橢圓曲線基於二位元場之有效對抗功率分析之方法

Efficient Countermeasures to Power Analysis of ECC on Binary Field

林裕舜(Yu-Shuen Lin)

指導教授 ： 汪順祥

大同大學/電機資訊學院/通訊工程研究所/碩士(2011年)

摘要

橢圓曲線加密系統 (ECC) 因為其使用較短長度的金鑰就可達到與傳統公開金鑰加密系統相同的安全性，故已經被應用在許多資源限制的環境裡。然而，簡單功率分析攻擊 (SPA) 和差分功率分析攻擊 (DPA) 這類利用 ECC 功率的旁通道攻擊 (SCA) 會使加密私鑰的內容被洩漏出來。為了對抗功率分析，近年來已有許多研究提出對抗方法，像是參考文獻[1]、[2]和[3]。在此篇論文中，我們藉由設計純量乘法演算法以及修改點運算的數學計算方式提出對抗功率分析的方法。與文獻所提出的方法比較得知我們提出的方法在運算時間上更有效率。

關鍵字

橢圓曲線加密系統 ； 純量乘法 ； 旁通道攻擊 ； 簡單功率分析攻擊 ； 差分功率

並列摘要

Elliptic curve cryptosystem (ECC) has been applied to many resource constraint environments because it requires shorter keys than traditional public-key cryptography systems in equal security level. However, the secret keys may be disclosed by side channel attacks (SCA) such as simple power analysis (SPA) and the differential power analysis (DPA) that exploit the power consumption of ECC devices. To oppose power analysis, many countermeasures have been proposed in recent years like [1], [2], and [3]. In this thesis, we propose some scalar multiplication methods with resistance against SPA and DPA by devising the scalar multiplication algorithm and modifying the arithmetic of point operations on the finite field . Compared with the Double-and-Add-Always scalar multiplication algorithm and Binary Expansion with Random Initial Point (BRIP), our countermeasures are efficient in terms of computation time.

並列關鍵字

ECC ； scalar multiplication ； SCA ； SPA ； DPA

參考文獻

[1] A. Hodjat, D. D. Hwang, and I. Verbauwhede, "A scalable and high performance elliptic curve processor with resistance to timing attacks," International Conference on Information Technology: Coding and Computing, Vol. 1, pp. 538-543, 2005.

[2] T. F. Al-Somani and A. Amin, "An Efficient High Performance Scalar Multiplication Method with Resistance against Timing Attacks," International Conference on Computer Systems and Applications, pp. 860-865, 2008.

[3] F. Zhang and Z. J. Shi, "An Efficient Window-Based Countermeasure to Power Analysis of ECC Algorithms," Fifth International Conference on Information Technology: New Generations, pp. 120-126, 2008.

[5] N. Koblitz, "Elliptic curve cryptosystems," In Mathematics of Computation, Vol. 48, no. 177, pp. 203-209, Jan. 1987.

[6] M. Joye and S. M. Yen, "Optimal left-to-right binary signed-digit recoding," IEEE Transactions on Computers, Vol. 49, pp. 740-748, Jul 2000.