LowLatency Semi-Systolic Array for Computing theModular AB2Multiplication Based on Shifted Polynomial Basis over Finite Fields

Abstract

Arithmetic operations in finite fields have been adopted in a variety of fields such as cryptographic algorithms and error correction codes.Especially, it is necessary to compute exponentiation over finite fields in cryptosystems and exponentiation is a time-consuming operation.This paper focuses on a modular AB^2 multiplication for being used to perform exponentiation over GF(2^n).Various architectures for computing the modular AB^2 multiplication has been developed. Since the existing modular AB^2 multipliers have high time and area complexities, we need to develop a modular AB^2 multiplier with lower time and area than existing multipliers.In this paper, a modular AB^2 multiplier using the semi-systolic architecture in finite fields based on the shifted polynomial basis. The proposed modular AB^2architecture has the low area and time complexities as compared to other modular AB^2multipliers.