橢圓曲線密碼處理器之設計與實作

Design and Implementation of Elliptic Curve Cryptographic Processor

白丞鈞(Chen-Chun Pai)

指導教授 ： 劉宗德

國立臺灣大學/電機資訊學院/電子工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201800635

摘要

現今，在資訊爆炸且快速流通的社會，保障個人訊息安全和驗證身分的需求日益增長，在資訊安全領域中，對稱式加密系統(Symmetric Encryption)適用於大量明文加密和密文解密，加解密速度快，但是卻有金鑰管理的問題。所以要合併使用非對稱加密系統並應用於金鑰交換和身分驗證等功能，現行的密碼系統如:RSA、ECC(Elliptic Curve Cryptography)、Diffie-Hellman。橢圓曲線密碼學是近幾年被大量研究的一個密碼系統，相較於RSA它可以使用較短的金鑰長度來達到相同安全等級，但是較少有相關硬體設計的研究。
本論文主要在設計並實現一個橢圓曲線密碼處理器。為了達到高效能同時又可以兼顧較低的能量消耗，我們從系統的角度去討論整體的設計，涵蓋最上層的演算法到最底層的運算硬體設計。此外我們也討論側通道攻擊的防禦問題，並在演算法的設計上著墨，可以使用較少的硬體資源下達到防禦側通道攻擊的功能。
如上所述，我們提出一個新的演算法用於橢圓曲線上點的乘法計算。這個演算法可以防禦側通道攻擊，跟過去文獻使用的演算法比較，可以降低運算資源、減少運算時間和降低功耗。我們也分析在下層硬體電路要如何搭配此演算法才能凸顯該演算法的優勢，達到更佳的效能。
最後為了實踐我們提出的演算法，使用TSMC 90nm製程，將完整橢圓曲線密碼處理器製作出來。這個晶片為192位元長橢圓曲線密碼處理器，可以分別操作於GF(P192)與GF(2163)有限體，於0.85ms 16uJ和 0.65ms 9.2uJ下完成一次橢圓曲線點乘法運算，相比於相關文獻，此硬體有最低的能量消耗，同時也兼顧一定的效能，證明提出的演算法具有一定的應用價值，優異的低能量消耗適合於物聯網的應用相關，最後我們也透過蒐集能量軌跡來驗證可以防禦側通道攻擊。

關鍵字

橢圓曲線密碼學 ； 公鑰加密 ； 硬體安全 ； 側通道攻擊 ； 物聯網

並列摘要

Nowdays, the demands of protecting personal private data and identity verification significantly increases in an information explosion society.Symmetric encryption is suitable for encrypting and decrypting lots of data in a short time, but it has key management problem. Asymmetric encryption or so called public-key cryptosystems (PKC) is developed to solve key management problem. Symmetric encryption needs to be combined with asymmetric encryption systems for key exchange and identity verification. Some popular asymmetric encryption schemes includie RSA, ECC (Elliptic Curve Cryptography), Diffie-Hellman.
Compared to RSA, ECC achieve same security level with shorter key length. Therefore, this dissertation presents the design and implementation of an ECC processor. To achieve high performance and low power consumption, we investigate the important crypto processor design concepts including the choosing of the algorithm, the coordinate, and the modular operation circuits. In addition, we discuss the side-channel attacks (SCA) problem and try to solve it on algorithm level to save hardware resources. Based on the efforts mentioned above, we propose a new algorithm for elliptic curve scalar multiplication (ECSM). Compared with other works, this algorithm can not only resist side-channel attack but also consume less hardware resources. We also analyze the correspoding hardware architectures implementing for optimum performance.
To verity our proposed algorithm, a 0.39mm2, 192- and 163-bit dual field ECC chip is implemented in TSMC 90nm CMOS technology. This chip accomplishes 0.85/0.65ms and 16/9.2μJ for one GF(p)/GF(2m) elliptic curve scalar multiplication (ECSM). In comparison with related works, it has the lowest energy consumption, while maintaining a comparable performance which demonstrates that our algorithm is valuable for mobile devices or Internet of Things (IoT) applications. Finally, we collect the power traces of the chip to verify its capacity to resist side-channel attacks.

並列關鍵字

Elliptic Curve Cryptography ； Public-key Cryptosystems ； Hardware Security ； Side-channel Attacks ； Internet of Things

參考文獻

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