing scheme with the moduli of the same degree. And finally we estimate the information rate of the new scheme.