Parity Check based redistribution of secret shares

In 2002, Wong-Wang-Wing presented a verifiable redistributing secret shares protocol, where the new parties must have been honest. They used Feldman´s Verifiable Secret Sharing scheme, which assumed that the discrete logarithm is hard. In 2013, Nojoumian and Stinson presented information-theoretically (unconditionally) secure schemes under assumption that at most t out of 4t+1 parties are actively corrupt, where only the threshold (but not the number of parties) can be changed. We present an unconditionally secure solution assuming that at most t out of 3t+1 parties are actively corrupt. Our protocol uses properties of the parity-check matrix of a Generalized Reed-Solomon code. Moreover, we introduce a new open problem in the area of Reed-Solomon decoding.