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ECC标量乘算法在抗边信道攻击上的应用研究

发布时间:2019-01-01 15:37
【摘要】:随着移动互联网和电子商务的快速发展,信息安全问题令人堪忧。保障信息安全的重要方法和手段是密码技术。椭圆曲线密码(ECC)较之于RSA等其他传统公钥密码,具有安全性高、计算量小、处理速度快、存储空间占用少、带宽要求低等优点,尤其适用于处理能力、存储空间、带宽、功耗等受限的环境中,因而得到了广泛关注。然而近年来,一种称之为边信道攻击(SCA)的新的密钥攻击手段,对ECC带来了巨大的威胁。标量乘法是ECC最关键、最耗时的运算,其安全性和效率关乎着ECC的整体安全性和实现效率。虽然现有的ECC标量乘法有较好的安全性和计算效率,但仍难满足很多特定场合的需要,因此提高标量乘法的安全性和效率是必要的。为提高ECC的安全性和效率,本文在现有的边信道攻击和标量乘法的基础上,提出了两种能防御边信道攻击的ECC标量乘法:一是基于二进制算法的安全高效标量乘法,该算法利用窗口方法计算速度快的特点,在不插入伪操作的前提下使标量乘法中的点加和倍点运算不可区分,同时将标量进行重编码来防止密钥相关信息泄漏,理论分析证明,新算法既能够对抗边信道攻击,又减少了窗口方法需要的存储空间;二是基于多基表示的安全高效标量乘法,首先,在仿射坐标上改进了二进制域上7P的快速算法,然后,通过引入随机数和基点掩码技术隐藏算法的相关边信道信息,从而增强算法的安全性,最后,结合快速的半点运算和多基表示标量,提高算法的效率,在VC++6.0和MATLAB 2010b的实验环境下,对该算法的效率进行了测试,实验结果证明,新算法提高了以往多基标量乘法的效率。因此,两种算法均可应用到智能卡等存储资源受限的领域中,使得ECC对敏感数据的加解密更安全、更高效。
[Abstract]:With the rapid development of mobile internet and e-commerce, the problem of information security is worrying. Cryptography is an important method and means to ensure information security. Compared with other traditional public key cryptography such as RSA, Elliptic Curve Cryptography (ECC) has the advantages of high security, less computation, fast processing speed, less storage space, low bandwidth requirement and so on. It is especially suitable for processing power, storage space, bandwidth, etc. Because of the limited power consumption and other environments, it has been paid more and more attention. However, in recent years, a new key attack called edge channel attack (SCA) has posed a great threat to ECC. Scalar multiplication is the most critical and time-consuming operation in ECC. Its security and efficiency are related to the overall security and implementation efficiency of ECC. Although the existing ECC scalar multiplication has better security and computational efficiency, it is still difficult to meet the needs of many special situations. Therefore, it is necessary to improve the security and efficiency of scalar multiplication. In order to improve the security and efficiency of ECC, on the basis of existing edge channel attacks and scalar multiplication, two kinds of ECC scalar multiplication which can defend against edge channel attacks are proposed in this paper: one is security efficient scalar multiplication based on binary algorithm. The algorithm makes use of the fast computing speed of the window method and makes the point addition and doubling operations in scalar multiplication indistinguishable without inserting pseudo operations. At the same time, the scalar is re-coded to prevent the leakage of key related information. The new algorithm can not only resist the side channel attack, but also reduce the storage space required by the window method. The second is the efficient scalar multiplication based on multi-base representation. Firstly, the fast algorithm of 7P in the affine coordinate is improved, and then the correlation channel information of the algorithm is hidden by introducing random numbers and base-point masking techniques. In order to enhance the security of the algorithm, the efficiency of the algorithm is improved by combining the fast half-point operation and multi-base representation scalar, and the efficiency of the algorithm is tested under the environment of VC 6.0 and MATLAB 2010b. The experimental results show that the algorithm is efficient. The new algorithm improves the efficiency of the previous multibase scalar multiplication. Therefore, both algorithms can be applied to storage resource constrained areas such as smart cards, which make ECC encryption and decryption of sensitive data more secure and efficient.
【学位授予单位】:贵州大学
【学位级别】:硕士
【学位授予年份】:2015
【分类号】:TN918.4

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