中文摘要：

为椭圆曲线密码体制（ECC）提出了一种高效且安全的标量乘方法。该方法划分标量为两个等长的子比特串，并基于命题逻辑操作从中抽取共同子比特串，以节省标量乘操作中计算共同子比特串的操作次数，从而提高了标量乘的计算效率，并且又能防御所谓的侧信道攻击（SCA）。效率评估证明，该标量乘方法的效率要比现有实现侧信道安全的标量乘方法高出约50％。功耗实验证明，该标量乘方法是能够保证侧信道安全的。现有的安全方案都是在二进制方法的基础上增加额外操作来保证侧信道安全的，这大大增加了计算开销，从而影响ECC在资源有限的计算设备上的实现，而这种新的标量乘方法既没有增加计算开销，又能确保ECC有效防御SCA。

英文摘要：

This paper proposes an efficient and secure scalar muhiplication method for elliptic curve cryptosystems （ECCs）. The method partitions the scalar into two equal bit strings and extracts common substrings from the two parts based on the propositional logic theory to save the common substring computations in scalar multiplication operations. Thus, it can im- prove the efficiency for scalar multiplication, and secure ECCs against so-called side-channel attacks. The computational results demonstrate that the proposed method is approximately 50% more efficient than almost all existing secure solu- tions. The side-channel experiments prove that the proposed method can be secure against side-channel attacks. Existing solutions reach the goal of security by inserting dummy operations, which largely increase the computational cost and prohibit the deployment of ECCs in computation resource-restricted devices. However, the proposed secure method does not penalise the computational cost.