Fast Elliptic Curve Multiplications Resistant against Side Channel Attacks
Fast Elliptic Curve Multiplications Resistant against Side Channel Attacks
复制标题
快速椭圆曲线乘法可抵抗侧信道攻击
DOI：
10.1093/ietfec/e88-a.1.161
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
T. Takagi
中科院分区：
文献类型：
--
作者：
T. Izu;T. Takagi
本文提出了基于蒙哥马利型标量乘法的快速椭圆曲线乘法算法抵抗侧道通道攻击的算法。所提出的标量乘法可以应用于序场上的所有曲线，例如，在特征大于3的有限磁场上的任何标准化曲线。有限字段上的任何类型的曲线。然后，我们将两个添加公式封装到一个公式Xecadddbl中，该公式可以完成一个更快的计算，因为可以共享两个公式的辅助变量。我们还为新公式开发了一个新型的加法链，我们可以通过该链来计算标量乘以。对于160位标量乘法，我们的标量乘积比以前的Coron的虚拟操作方法的改进约为18％。我们的方法不需要列表预先计算的点，它适用于内存约束计算体系结构（例如智能卡）的实现。此外，我们优化了使用SIMD操作的并行化实现的提出算法。与Fischer等人提出的类似方案相比，我们的方案速度约为16％。
This paper proposes fast elliptic curve multiplication algorithms resistant against side channel attacks, based on the Montgomery-type scalar multiplication. The proposed scalar multiplications can be applied to all curves over prime fields, e.g., any standardized curves over finite fields with characteristic larger than 3. The method utilizes the addition formulas xECDBL and xECADD assembled by only x-coordinates of points, and is applicable for any types of curves over finite fields. Then, we encapsulate two addition formulas into one formula xECADDDBL, which accomplishes a faster computation because several auxiliary variables of two formulas can be shared. We also develop a novel addition chain for the new formula, with which we can compute scalar multiplications. The improvement of our scalar multiplications over previous Coron's dummy operation method is about 18% for a 160-bit scalar multiplication. Our method requires no table-up of precomputed points and it is suitable for the implementation on memory constraint computing architectures, e.g., smart cards. Moreover, we optimize the proposed algorithms for parallelized implementations with SIMD operations. Compared with the similar scheme proposed by Fischer et al., our scheme is about 16% faster.