陳君明Chen, Jiun-Ming臺灣大學:數學研究所王友呈Wang, You-ChenYou-ChenWang2010-05-052018-06-282010-05-052018-06-282009U0001-1808200910365800http://ntur.lib.ntu.edu.tw//handle/246246/180627In this paper, we review a number of methods to calculate the scalar multiplications, including the DBNS that has been gaining popularity in recent years. We review the side channel attacks that can break the cryptosystems by gaining some side channel information from the physical implementation of the cryptosystems. We propose a new algorithm with three schemes that apply the side channel atomicity using Lopez & Dahab coordinates to avoid the side channel attacks. The new algorithm we provided is about 30% faster than the algorithm previously used with Jacobian coordinates.Acknowledgements ......................................... ibstract in Chinese ..................................... iibstract in English .................................... iiiontents ................................................ ivist of Figures ......................................... viist of Tables .......................................... vi Introduction ........................................... 1 1.1 EC-DH .............................................. 2 1.2 ECDSA .............................................. 3 1.3 ECIES .............................................. 4 Basic Scalar Multiplications on General Elliptic Curves 6.1 Binary Method ........................................ 6.2 Non-Adjacent Form (NAF) .............................. 7.3 Window Method ........................................ 8.4 Montgomery Method ................................... 11.5 Fixed-base Window Method ............................ 12.6 Fixed-base Comb Method .............................. 14 Other Special Scalar Multiplications .................. 18.1 Simultaneous Multiple Scalar Multiplication ......... 18.2 Joint Sparse Form (JSF) ............................. 19.3 Interleaving Method ................................. 20.4 -adic Non-adjacent Form (TNAF) on Koblitz Curve ... 21.5 Scalar Multiplications on Koblitz Curve ............. 27.6 Halving Method ...................................... 29 Double-Base Number System ............................. 36.1 DBNS Representation ................................. 36.2 Double-Base Chain ................................... 39.3 DBNS Scalar Multiplication .......................... 42 Side Channel Attacks .................................. 44.1 Power Analysis Attacks .............................. 44.1.1 Simple Power Analysis ............................. 44.1.2 Differential Power Analysis ....................... 46.2 Electromagnetic Analysis Attacks .................... 48.3 Fault Analysis Attacks .............................. 48.4 Timing Attacks ...................................... 50.5 Error Message Analysis .............................. 50 Strategies against Side Channel Attacks ............... 52.1 Side Channel Atomicity .............................. 52.2 Strategy for DBNS against Side Channel Attacks ...... 58.3 Analysis ............................................ 64 Conclusions ........................................... 67ppendix ................................................ 68eferences .............................................. 74application/pdf621334 bytesapplication/pdfen-US橢圓曲線密碼系統純量乘法雙基底數系旁道攻擊旁道原子性ECCscalar multiplicationDBNSside channel attacksside channel atomicitythesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/180627/1/ntu-98-R95221019-1.pdf