Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/19418
標題: 利用伺服器輔助加速有限運算能力裝置之橢圓曲線點乘法運算
Server-aided elliptic curve point multiplication for resource-limited devices
作者: 劉文雄
Liu, Wen-Shung
關鍵字: Elliptic Curve;橢圓曲線;Elliptic Curve Cryptosystem;Server-aided;橢圓曲線密碼系統(ECC);伺服器輔助
出版社: 資訊科學系所
引用: [1] 張榮吉;<在Ad hoc網路環境下建立共同金鑰技術>;臺北;淡江大學資訊工程學系碩士論文;2002年。 [2] 王偲穎;<動態會議金錀分配機制之研究>; 臺北;世新大學;資訊管理學系碩士論文;2005年。 [3] ANSI X9.62, Public Key Cryptography for the Financial Services Industry: The Elliptic Curve Digital Signature Algorithm(ECDSA),1998。 [4] B. Chevallier-Mames, J-S. Coron, N. McCullagh, D. Naccache and M. Scott, Secure delegation of elliptic-curve pairing. Cryptography ePrint report.,2005/150。 [5] Daniel M. Gordon, A survey of Fast Exponentiation Methods, Center for communications research, 4320 westerra court.,1997。 [6] Darrel Hankerson, Implementing Elliptic curve cryptography ( a narrow survey ) , Institute of computing – UNICAMP Campinas, Brazil.,April 2005。 [7] IEEEP 1363-2000. IEEE standard Specifications for Public Key Cryptography. IEEE Computer Society.,2000。 [8] I.Blake, G.. Seroussi, and N. Smart, “ Elliptic Curves in Cryptography”, Cambridge University Press, 1999。 [9] ISO/IEC 11770-3, “Information Technology-Security Techniques-Key Management-Part 3: Mechanisms Using Asymmetric Techniques”, 1999. [10] Jurisic, A., and Menezes, A. “Elliptic Curves and Cryptography.” Dr. Dobb’s Journal, April 1997。 [11] Kim, Yongdae, Perrg, Adrian, and Tsudk, Gene; “Group Key Agreement Efficient in Communication”; IEEE Transactions on Computers; Vol.53, No.7, pp.905-921; 2004。 [12] NIST, FIPS 186-2, “Digital Signature Standard”, http://csrc.nist.gov/publications/fips/fips186-2/fips186-2-change1.pdf, 2001 [13] N.Kanayama, T. Kobayashi, T. Saito, and S. Uchiyama, “ Remarks on elliptic curve discrete logarithm problems”, Journal of IEOCE Transactions on Fundamentals of Electronics, Communications and Computer Science, Vol.E83-A, no.1, Jan 2000. [14] N. Koblitz, “A Course in Number Theory and Cryptography”, 2nd ed., Springer-Verlag, 1994. [15] N. Koblitz, Elliptic Curve Cryptosystems, Math. Computat, Vol 48, pp.203-209.1987。 [16] Specification of the Bluetooth system, v.1.2 Core specification. Available from http://www.bluetooth.org/ [17] V.S. Miller, Use of elliptic curves in cryptography, Advances in Cryptology-Crypto''85, LNCS 218, Springer- Verlag, pp.417-426.1986。 [18] W. Stallings, “Cryptography and Network Security: Principles and Practice”, 3nd ed., Prentice-Hall, 2003. [19] Yuto Kawahara, Tsuyoshi Takagi, and Eiji Okamoto, Efficient implementation of Tate Pairing on a Mobile Phone using Java, Cryptology ePrint report.2006/299。
摘要: 
近年來,橢圓曲線密碼系統(Elliptic Curve Cryptosystem,ECC)已廣泛地被一些公認的國際組織如ANSI、IEEE、ISO、NIST制訂為標準並應用於一些商業行為上,如橢圓曲線數位簽章演算ECDSA。由於在相同的安全性方面,ECC所需要的密碼學金鑰長度較RSA短。因此ECC非常適用於智慧卡、手機、個人數位助理(PDA)等無線行動裝置使用。而這些無線行動裝置有一共通的問題為運算能力較弱、記憶體容量較小。
ECC基本運算係執行一點乘法運算K*P,其中K為正整數而P為橢圓曲線上的一個點。KP的點乘法運算為ECC中最複雜及需較多時間之計算。當我們把ECC應用在有限裝置上時,橢圓曲線點乘法運算便會是使用上的一個瓶頸,因為它需要花費較長的時間在此一計算。因此如何在有限資源環境下,讓有限裝置KP的運算能加快、節省時間,為本文所要討論之重點。
本文提出一個伺服器輔助(server-aided)的方法來達到加速橢圓曲線點乘法運算,首先有限裝置傳送K''到Server然後藉由運算能力強大的server幫忙計算K''P之值,回傳K''P值經有限裝置驗證K''P無誤後,便可快速計算得到KP。如此可解決有限裝置計算能力較弱的問題,且本方法不需利用太多額外的記憶體,可節省記憶體。

Elliptic Curve Cryptosystem (ECC) has widely received increased commercial acceptance as evidenced by its inclusion in standards by accredited standards organizations such as ANSI, IEEE, ISO and NIST in recent years. It is believed that the key length of elliptic curve cryptosystems can be shorter than that of RSA with the same security strength. Therefore, ECC is suitable for the resource-limited devices such as smart card, cell phone, PDA or other wireless movie mobiles. The problem are that the processing power of the resource-limited device is low and that memory is small.
Point multiplication (KP), is an elliptic curve operation which dominates the execution time of elliptic curve cryptosystems. How to make the point multiplication of the resource-limited device more efficient by using the powerful server is considered in this paper.
We propose a new method, with the powerful server to calculate the K''P when client transfers the K'' to server. After the client has verified the K''P, it can efficiently calculate the KP.
URI: http://hdl.handle.net/11455/19418
其他識別: U0005-0807200711492900
Appears in Collections:資訊科學與工程學系所

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