Scalar multiplication kP is the operation most frequently targeted in Elliptic Curve (EC) cryptosystems. To protect against single-trace Side-Channel Analysis (SCA) attacks, the atomicity principle and various atomic block patterns have been proposed in the past. In this work we use our software and hardware implementations to demonstrate that binary right-to left and left-to-right kP algorithms, when implemented with Chevallier-Mames atomic block patterns, are still vulnerable to single-trace SCA attacks. The vulnerability remains true for the left-to-right kP algorithm with projective coordinate randomization.

翻译：标量乘法 kP 是椭圆曲线密码系统中最为频繁受攻击的操作。为防范单迹线侧信道攻击，过去已提出了原子化原则及多种原子块模式。本研究通过软件与硬件实现证明，采用Chevallier-Mames原子块模式的二元从右向左及从左向右kP算法，仍易受单迹线侧信道攻击。即便引入了射影坐标随机化，从左向右kP算法的这一脆弱性依然存在。