Koblitz曲线上抵抗简单功耗分析的有效算法

Efficient algorithm with resistance to simple power analysis on Koblitz curves

在一类特殊的椭圆曲线——Koblitz曲线上,使用窗口长度为w的非邻接形式（TNAFw）的算法可以提高椭圆曲线的标量乘计算,但是容易受到边信道攻击.提出了一种新的抵抗简单功耗分析的有效算法,其基本思想是通过在使用TNAFw算法的标量乘中添加冗余操作抵抗对使用TNAFw算法的标量乘的简单功耗分析.该算法进一步优化了预计算点个数和计算时间,与SPA-resistant TNAFw（STNAFw）算法相比,预计算点个数减少了约50%,计算时间减少了约18%-28%.

Koblitz curves belong to a special class of binary curves on which the scalar multiplication can be computed very efficiently by the method of width w radix-τ NAF expansion （TNAFw）. The scalar multiplication using TNAFw is vulnerable to side channel attacks. A new efficient algorithm is proposed against simple power analysis. Its basic idea is to insert dummy operations in the scalar multiplication using TNAFw so as to resist simple power analysis. This algorithm further optimizes computational cost and the pre-computation table. Compared with the SPA- resistant TNAFw （ STNAFw ） algorithm, the number of pre-computation points is reduced about 50% and its computation time is reduced about 18% - 28%.