Research Article
A Technique to Speed up the Modular Multiplicative Inversion over GF(P) Applicable to Elliptic Curve Cryptography
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 47 - Issue 16 |
| Published: June 2012 |
| Authors: V. Sridhar, Anil Kumar M .N |
10.5120/7273-0412
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V. Sridhar, Anil Kumar M .N . A Technique to Speed up the Modular Multiplicative Inversion over GF(P) Applicable to Elliptic Curve Cryptography. International Journal of Computer Applications. 47, 16 (June 2012), 21-25. DOI=10.5120/7273-0412
@article{ 10.5120/7273-0412,
author = { V. Sridhar,Anil Kumar M .N },
title = { A Technique to Speed up the Modular Multiplicative Inversion over GF(P) Applicable to Elliptic Curve Cryptography },
journal = { International Journal of Computer Applications },
year = { 2012 },
volume = { 47 },
number = { 16 },
pages = { 21-25 },
doi = { 10.5120/7273-0412 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2012
%A V. Sridhar
%A Anil Kumar M .N
%T A Technique to Speed up the Modular Multiplicative Inversion over GF(P) Applicable to Elliptic Curve Cryptography%T
%J International Journal of Computer Applications
%V 47
%N 16
%P 21-25
%R 10.5120/7273-0412
%I Foundation of Computer Science (FCS), NY, USA
Abstract
This paper presents a technique to speed up the computation of inversion of NIST recommended elliptic curve with modulus p521-1. The property of multiplicative inverse between pair of numbers over Meresenne's prime is used to reduce the number of iterations in the Binary Inversion Algorithm in GF(p). This increases the speed requirement for point operations applicable to Elliptic Curve Cryptography. This paper proposes an model of the architecture to achieve the above objective which uses parallelism in multiplicative inversion arithmetic block to speed up the computation.
References
- N. Koblitz, "Elliptic curve cryptosystems", Math. comput. , vol. 48,pp. 203-209,1987.
- V. Miller, "Use of elliptic curves in cryptography", in Advances in Cryptology (CRYPTO), Newyork:Springer, 1986,vol. 218,pp. 417-426.
- A. Daly, W. Marnane, T. Kerins, E. Popovici, An FPGA implementation of a GF(p) ALU for encryption processors, Microprocessors and Microsystems, vol. 28,2004,pages 253-260.
- Santhosh Ghosh, Monjur Alam,Indranil Sen Gupta , Dipanwita Roy Chowdhury, IIT Kharagpur,10th Euromicro Conference on Digital System Design Architectures, Methods and Tools(DSD 2007).
- G. B. Agnew, R. C. Mullin and S. A Vanstone", An implementation of elliptic curve cryptosystems over F2155", IEEE J. Selected Areas of Communication, vol. 11,n05,pp. 804-813, Jun. 1993.
- J. Goodman and A. Chandrakasan, "An energy efficient reconfigurable public-key cryptography processor architecture", in Cryptographic Hardware and Embedded Systems (CHES). New York: Springer, 2000, vol. 1965,pp. 175-190.
- A. Satoh and K. Takano, "A Scalable dual-field elliptic curve cryptography processor", IEEE Transaction on Computers, vol. 52,no. 4,pp. 449-460,Apr. 2003
- Kimmo Jarvinen and Jorma Skytta, "On Parallellization of High-Speed Processors for Elliptic Curve Cryptography", IEEE transactions on VLSI Systems vol. 16, no. 9,Sept. 2008.
- Kendall Anayi,Hamad Alrimeih and Daler Rakhmatov, "Flexible Hardware Processor for Elliptic Curve Cryptography", IEEE Transactions on VLSI Systems, vol. 17,No. 8,August 2009.
- A. Satoh and K. Takano, "A scalable dual-field elliptic curve cryptographic processor", IEEE Trans. Comput. , vol. 52,no. 4,pp. 449-460, April 2003.
- G. Orlando and C. Paar, " A scalable GF(p) Elliptic Curve Processor Architecture for Programmable Hardware", pp. 356-371, CHES 2001, LNCS 2162.
- S. B. Ors, L. Batina and B. Preneel, " Hardware implementation of elliptic curve processor over GF(p)", in Proc. 14th IEEE International Conference on Application-Specific Systems, Architectures and Processors, Jun 2003, pp. 433-443.
- Ciaran J. Mcivor, Marie McLoone, "Hardware Elliptic Curve Cryptographic Processor Over GF(p)", IEEE Trans. On Circuits and Systems-1, vol. 53,No. 9, September 2006.
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