A Custom Instruction Approach for Hardware and Software Implementations of Finite Field Arithmetic over $$\mathbb{F}_{{2^{{163}} }} $$ using Gaussian Normal Bases

This paper presents a comprehensive analysis of the design of custom instructions in a reconfigurable hardware platform dedicated to accelerate arithmetic operations in the binary field $$\mathbb{F}_{{2^{{163}} }} $$, using a Gaussian normal basis representation. The resulting platform is capable of running real applications, thus allowing a precise measurement of the execution overheads, and a fair comparison of the hardware and software speedups at several implementation levels. By using this approach, we determine which field operations (e.g., multiplication) are better suited to constrained environments, and which ones provide an enhanced performance in general-purpose systems. Experimental results reveal that by using our fastest field multiplier implemented as a custom instruction in a combined hardware/software approach, we accelerate point multiplication (the fundamental operation in Elliptic Curve Cryptography) over 126 times.

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