抵抗能量攻擊法的雙域橢圓曲線密碼運算單元之設計與實現

Design and Implementation of a Dual-Field Elliptic Curve Cryptographic Processor with Power Analysis Countermeasures

陳耀琳(Yao-Lin Chen)

指導教授 ： 李鎮宜

國立交通大學/電機學院/電子工程系所/碩士(2010年)

https://doi.org/10.6842/NCTU.2010.00468

摘要

在這篇論文中，我們提出了一個可支援雙域有限域運算以及可支援任意橢圓曲線運算的雙域橢圓曲線密碼運算單元。透過我們提出的通用演算法，這個運算單元的執行週期數大幅的降低。藉由我們提出的面積共用方法以及梯子選擇法，我們160位元以及256位元的雙域橢圓曲線密碼運算單元的面積在聯電90奈米製程下只須0.29mm2和0.45mm2。此外，運算單元的操作面積也可以透過我們提出的指數判定器以及資料路徑分離法可大幅的提升。我們也提出一個可以對抗能量攻擊法的雙域橢圓曲線密碼運算單元。透過我們提出的通用亂數演算法，我們面積的損失僅僅8.4%。

關鍵字

橢圓曲線密碼 ； HASH(0x9100cc4) ； 有限域運算 ； HASH(0x9101c00) ； 模數除法運算 ； HASH(0x9101cf0) ； 能量攻擊法

並列摘要

In this thesis, we propose a high-performance dual-field elliptic curve cryptographic processor (DECP) architecture that can support all finite field operations and elliptic curve (EC) functions with arbitrary field and curve. Based on our proposed fast unified division algorithm, the operation cycles can be significantly reduced. Compared with previous works using high radix multiplication in projective coordinate, our 160-bit and 256-bit DECPs can achieve competitive performance in terms of execution cycles with only 0.29mm2 and 0.45mm2 silicon area in UMC 90nm CMOS technology by exploiting hardware sharing and ladder selection techniques. In addition, the operating frequency in prime field and binary field can be increased due to the proposed data-path separation and degree checker. To resist power analysis attack, we propose a DECP with power analysis countermeasures architecture based on the proposed unified random algorithms with only 8.4% area overhead.

並列關鍵字

Elliptic curve cryptography ； HASH(0x9101e34) ； Finite field operations ； HASH(0x9101f00) ； Modular division operation ； HASH(0x9102c30) ； Power analysis attack

參考文獻

[31] Y.-J. Liu, “An implementation of universal dual-field scalar multiplication on elliptic curve cryptosystems,” Master’s thesis, National Chiao Tung University, 2007.

[2] D. Hankerson, A. Menezes, and S. Vanstone, Guide to Elliptic Curve Cryptography. Springer, 2004.

[4] ——, Advances in Elliptic Curve Cryptography. Cambridge University Press, 2005.

[5] H. Cohen and G. Frey, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Chapman and Hall/CRC, 2006.

[6] W. Trappe and L. C. Washington, Introduction to Cryptography with Coding Theory, 2nd ed. Pearson Education International, 2006.