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研究生:林三煬
研究生(外文):San-Yang Lin
論文名稱:雙場橢圓曲線加密處理器
論文名稱(外文):A Dual Field Elliptic Curve Cryptographic Processor
指導教授:吳誠文
指導教授(外文):Cheng-Wen Wu
學位類別:碩士
校院名稱:國立清華大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:61
中文關鍵詞:橢圓曲線加密處理器
外文關鍵詞:Elliptic CurveCryptographic Processor
相關次數:
  • 被引用被引用:1
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  • 下載下載:25
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隨著有線、無線通訊的發展,安全性的考量變的越來越重要。如果沒有可靠的安全機制,許多應用將受到很大的限制,諸如:電子商務,網路銀行。密碼學是一個很有用的安全機制,利用它可以使得資料在不安全的環境中傳送而不會遭人竊取,基本上它分為二種加密系統,一種為對稱加密系統,例如DES、AES等,它利用同一把金鑰來做加解密的工作,此種加密速度較快,但金鑰的傳送需要另一安全的通道來傳送。另一種為非對稱加密系統,例如ECC、RSA同為公開金鑰的加密演算法,它需要二把金鑰才可以把加密的資料給還原,由於其中的一把金鑰是在不公開的環境下,故此它的安全性是無庸置疑的。橢圓曲線加密演算法裡主要是有限場數學運算,在一般的處理器並沒有為此目的而設計的硬體,也因此軟體來實現的話會造成處理速度的緩慢與能源沒有效率的消耗,這對行動電子商品會造成使用時間的縮短,所以的確需要一個專門負責加解密的硬體來加解密資料。我們設計一個ECC加密處理器。這個加密處理器支援雙場運算。實驗結果顯示這個加密處理器可以跑在時脈384MHz,面積約200Kgate,平均一個163 bit ECC運算耗時0.46ms,在適當的處理clock gating時,消耗功率約為152mW。
The recent trends towards global networking and mobile computing have led to the proliferation of wireless networks which enable users to remain connected to the global web without being tied down to a fixed, wired link. The lack of a coherent wireless network security architecture has resulted in many different types of cryptographic primitives being used, requiring some form of
algorithm in order to maximize the portable systems’utility. In order to facilitate the secure transmission of funds over the Internet, cryptography must be used. Cryptography is therefore a key enabling technology for the Internet and E-commerce systems. Elliptic Curve ryptography (ECC) is evolving as an attractive alternative to other public-key cryptosystems such as the Rivest-Shamir-Adleman algorithm (RSA) by offering the smallest key size and the highest strength per bit and makeing it suitable for smart cards, cellular phones or any other resource constrained
applications. We propose an elliptic curve cryptographic processor than can support Galois fields GF(p) and GF(2^n) for arbitrary prime numbers and irreducible polynomials by a multi-function arithmetic unit (MAU). The MAU contained one montgomery multiplier, two binary field multipliers and one binary field divider accelertate the throughtput of the EC scalar multiplication. It can handle any gereric curves up to a field degree of 255. The experimental result
reports that the ECC processor can run at a clock rate of 384MHz and the hardware area of the ECC processor is about 200K gates. A 256-bit EC scalar multiplication takes 1.1 ms in GF(2^n) and 5.6ms in GF(p).
1 Introduction . . . . 8
1.1 DemandofSecurity . . . . 8
1.2 PreviousWorks . . . . 9
1.3 Elliptic Curve Cryptographic Hardware . . . . . . . . . . 10
1.4 Organization . . . . . . 10
2 Cryptosystems . . . . . . 12
2.1 Fundamentals . . . . . . 12
2.2 Symmetric Key Cryptosystem . . 13
2.3 Asymmetric Key Cryptosystem. . 14
2.3.1 Discrete Logarithm Problem . 15
2.3.2 CertificationAuthority . . . 16
2.3.3 One-wayHashingFunction . . . 16
2.3.4 ECCvs. RSA . . . . . . . . . 16
3 Mathematical Background . . . . 19
3.1 Groups and Fields . . . . . . 19
3.2 GaloisFields . . . . . . . . 20
3.3 Modular Arithmetic . . . . . . 21
3.4 Polynomial Basis . . . . . . . 21
4 Introduction to Elliptic Curves 23
4.1 Elliptic Curve Groups over Real Numbers . . . . . . . . . . . . . 23
4.1.1 Elliptic Curve Addition: A Geometric Approach . . . . . . . . . . . . . 24
4.2 Elliptic Curve Groups over Fp . . . . . . . . . . . . . . . . 25
4.3 Elliptic Curve Groups over F2m 27
4.4 A Crypto Example for Elliptic Curve . . . . . . . . . . . . . . 28
5 Elliptic Scalar Multiplication 30
5.1 Scalar Multiplication Algorithm . . . . . . . . . . . . 30
5.2 ECCArithmetic . . . . . . . . 31
5.2.1 Modular Multiplication in GF(p) 33
5.2.2 GF(2n) Multiplication . . . 34
5.2.3 GF(2n) Inversion . . . . . . 35
6 Elliptic Curve Crypto-Processor Design 36
6.1 Features of Crypto-Processor . 37
6.2 IOInterface . . . . . . . . . 37
6.3 Controller . . . . . . . . . 39
6.4 ArithmeticUnit . . . . . . . . 39
6.4.1 RegisterFile . . . . . . . . 39
6.4.2 Comparator Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.4.3 AdderUnit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.4.4 ArithmeticDatapath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3
7 Experimental Results 47
7.1 ComplexityAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7.2 SimulationFlow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
7.3 DFT Consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
7.4 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
8 Conclusions & Future Work 54
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
8.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
A Microcode for EC Scalar Multiplication 56
4
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