臺灣博碩士論文加值系統

由於近年來無線通訊以及網際網路的快速且蓬勃的發展，使得通訊安全顯得格外重要。如果無法提供一個安全的通訊環境，則無線通訊以及網際網路的應用，如：網路購物、網路銀行，將會受到限制。在此篇論文中，我們提出一個修改過的快速不相鄰表示轉換法（on-the-fly non- adjacent-form　conversion），以及在2163有限場下的一個較有效率的橢圓曲線乘法處理器。此處理器的運算時間為155265個計數器時間，且可以抵抗時間攻擊法（timing attack）。

In the recent, wireless communication and global network bave been broadly developed, so the security of communication is very important. If there is no secure environment, the applications, like E-commerce system and Internet Commercial Bank, will be limited. In this thesis, we devise a modified on-the-fly non-adjacent-form (NAF) conversion without look-up-table and propose an efficient Elliptic curve cryptography (ECC) processor over GF(2163) which is resistant to timing attacks. It is shown that the delay of our processor is 155265 clock cycles For the case of GF(2163).

ACKNOWLEDGEMENT (in Chinese) I
ABSTRACT (in Chinese) II
ABSTRACT (in Chinese) III
CONTENTS IV
LIST OF TABLE VI
LIST OF FIGURE VII
CHAPTER 1 INTRODUCTION 1
1.1 Introduction 1
1.2 Mathematical Background 2
1.2.1 Finite field 2
1.2.2 The finite field GF(p) 2
1.2.3 The finite field GF(2m) 3
1.3 Elliptic Curves 5
1.3.1 Elliptic curves over GF(p) 8
1.3.2 Elliptic curves over GF(2m) 9
CHAPTER 2 ECC PUBLIC KEY CRYPTOGRAPHY 11
CHAPTER 3 POINT MULTIPLICATION ALGORITHM 13
3.1 Hardware Costs Issue 13
3.2 Point Multiplication Algorithm Issue 14
3.3 Security Issue 15
CHAPTER 4 PROPOSED ARCHITECTURE 17
4.1 Modified Schedule Architecture 17
4.2 Modified On-the-Fly Conversion 24
4.3 ECC Processor Design 27
4.4 Performance Analysis 29
CHAPTER 5 CONCLUDION 30
REFERENCES 31

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