特定素域上模运算的研究与硬件实现

基于素域上的椭圆曲线密码体制（ECC）被广泛应用，其中模运算是ECC中影响速度与资源的关键因素，本文对模运算进行了研究与硬件实现。采用提前模约减的方法，首先用二进制形式表示待求模的数并对其进行分组，其次分别提取每组的公因子并对公因子进行模约减，接着用约减后的数代换公因子并整理，最后进行模运算。该方法降低了模运算的复杂度，提高了运算效率。硬件仿真结果表明，本文研究的两种方法与Barrett约减算法相比，速度明显提高，资源大大减少。

Research and Hardware Implementation of Modular Arithmetic over a Particular Prime Field

Elliptic curve cryptosystems （ECC） on primitive finite fields plays an important role in current public-key cryptography. Modular arithmetic is the key factor of ECC that affect speed and resources. This paper uses the method of module reduction in advance, grouping and extracting the common factor of the figure which needs to be conducted the modular arithmetic and the subsequent modular reduction of the common factor efficiently reduce the complexity of the modular arithmetic, consequently, improve operation efficiency. The results suggest that the two methods in this paper, compared with Barrett reduction algorithm, speed were respectively increased, and resources respectively decreased.