基于边带信道原子的安全快速椭圆曲线密码点乘算法  

Fast and secure elliptic curve scalar multiplication algorithm based on side channel atomicity

作　　者：秦宝东[1] 孔凡玉[2] 

机构地区：[1]西南科技大学计算机科学与技术学院,四川绵阳621010 [2]山东大学网络信息安全研究所,济南250100

出　　处：《计算机应用》2009年第11期2983-2986,共4页journal of Computer Applications

基　　金：西南科技大学青年基金资助项目(08zx3118);山东省优秀中青年科学家科研奖励基金计划资助项目(2008BS01011)

摘　　要：简单功耗分析对椭圆曲线点乘算法的安全性具有很大的威胁,在某种程度上可以恢复出密钥。提出一种抵抗简单功耗攻击的快速边带信道原子点乘算法。算法的倍点和点加运算采用形如S-A-N-A-M-N-A(平方-加法-逆运算-加法-乘法-逆运算-加法)的边带信道原子结构,其运算量为:在Jacobian坐标系下倍点运算量为5M+5S+15A,混加运算量为6M+6S+18A;在改进的Jacobian坐标系下,倍点运算量为4M+4S+12A,混加运算量为7M+7S+21A。在效率方面,新的点乘算法比以往的边带信道原子点乘算法的运算速度有较大提高。例如对于采用NAF编码的192bit的点乘算法,当S/M=0.8时,效率提高约7.8%～10%,当S/M=0.6时,提高约18%～20%。Simple power analysis is the most devastating attack on the security of elliptic curve scalar multiplication and can retrieve the secret key in some degree. A fast and secure side channel atomic elliptic curve scalar multiplication algorithm was put forward using the side channel atomic block S-A-N-A-M-N-A. In Jacobian coordination, the new algorithm used only 5M ＋ 5S ＋ 15A for doubling and 6M ＋ 6S ＋ 18A for mixed addition. In modified Jacobian coordination, the new algorithm used only 4M ＋4S ＋ 12A for doubling and 7M ＋7S ＋21A for mixed addition. Compared with the previous methods, the new method can improve the speed by about 7.8% - 10% if S/M = 0.8 or 18% - 20% if S/M = 0.6 for 192 bit scalar using NAF recoding.

关 键 词：点乘 简单功耗分析 边带信道攻击 Jacobian坐标系 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]