Method for reducing a value modulo a shared secret

Abstract

A method is provided for reducing a known value modulo a shared secret value among network devices exchanging messages in a network. The reduction results in a share of reduced value for each network device of a reduced value. Each network device has its share of known value and its share of shared secret value. It performs an inversion step for deriving from the share of shared secret value a share of the inverse of the shared secret value by using an approximation process, resulting in a share of inverse value; a multiplication step for deriving from the share of inverse value by use of the share of known value a share of multiplied inverse value; a rounding step for rounding the share of multiplied inverse value; and a calculation step for deriving the share of reduced value from the share of known value, the rounded share of multiplied inverse value, and the share of shared secret value. The method reduces values with a public modulus but also enables several network devices to reduce their known values with a modulus shared among them, but not becoming public. After the reduction, a faster computation with the reduced values or the shares thereof can be achieved. The proposed method can be implemented in threshold protocols in which computation occurs in a group where a modulus is not known but distributed. Furthermore, a network device is provided comprising a processor for executing the method incorporated in a computer program product.