Method and Algorithm for Implementation of Decoding Operation in the Threshold Cryptomodule of Secret Separation Using a Minimally Redundant Modular Number System

Abstract

The article presents a new development of method and algorithm for performing secret separation in a threshold cryptomodule with masking transformation of the decoding operation. To solve this problem a recursive binary exponent division scheme and computational technology on the ranges of large numbers of the table-adder type, based on minimally redundant modular arithmetic (MRMA) are applied. A distinctive feature of the developed approach is usage the secret-original domain of finite residue rings for modules that have the form of powers of the number 2. This significantly reduces the complexity of the resulting decoding MRMA-procedure. Decomposition of scalable residues into large modules allows you to efficiently map the computational process being implemented to sets of easily implemented data extraction operations from table memory and their summation, providing a high level of performance, uniformity, and unification of basic structures. In terms of speed, the created MIMA decoding algorithm surpasses non-redundant analogues by at least l(19l-3)/(22l-6) times (l is the number of subscribers restoring the secret original). When l = 7...40 a (6.15...34.65)-fold increase in productivity is achieved.