To curtail the calculation quantity of power residue operation at moving terminals in the cipher communication with a star type moving radio communication system.

Plural sets of arbitrary exponents R and their power-residue values A (=gRmod p; (p) is a prime number or the power of this prime number, (g) is the element of GF (p)) are calculated in a base station 1 of the start type communication system. Plural sets of (R, A) are broadcast communicated to all the terminals from the base station 1. The respective terminals select the sets of an arbitrary number of the sets from these sets. The exponents R are synthesized by addition (or subtraction) and the power-residue values A are synthesized by multiplication (or division). At the respective terminals, the secret exponents and their power-residue values may be determined by the small calculation quantity involving the multiplication and division alone without the execution of the power residue operation. The determination of the secret exponents arbitrarily selected at the respective terminals is of a problem in discrete logarithm and is difficult even in the base station 1. As a result, the burdens at the terminals in a Diffie-Hellman Key Sharing Scheme or the like are decreased.