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首页> 外文期刊>International Journal on Computer Science and Engineering >ON THE DESIGN OF PROJECTIVE BINARY EDWARDS ELLIPTIC CURVES OVER GF (P) BENEFITING FROM MAPPING ELLIPTIC CURVES COMPUTATIONS TO VARIABLE DEGREE OF PARALLEL DESIGN
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ON THE DESIGN OF PROJECTIVE BINARY EDWARDS ELLIPTIC CURVES OVER GF (P) BENEFITING FROM MAPPING ELLIPTIC CURVES COMPUTATIONS TO VARIABLE DEGREE OF PARALLEL DESIGN

机译：从映射椭圆曲线计算到并行设计的不同程度受益的GF（P）上射影二元爱德华椭圆曲线的设计

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Finding multiplicative inverse (Modular Inversion) operation is the most time-consuming operation in Elliptic Curve Crypto-system (ECC) operations which affects the performance of ECC. Moreover, several factors that affect the design of ECC have not been intensively investigated in the majority of researches related to ECC, Such as system utilization, area, resources-consuming and area*time cost factors, which play significant role in designing efficient ECC for different applications. This work applies Binary Edwards ECC point doubling operation over GF(p) using projective coordinates instead of affine coordinates due to its ability to remove the long time inversion operation by converting it to a number of multiplication operations. We also utilize the inherent parallelism in ECC operations by mapping its computations to parallel hardware design, in order to improve the performance of ECC. Our results show that the shortest time delay is achieved using 7-Parallel Multipliers (PM) design with projection (X/Z, Y/Z), which overcomes both serial design and the design with affine coordinates. Furthermore, this research proposes a variety of design choices by varying the degree of parallelism to tune-up several factors that affect ECC in order to investigate possible enhancements. It is shown by our experiments that the hardware utilization can be improved by 55%, with less area, and acceptable timeconsuming level compared to other designs in the same projection. In other words, we compromise th performance to enhance system utilization degree, and AT cost, and to reduce area and resourceconsuming. This trade-off between factors is useful to determine the efficient design to be used for different ECC applications based on their requirements and available resources. Especially, when the time-consuming is not the main priority.
机译：在椭圆曲线加密系统（ECC）运算中，找到乘法逆运算（模数反转）是最耗时的运算，这会影响ECC的性能。此外，在大多数与ECC相关的研究中，尚未对影响ECC设计的几个因素进行深入研究，例如系统利用率，面积，资源消耗和面积*时间成本因素，这些因素在设计高效ECC方面起着重要作用。不同的应用程序。这项工作使用投影坐标而不是仿射坐标在GF（p）上应用Binary Edwards ECC点加倍运算，因为它具有通过将其转换为多个乘法运算来消除长时间反转运算的能力。我们还通过将ECC的计算映射到并行硬件设计来利用ECC操作中固有的并行性，以提高ECC的性能。我们的结果表明，使用具有投影（X / Z，Y / Z）的7并行乘法器（PM）设计可实现最短的时延，从而克服了串行设计和仿射坐标设计。此外，本研究通过改变并行度来调整影响ECC的几个因素以提出可能的增强方案，从而提出了多种设计选择。通过我们的实验表明，与相同投影中的其他设计相比，硬件利用率可以提高55％，面积更小，并且可以接受的耗时水平。换句话说，我们会牺牲性能来提高系统利用率和AT成本，并减少面积和资源消耗。这些因素之间的折衷对于根据其要求和可用资源来确定要用于不同ECC应用程序的有效设计很有用。特别是在不是耗时的主要优先事项时。

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