Method for Performing a Decoding Operation in a Threshold Mrma Cryptosystem of Secret Separation with Masking Transformation

Abstract

Introduction: the article proposes a new method for recovering a spatially shared secret within the threshold principle based on sets of partial secrets belonging to subscriber groups, the number of which is limited from below by a specified threshold. Materials and methods of the research: to reduce the time spent on performing this operation, minimally redundant modular arithmetic (MRMA) is used as a computer arithmetic base. Unlike non-redundant analogs, MRMA possesses more efficient non-modular procedures, which makes it possible to optimize the decoding operation in the threshold MRMA-crypto-scheme of secret sharing. The results of the research and their discussion: a distinctive feature of the developed approach is the use of change areas for the original secret, which are rings of residues in moduli of the form of powers of 2. This greatly simplifies the decoding operation performed by the binary exponential division method. Conclusions: due to the noted features, the developed method for reconstructing the original secret using secret-mask codes surpasses the non-redundant counterparts by at least times (l is the number of subscribers restoring the original secret). At l = 7÷ 40, а (6.15 ÷ 34,65) - fold increase in productivity is achieved.