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研究生:陳立翰
研究生(外文):Li-Han Chen
論文名稱:以FPGA實現抵抗SPA攻擊之GF(2^191)橢圓曲線點乘法
論文名稱(外文):FPGA Implementation of SPA-resistant Elliptic Curve Scalar Multiplication over GF(2^191)
指導教授:汪順祥
指導教授(外文):Shuenn-Shyang Wang
口試委員:汪順祥
口試委員(外文):Shuenn-Shyang Wang
口試日期:2014-07-28
學位類別:碩士
校院名稱:大同大學
系所名稱:電機工程學系(所)
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:2014
畢業學年度:102
語文別:英文
論文頁數:50
中文關鍵詞:旁通道攻擊純量乘法橢圓曲線加密系統2個位元
外文關鍵詞:scalar multiplicationECC2 bitsSPA
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橢圓曲線加密系統(ECC)被廣泛運用在網路安全上,其中純量點乘法是其核心運算,在這篇論文中,我們提供可以對抗簡單功率分析攻擊(SPA)的有效率純量點乘法之演算法和架構。所提出之純量點乘法的演算法是經由一次處理兩個位元以及修改運算使得每次的運算功率相同來對抗簡單功率分析攻擊。
Scalar multiplication is the kernel in elliptic curve cryptosystems (ECC) which has been widely applied for network security. In this thesis, we propose some efficient algorithms and architectures of ECC scalar multiplication which can resistant against power analysis attacks. The proposed algorithms of ECC scalar multiplication are developed based on processing every 2 bits of the scalar k each time. The proposed algorithms make the operations of each loop be equal and thus perform the same power output sequence to resist simple power analysis (SPA) attcks.
ACKNOWLEDGMENTS I
ABSTRACT II
CONTENTS IV
LIST OF TABLES V
LIST OF FIGURES VI
CHAPTER 1 1
1.1 Introduction 1
1.2 Thesis Organization 3
CHAPTER 2 4
2.1 The Mathematic Background of Elliptic Curve 4
2.1.1 Elliptic Curves 4
2.1.2 Elliptic Curves over 7
2.1.3 Affine Coordinate 8
2.1.4 Scalar Multiplication 8
2.1.5 ECC Based on Projective Point Arithmetic 12
3.1 Introduction 14
3.2 Montgomery Scalar Multiplication Architecture 14
3.2.1 Montgomery scalar multiplication algorithm 14
3.2.2 Montgomery Point Addition Module 15
3.2.3 Montgomery Point Doubling Module 17
3.2.4 Montgomery Scalar Multiplication Architecture 19
3.3 Finite Field Arithmetic 20
3.3.1 Addition Operation 20
3.3.2 Squaring Operation 21
3.3.3 Multiplication Operation 21
3.3.4 Reduction Step 23
3.3.5 Inversion Operation 24
3.4 Proposed Algorithms of Scalar Multiplication 26
3.5 PERFORMANCE ANALYSIS 33
CHAPTER 4 34
CHAPTER 5 38
REFERENCES 39
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