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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳君明(Jiun-Ming Chen) | |
| dc.contributor.author | You-Chen Wang | en |
| dc.contributor.author | 王友呈 | zh_TW |
| dc.date.accessioned | 2021-06-15T02:22:06Z | - |
| dc.date.available | 2010-08-21 | |
| dc.date.copyright | 2009-08-21 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-08-19 | |
| dc.identifier.citation | [1] V. S. Miller. Use of elliptic curves in cryptography. CRYPTO'85, vol. 218 of Lecture Notes in Computer Science, pp. 417-426.
[2] N. Koblitz, Elliptic curve cryptosystems, in mathematics of Computation 48, 1987, pp. 203-209 [3] E. W. Knudsen Elliptic Scalar Multiplication Using Point Halving, ASIACRYPT'99, LNCS, vol. 1716, pp. 135-149, 1999. [4] P. Kocher, J. Jaffe, and B, Jun, Differential Power Analysis, Crypto 99 Proceedings, LNCS, Vol. 1666, 1999. [5] J. A. Solinas, Effcient Arithmetic on Koblitz Curves, Designs, Codes and Cryptography, 19, 195-249, 2000. [6] M. Joye, and S.M. Yen, The Montgomery powering ladder, vol.2523 of LNCS, pp. 291-302, Springer-Verlag, 2003. [7] M. Ciet, M. Joye, K. Lauter, and P. L. Montgomery, Trading Inversions for Multiplications in Elliptic Curve Cryptography, Cryptology ePrint Archive, Report 2003/257, 2003. [8] D. Hankerson, A. Menezes, and S. Vanstone, Guide to elliptic curve cryptography. Springer, 2004. [9] B. Chevallier-Mames, M. Ciet, and M. Joye, Low-cost solutions for preventing simple side-channel analysis: side-channel atomicity, IEEE Transactions on Computers 53(6):760-768, 2004. [10] M. Hedabou, P. Pinel, and L. Beneteau, A comb method to render ECC resistant against Side Channel Attacks, 2004. [11] C. Doche, and L. Imbert, Extended Double-Base Number System with applications to Elliptic Curve Cryptography, LNCS, vol. 4329. pp. 335-348, 2006. [12] M. Joye, Fault Attacks An Algorithmic Perspective, Summer school on cryptographic hardware, side-channel and fault attacks, 2006. [13] H. Cohen, and G. Frey, Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman & Hall/CRC, 2006. [14] C. Doche, and L. Habsieger, A Tree-Based Approach for Computing Double-Base Chains, ACISP 2008, LNCS, vol. 5107, pp. 433-446, 2008. [15] V. Dimitrov, L. Imbert, and P. K. Mishra, The double-base number system and its application to elliptic curve cryptography, Mathematics of Computation, vol.77, no. 262, pp. 1075-1104, 2008. [16] Gu Haihua, Gu Dawu, Liu Ya, Effcient Scalar Multiplication for Elliptic Curves over Binary Fields, Wuhan University Journal of Natural Sciences, vol. 13. pp.717-720, 2008. [17] H. Bar-El, Introduction to Side Channel Attacks. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43470 | - |
| dc.description.abstract | In 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. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T02:22:06Z (GMT). No. of bitstreams: 1 ntu-98-R95221019-1.pdf: 621334 bytes, checksum: be3de43fca6ac31eef2a09294744f996 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Acknowledgements ......................................... i
Abstract in Chinese ..................................... ii Abstract in English .................................... iii Contents ................................................ iv List of Figures ......................................... vi List of Tables .......................................... vi 1 Introduction ........................................... 1 1.1 EC-DH .............................................. 2 1.2 ECDSA .............................................. 3 1.3 ECIES .............................................. 4 2 Basic Scalar Multiplications on General Elliptic Curves 6 2.1 Binary Method ........................................ 6 2.2 Non-Adjacent Form (NAF) .............................. 7 2.3 Window Method ........................................ 8 2.4 Montgomery Method ................................... 11 2.5 Fixed-base Window Method ............................ 12 2.6 Fixed-base Comb Method .............................. 14 3 Other Special Scalar Multiplications .................. 18 3.1 Simultaneous Multiple Scalar Multiplication ......... 18 3.2 Joint Sparse Form (JSF) ............................. 19 3.3 Interleaving Method ................................. 20 3.4 -adic Non-adjacent Form (TNAF) on Koblitz Curve ... 21 3.5 Scalar Multiplications on Koblitz Curve ............. 27 3.6 Halving Method ...................................... 29 4 Double-Base Number System ............................. 36 4.1 DBNS Representation ................................. 36 4.2 Double-Base Chain ................................... 39 4.3 DBNS Scalar Multiplication .......................... 42 5 Side Channel Attacks .................................. 44 5.1 Power Analysis Attacks .............................. 44 5.1.1 Simple Power Analysis ............................. 44 5.1.2 Differential Power Analysis ....................... 46 5.2 Electromagnetic Analysis Attacks .................... 48 5.3 Fault Analysis Attacks .............................. 48 5.4 Timing Attacks ...................................... 50 5.5 Error Message Analysis .............................. 50 6 Strategies against Side Channel Attacks ............... 52 6.1 Side Channel Atomicity .............................. 52 6.2 Strategy for DBNS against Side Channel Attacks ...... 58 6.3 Analysis ............................................ 64 7 Conclusions ........................................... 67 Appendix ................................................ 68 References .............................................. 74 | |
| dc.language.iso | en | |
| dc.subject | 純量乘法 | zh_TW |
| dc.subject | 橢圓曲線密碼系統 | zh_TW |
| dc.subject | 旁道攻擊 | zh_TW |
| dc.subject | 雙基底數系 | zh_TW |
| dc.subject | 旁道原子性 | zh_TW |
| dc.subject | DBNS | en |
| dc.subject | ECC | en |
| dc.subject | scalar multiplication | en |
| dc.subject | side channel attacks | en |
| dc.subject | side channel atomicity | en |
| dc.title | 橢圓曲線密碼系統純量乘法之雙基底數系中抵擋旁道攻擊之策略 | zh_TW |
| dc.title | Strategies for Double-Base Number Systems against Side Channel Attacks in ECC Scalar Multiplications | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 楊柏因,鄭振牟 | |
| dc.subject.keyword | 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, | zh_TW |
| dc.subject.keyword | ECC,scalar multiplication,DBNS,side channel attacks,side channel atomicity, | en |
| dc.relation.page | 75 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-08-19 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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