Apparatus and method for calculating Bc (mod n)

摘要

Apparatus method for calculating the remainder of BC modulo n at high speed with minimum hardware resources, while securing the safety of the key in a cryptographic system. The apparatus comprises circuitry including registers for executing an initial and normal cycles, cumulating and storing the calculation result of each cycle and for outputting from a least significant bit. The initial cycle of the calculation includes a step of calculating a remainder of an m-bit input modulo n and a step of holding the result of the calculation. The normal cycle of the calculation includes a step of doubling the result of the calculation, and calculating a remainder of the doubled result of the calculation modulo n and a step of holding the next result of the calculation and for repeatedly executing the normal cycle m-2 times after the first normal cycle. The calculation result of each previous normal cycle is used in each successive normal cycle.