Fast Elliptic Curve Point Multiplication Algorithm Optimization

Hai Bin Zhang; Xiao Ping Ji; Bo Ying Wu; Guang Yu Li

doi:10.4028/www.scientific.net/AMM.441.1044

Paper Titles

Research on Compression Storage of Massive Agricultural Data Based on Cloud Environment
p.1025

The Research on the Internet of Things Industry Chain for Barriers and Solutions
p.1030

Time Triggered and Event Triggered Codesign in CAN Bus Network
p.1036

The Design and Implement of Marine MF/HF Radio Simulator
p.1040

Fast Elliptic Curve Point Multiplication Algorithm Optimization
p.1044

Study on Simulation Cloud Computing of Power System
p.1049

The Study of the Apple Juice Evaporation Characteristics on a Heat Pipe Evaporator
p.1055

TRIZ Evolution Theory Applied to Man-Made Boards
p.1060

Integrated TRIZ and MEMS in Eco-Innovative Design
p.1064

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 441Fast Elliptic Curve Point Multiplication Algorithm...

Fast Elliptic Curve Point Multiplication Algorithm Optimization

Abstract:

Scalar point multiplication operation on elliptic curve is the most expensive part of the elliptic curve cryptosystem, also has always been the hot spot of the research. Recoding the positive integer and reducing the amount of inversion in the operation are the two main ideas. In this article, we use the balanced ternary form to recode the positive integer, at the same time, improve the part of calculation way of, reducing the amount of inversion, decreasing operation cost, and improving operation efficiency

You might also be interested in these eBooks

Machinery Electronics and Control Engineering III

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volume 441)

Pages:

1044-1048

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.441.1044

Citation:

Cite this paper

Online since:

December 2013

Authors:

Hai Bin Zhang, Xiao Ping Ji, Bo Ying Wu, Guang Yu Li

Keywords:

Elliptic Curve Cryptosystem, Inversions, Scalar Point Multiplication

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] C.P. Peeger and S.L. Peeger: Security in Computing[M], Prentice-Hall, Upper Saddle River, New Jersey, (2006).

Google Scholar

[2] W. Diffie, M. Hellman: New directions in cryptography[J], IEEE Transactions on Information Theory, 1976, Vol 11, No. 22(6) pp.644-654.

DOI: 10.1109/tit.1976.1055638

Google Scholar

[3] I.F. Blake,G. Seroussi and N.P. Smart: Advances in Elliptic Curve Cryptography[M], Cam-bridge University Press, (2005).

Google Scholar

[4] IEEE P1363a Committee. IEEE P1363a/D9—standard specifications for public key cryptography: Additional techniques[J]. (2001), 2(001).

Google Scholar

[5] D. Hankerson: Elliptic Curve Discrete Logarithm Problem[M]. Encyclopedia of Cryptography and Security. Springer US, (2011): 397-400.

DOI: 10.1007/978-1-4419-5906-5_246

Google Scholar

[6] DM. Gordon: A survey of fast exponentiation methods[J]. Journal of algorithms, (1998), 27(1): 129-146.

Google Scholar

[7] N. Koblitz: Elliptic curve cryptosystems[J]. Mathematics of computation, (1987), 48(177): 203-209.

DOI: 10.1090/s0025-5718-1987-0866109-5

Google Scholar

[8] K. Eisentrager, K. Lauter and P L. Montgomery: Fast elliptic curve arithmetic and improved Weil pairing evaluation[M]. Topics in cryptology—CT-RSA 2003. Springer Berlin Heidelberg, (2003): 343-354.

DOI: 10.1007/3-540-36563-x_24

Google Scholar

[9] D. Chudnovsky and G. Chudnovsky: Sequences of numbers generated by addition in formal groups and new primality and factoring tests[J]. Advances in Applied Mathematics, (1987), 7: 385-434.

DOI: 10.1016/0196-8858(86)90023-0

Google Scholar

[10] M. Ciet,M. joye,K. Lauter and P.L. Montgomery: Trading Inversions for Multiplications in Elliptic Curve Cryptography, Designs, Codes and Cryptography, (2006), 39: 189-206.

DOI: 10.1007/s10623-005-3299-y

Google Scholar