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    基于FPGA的高速椭圆曲线标量乘法结构

    High Performance Architecture for Elliptic Curve Scalar Multiplication Based on FPGA

    • 摘要: 椭圆曲线密码系统是最近十几年来获得迅速发展的一类密码系统.为了提高椭圆曲线密码系统的处理速度,针对其中最关键的运算——椭圆曲线标量乘法设计并实现了一种基于FPGA的硬件结构,完成GF(2/+m)上的椭圆曲线标量乘法计算.该结构最大程度地对标量乘算法的内部模块进行了并行处理,缩短最大延迟路径,从而达到提高运算速度的目的.这一结构在FPGA上实现后,计算一次GF(2/+/163/)上的椭圆曲线标量乘法只需要36μs,这一性能是目前国际上已知的基于FPGA的标量乘法器中最好的.

       

      Abstract: Elliptic curve scalar multiplication (ECSM) is the most important operation in elliptic curve cryptography (ECC). The study of its implementation performance and optimization has attracted great interests of researchers due to the rapid development and deployment of ECC recently. Focusing on designing high performance hardware architecture for this operation, first a digit-serial/parallel finite field multiplier with word width D is developed, which completes one multiplication over GF(2/+m) in m/Dcycles. Using this multiplier, a hardwired logic design for performing elliptic curve scalar multiplication over GF(2/+m) is proposed. This architecture maximizes the parallelism that the projective coordinates version of the Montgomery scalar multiplication algorithm can achieve, and also shortens the maximum delay path. It completes one scalar multiplication over GF(2/+m) in about (5m-6) cycles. When implemented on Xilinx Virtex4-LX200 FPGA, using multipliers with word width 16, it occupies about 46% of all computation resources available, achieves a frequency of 225MHz, and takes only 36μs to complete one elliptic curve scalar multiplication operation for arbitrary elliptic curves, arbitrary points and integers over GF(2/+/163/). This result outperforms all comparable FPGA-based elliptic curve scalar multipliers in the world. On the other hand, this architecture can be easily reconfigured to adapt different security levels and performance requirements.

       

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