Automatic generation system for multiple-valued galois-field parallel multipliers

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3 Citations (Scopus)


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 ≥ 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(GF(pm)) multipliers for different p-values. In addition, we evaluate the performance of three types of GF(2m) multipliers and typical GF(GF(pm)) multipliers (p ≥3) 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(GF(pm)) having extension degrees greater than 128.

Original languageEnglish
Pages (from-to)1603-1610
Number of pages8
JournalIEICE Transactions on Information and Systems
Issue number8
Publication statusPublished - 2017 Aug


  • Automatic generation
  • Formal design
  • GF arithmetic circuits
  • Multiple-valued logic
  • Parallel multipliers


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