This paper presents a system for the automatic generation of Galois-field (GF) arithmetic circuits, named the GF Arithmetic Module Generator (GF-AMG). The proposed system employs a graph-based circuit description called the GF Arithmetic Circuit Graph (GF-ACG). First, we present an extension of the GF-ACG to handle GF(pm) (p &ge; 3) arithmetic circuits, which can be efficiently implemented by multiple-valued logic circuits in addition to the conventional binary circuits. We then show the validity of the generation system through the experimental design of GF(3m) multipliers for a ternary logic circuit. In addition, we evaluate the performance of typical GF(2m) multipliers empirically generated by our system. We confirm from the results that the proposed system can generate a variety of GF parallel multipliers, including practical multipliers over GF(2m) and GF(3m) having degrees greater than 128.