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This paper presents an efficient approach to verifying higher-degree Galois-field (GF) arithmetic circuits. The proposed method describes GF arithmetic circuits using a mathematical graph-based representation and verifies them by a combination of algebraic transformations and a new verification method based on natural deduction for first-order predicate logic with equal sign. The natural deduction...
This study presents a formal approach to designing pipelined arithmetic circuits over Galois fields (GFs). The proposed method extends a graph-based circuit description known as a Galois-field arithmetic circuit graph (GF-ACG) to Linear-time Temporal Logic (LTL) in order to represent the timing property of pipelined circuits. We first present the extension of GF-ACG and its formal verification using...
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...
This paper presents a graph-based approach to designing arithmetic circuits over Galois fields (GFs) based on a polynomial ring (PR) representation, which is a redundant representation for GF arithmetic. The proposed method extends a graph-based circuit description, called a Galois-field arithmetic circuit graph (GF-ACG), which was originally proposed for no redundant GF arithmetic. First, the extension...
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