椭圆曲线密码
计算机科学
现场可编程门阵列
椭圆曲线点乘
算术
并行计算
加法器
乘数(经济学)
椭圆曲线
计算机硬件
延迟(音频)
数学
公钥密码术
加密
数学分析
经济
宏观经济学
操作系统
电信
作者
Khalid Javeed,Ali A. El-Moursy
摘要
Abstract Elliptic curve point multiplication is the main primitive required in almost all security schemes using elliptic curve cryptography (ECC). It is the leading computationally intensive operation that sets the overall performance of the associated cryptosystem. This work presents a highly novel area–time efficient elliptic curve point multiplier over a general prime field . It is based on an efficient radix‐2 3 parallel multiplier, which performs a ‐bit multiplication in clock cycles. On the system level, the twisted Edwards curves with unified point addition using projective coordinates are adopted, where an efficient scheduling technique is presented to schedule several operations on deployed modular arithmetic units. Due to the introduced optimization at different stages of the design, latency, hardware resource requirement, and total clock cycle count are reduced significantly. Synthesis, and implementation of the proposed design over different Xilinx FPGA platforms are completed using the Xilinx ISE Design Suite tool for key sizes of 192, 224, and 256 bits. The 256‐bit Xilinx Virtex‐7 FPGA implementation reveals that it completes a single point multiplication operation in 0.8 ms and occupies 6.7K FPGA slices in a clock cycle count of 132.2K. It produces significantly better area–time product and throughput per slice than the contemporary designs. The proposed design also has the potential to counter simple power analysis and timing attacks. Thus, it is an elegant solution to develop ECC‐based cryptosystems for applications, where both speed and hardware resource consumption are important.
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