橢圓曲線密碼學目前被認為是最有前景且廣泛被使用的非對稱式密碼學，因為它可以以更短的密鑰長度提供同等的安全性。橢圓曲線點乘積是基於ECC的系統中最重要且成本最高的運算。橢圓曲線點乘積由許多模算術運算組成，包括模乘法、加法和減法。因此，橢圓曲線點乘處理器的效率很大程度上取決於其模算數運算單元的性能。然而，目前的橢圓曲線點乘處理器在不同的模組中執行這些模算術運算，可能導致硬體利用效率低下。為了解決這個問題，在本文中，我們提出了統一模算術單元，這些單元可以有效地計算在橢圓曲線點乘積中所需的所有模運算，我們也利用所提出的統一模算術單元實現了一個高性能的橢圓曲線點乘積處理器。因此該設計可以顯著節省面積並極大提升橢圓曲線點乘處理器的性能。此外，我們也優化了Hamburg's Montgomery ladder的排程，以簡化控制邏輯並提高硬體利用效率。實驗結果顯示，與現有的橢圓曲線點乘處理器相比，具有統一的模運算單元的橢圓曲線點乘處理器具有非常低的面積、相當高的工作頻率，以及比現有的橢圓曲線點乘處理器更小的面積與時間之乘積。

Elliptic Curve Cryptography (ECC) is the most promising and widely used asymmetric cryptography since it can provide the same security level with a much shorter key length. The elliptic curve point multiplication (ECPM) is the most important and costliest operation in ECC-based systems. ECPM comprises many modular arithmetic operations, including modular multiplication, addition, and subtraction. Therefore, the efficiency of an ECPM processor highly depends on the performance of its modular arithmetic units. However, present ECPM processors perform these modular operations in separate modules, which may lead to low hardware utilization efficiency. To solve the problem, in this work, we propose a unified modular arithmetic unit (UMAU) that can support all the required modular operations in ECPM efficiently. Furthermore, we utilized the proposed UMAUs to realize a high-performance ECPM processor. As a result, the area of an ECPM processor can be significantly saved, and the performance can be enhanced. Additionally, we optimize the scheduling of Hamburg’s Montgomery ladder to simplify the control logic and enhance hardware utilization efficiency. Experimental results show that the ECPM processor with the proposed UMAU achieves lower area, higher operating clock frequency, and much less area-time product than the present ECPM processors.

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