一种基于随机混合坐标表示的防功耗分析标量乘法实现方法

Power Analysis Resistant Method for Scalar Multiplication Based on Randomized Mixed Coordinates

提出了一种新的防功耗分析(包括简单和差分功耗分析simpleanddifferentialpoweranalysis)的椭圆曲线标量乘法实现方法,该方法实现简单,并且适合于各种不同有限域上椭圆曲线标量乘法的实现.该方法以模乘和模加减操作为最小调度单位,将标量乘法转换成完全随机的模乘和模加减操作序列;基于随机混合坐标表示实现点的加法和倍加操作,并随机地从点的加法和倍加操作序列中选取后续的模乘和模加减操作;任务调度与模乘和模加减操作的执行是并行的.另外,本文定量分析了该实现方法对于功耗分析的防护能力以及运算性能.

To protect point multiplication against simple and differential power analysis, a new method is presented. The easily implemented method is suitable for any elliptic curves over any finite fields. In this method, the modular multiplication and the modular addition/subtraction are considered as the primitive operations. Then the scalar multiplication is transformed to the random sequence of the primitive operations. Based on the randomized mixed coordinates, this method selects the sequential primitive operations from the point addition or double randomly. Besides, the scheduler and the computation are processed in parallel. Also this paper gives the quantitative analysis of the performance and ability for the power analysis.