低複雜度及具錯誤偵測功能之有限場乘法器

由於資訊科技之熱烈發展，如何去避免私密資料遭到密碼攻擊而造成資訊外洩損失之相關議題變得相當重要。且由於行動裝置與嵌入式系統快速發展，因此如何在硬軟體資源有限之行動系統中，滿足資訊安全需求成為相當重要之議題，資訊安全則依賴密碼系統的防護，所以密碼系統的發展受到相當多學者專家的注意及興趣。為防止密碼系統遭受密碼攻擊造成資料外洩的損失，最好的方式即為讓密碼系統本身具有錯誤偵測能力，不讓破解密碼者利用密碼系統輸出錯誤的訊息進而輕易破解密碼系統。另外，亦可使用具高度加密等級之金鑰系統來防護密碼系統如公開金鑰系統。於公開金鑰系統中，RSA雖可提供高度的加密效果，但橢圓曲線密碼系統可利用更短的金鑰長度來達到相較於RSA相同的加密等級，此特性除了可節省加密所需之硬體複雜度，亦能縮短資料在加密過程中運算時間。橢圓曲線密碼系統之核心數值運算為有限場數值運算，於其中，乘法運算尤其重要，因大多數值運算如乘法反元素、指數運算、及除法等皆可利用乘法運算來完成，故乘法運算相對重要，卻也較複雜及耗時。綜合上述，本論文除了因應資源有限之嵌入式亦或是行動裝置做出滿足低成本與高運算效率需求外，亦針對抵抗植入錯誤式之密碼攻擊法之議題，重新設計有限場乘法器。

關鍵字

有限場數值運算；即時錯誤偵測；橢圓曲線密碼系統；多項式基底；雙重基底

並列摘要

Information security is heavily dependent on public key cryptosystems such as RSA. However, RSA is not available for the resource-constrained devices like embedded systems. Recent developed public key cryptosystem, Elliptic Curve Cryptosystem (ECC), is attractive for use in resource-constrained portable devices due to it can achieve the same security level, but uses less key length. Portable devices with restricted resources demand low hardware complexity and short execution time properties. Galois/Finite field multiplication is the most crucial operation in ECC. There are three popular types of bases for representing elements in finite field, termed polynomial basis (PB), normal basis (NB), and dual basis (DB). This study is focused on PB and DB multipliers. Recently, fault-based cryptanalysis has been proven to be an effective cryptanalysis method for both private and public key cryptosystems. Several error-detection approaches have been developed for finite field arithmetic architectures. In this dissertation, novel PB and DB multipliers with concurrent error detection capability will be proposed.

並列關鍵字

Finite Field ； Concurrent Error Detection ； Elliptic Curve Cryptosystem ； Dual Basis

參考文獻

[1] Announcing the Standard for Data Encryption Standard (DES), Federal Information Processing Standards Publications (FIPS), Dec. 30, 1993. http://www.itl.nist.gov/fipspubs/fip46-2.htm

[2] Announcing the Standard for Advanced Encryption Standard (AES), Federal Information Processing Standards Publications (FIPS), Nov. 26, 2001. http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf

[5] V. Miller, “Uses of Elliptic Curves in Cryptography,” Advances in Cryptology - CRYPTO’85, LNCS 218, 1986, pp.417-426.

[6] W. Stallings, Cryptography and Network Security-Principles and Practice, Prentice Hall, 2010.

[12] R. E. Blahut, Fast Algorithms for Digital Signal Processing. Reading Mass.: Addison-Wesley, 1985.

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低複雜度及具錯誤偵測功能之有限場乘法器

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