Rapid Parallel Computation of Point Multiplication for ECDSA Over Prime Field

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Elliptic Curve Digital Signature Standard (ECDSA) is used for smart applications and financial transaction on wireless applications. This ECDSA is implemented in two ways. One is ECDSA over binary field for hardware applications and another is ECDSA over prime field for software applications.  But these environments have a set of constraints during transaction period. They are limited memory space, lifetime, power consume, reuse and portability. So it is necessary to find out suitable implementations for ECDSA based on these constraints. This implementation has two important computation called as point addition and point multiplication. But the time complexity of point multiplication is higher than point addition. It takes high latency time compare to point addition. So it is necessary to find out suitable implementation for point multiplication. This article suggests a technique for point multiplication to reduce time complexity using parallel computation.
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Elliptic Curve Digital Signature Standard; Latency Time; Parallel Computation; Prime Field; Time Complexity

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A.Sakthivel and R.Nedunchezhian, Decreasing Number of Point Operations On ECC over 2n ,IJCA on Network Security and Cryptography NSC,pp.43, Dec 2011.

A.Sakthivel and R.Nedunchezhian, Decreasing Number of Point multiplication over ECC Zp using tree computations, in Proc IEEE international conference on Computing, Communication and applications (ICCCA), pp.1-5. Feb. 2012.

Erkay Savas and Çetin Kaya Koç, Finite Field Arithmetic for Cryptography, IEEE Circuuts and Systems Magazine, pp 40-57, Second Quarter 2010.

E. Savas and C.K. Koc, The Montgomery Modular Inverse- Revisited, IEEE Transactions on Consumer Electronics, vol. 49, no. 7, pp 763-767, July 2000.

Gary Locke and Patrick Gallagher, Federal Information Processing Standards Publication Digital Signature Standard (FIPS PUB 186-3), Information Technology Laboratory, National Institute of Standards and Technology, June, 2009.

John L.Hennessy & David A. Pattersom (2007): Computer Architecture a Quantitative Approach, Elsevier,4th Edition.

Kenny Fong, Darrel Hankerson, Julio Lopez, and Alfred Menezes, Field Inversion and Point Halving Revisited, IEEE Transactions on Consumer Electronics, vol. 53, no. 8,pp 1047 Aug 2004.

Patrick Longa and Ali Miri, Fast and Flexible Elliptic Curve Cryptography point arithmetic over Prime fields, IEEE Transactions on computers, vol.57, No.3, pp.289-302, May 2008.

Pradeep Kumar Mishra, Pipelined Computation of Scalar Multiplication in Elliptic Curve Cryptosystems, IEEE Transactions on computers,vol 55,No.8, pp1000,Aug 2006.

Sangook Moon, Jaemin Park and Yongsurk Lee, Fast VLSI Arithmetic Algorithms for High-Security Elliptic Curve Cryptographic Applications, IEEE Transactions on Consumer Electronics,Vol.47,No.3,pp. 700-708, Aug 2001.

Xiaoyu Ruan, and Rajendra S. Katti, Left-to-Right Optimal Signed-Binary Representation of a Pair of Integers, IEEE Transactions on computers,vol.54,no.2, pp 124,Feb 2005.

A. Sehad, N. Bessah, I.Touari, Y.Benfattoum, H.Khali, and M.Cheriet, A New PCA-based Face Authentication Approach for Smart-Card Implementation, International Review on Computers and Software, Vol.5,no.4, pp.384-389,July 2010.

Paras Mehta and Mario Muñoz Organero, Study of Security Mechanisms for Secure Mobile Commerce Architecture Through the Development of a Mobile Banking Application, International Review on Computers and Software, vol.4,n.1,pp.1-5, Jan 2009.

Mohammad Khatib, Qasem Abu Al-Haija and Azmi Jaafar, Hardware Architectures & Designs for Projective Elliptic Curves Point Addition Operation using Variable Levels of Parallelism, International Review on Computers and Software, Vol. 6, N. 2,pp. 227-236,March 2011.

Mohammad Alkhatib, Azmi Jaafar, Zuriati Zukarnain and Mohammad Rushdan, Trade-off between Area and Speed for Projective Edwards Elliptic Curves Crypto-System over Gf (P) Using Parallel Hardware Designs and Architectures, International Review on Computers and Software,Vol. 6, No. 4,pp. 615-625, July 2011.


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