【摘要】：隨著移動互聯(lián)網(wǎng)和電子商務的快速發(fā)展,信息安全問題令人堪憂。保障信息安全的重要方法和手段是密碼技術。橢圓曲線密碼(ECC)較之于RSA等其他傳統(tǒng)公鑰密碼,具有安全性高、計算量小、處理速度快、存儲空間占用少、帶寬要求低等優(yōu)點,尤其適用于處理能力、存儲空間、帶寬、功耗等受限的環(huán)境中,因而得到了廣泛關注。然而近年來,一種稱之為邊信道攻擊(SCA)的新的密鑰攻擊手段,對ECC帶來了巨大的威脅。標量乘法是ECC最關鍵、最耗時的運算,其安全性和效率關乎著ECC的整體安全性和實現(xiàn)效率。雖然現(xiàn)有的ECC標量乘法有較好的安全性和計算效率,但仍難滿足很多特定場合的需要,因此提高標量乘法的安全性和效率是必要的。為提高ECC的安全性和效率,本文在現(xiàn)有的邊信道攻擊和標量乘法的基礎上,提出了兩種能防御邊信道攻擊的ECC標量乘法:一是基于二進制算法的安全高效標量乘法,該算法利用窗口方法計算速度快的特點,在不插入偽操作的前提下使標量乘法中的點加和倍點運算不可區(qū)分,同時將標量進行重編碼來防止密鑰相關信息泄漏,理論分析證明,新算法既能夠對抗邊信道攻擊,又減少了窗口方法需要的存儲空間;二是基于多基表示的安全高效標量乘法,首先,在仿射坐標上改進了二進制域上7P的快速算法,然后,通過引入隨機數(shù)和基點掩碼技術隱藏算法的相關邊信道信息,從而增強算法的安全性,最后,結合快速的半點運算和多基表示標量,提高算法的效率,在VC++6.0和MATLAB 2010b的實驗環(huán)境下,對該算法的效率進行了測試,實驗結果證明,新算法提高了以往多基標量乘法的效率。因此,兩種算法均可應用到智能卡等存儲資源受限的領域中,使得ECC對敏感數(shù)據(jù)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.
【學位授予單位】：貴州大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TN918.4

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本文編號：2397755