Computationally secure threshold secret sharing scheme with minimal redundancy

When designing and using distributed storage systems with cloud technology, the security issues become crucial. One of the promising mechanisms is the computationally secure threshold secret sharing scheme. We propose a computationally secure secret sharing scheme based on the minimally redundant modular code. It reduces the computational complexity of data encoding and decoding and reduce data redundancy. We show that it is computationally secure and provides data redundancy equivalent to the redundancy of the Rabin system. We demonstrate that the minimally redundant modular code does not satisfy the criterion of compactness of a sequence, but it can be used as an asymptotically ideal secret sharing scheme.