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International Journal of Scientific and Engineering Research
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ISSN Print: 2229-5518 3    
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scirp IJSER >> Volume 3,Issue 3,March 2012
Fpga Implementations of High Speed Elliptic Curve Cryptography: A Survey
Full Text(PDF, )  PP.364-378  
Shylashree N, Nagarjun Bhat, V Sridhar
:ECC; FPGA; SKC; PKC; NIST; NAF; Efficiency-Flexibility Tradeoffs; High Speed Hardware Implementation
An explosive acceptance of Elliptic Curve Cryptography (ECC) has been attained in the industry and academics. Elliptic Curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. The ECC is advantageous due to the provision of high level of security and the usage of small keys. In the field of Mobile, Wireless and Network servers, to sustain the high throughput the implementations of high speed crypto-systems are needed. ECC has been extensively used for hardware implementation of FPGA and DedicatedASIC. This paper attempts to conduct a detailed survey on different techniques for implementing FPGA using ECC to achieve high speed and flexibility.
[1].Stallings W, ―Network and internetwork security principles and practice‖.1995,Prentice Hall, New York,USA

[2] IEEE P1363, ―Standard Specifications for Public Key Cryptography,‖ 2000.

[3] ―Digital Signature Standard (DSS)‖, Federal Information Processing Standards Publication 186-2, National Institute of Standards and Technology. 2000.

[4] ANSI, ANSI X9.62 ―The elliptic curve digital signature algorithm (ECDSA‖).

[5] nsa.gov.. ―The Case for Elliptic Curve Cryptography‖. Retrieved from The National Security Agency Central Security Service.,2009.

[6] Wendy Chou, Dr. Lawrence Washington ,―Elliptic Curve Cryptography and Its Applications to Mobile Devices‖.Department of Mathematics, University of Maryland, College Park.

[7] Koblitz, N..―Elliptic curve cryptosystems.Mathematics of Computation‖,1987.

[8] Miller,V,‖Use of elliptic curves in cryptograph‖y.CRYPTO 85.1985.

[9] Lay, G.-J., & Zimmer, H. G..―Constructing elliptic curves with given group order over large finite fields‖. Proceedings of the First International Symposium on Algorithmic Number Theory. Springer Lecture Notes In Computer Science;1998,Vol. 877.

[10] Rosing, M..―Implementation Elliptic Curve Cryptography‖.Manning Pub.,1999.

[11] Blake, I. F .‖Advances in Elliptic Curve Cryptography‖. Cambridge University Press Series: London Mathematical Society Lecture Note Series,2005.

[12] I. Blake, G. Seroussi, N.P. Smart, ―Elliptic curves in cryptography‖, London Mathematical Society Lecture NoteSeries, 1999.

[13] MatthieuRivain,.‖Fast and Regular Algorithms for Scalar Multiplication over Elliptic Curves‖, 2011.

[14] Steffen Peter and Peter Langend¨orfer,‖An Efficient Polynomial Multiplier in GF(2m) and its Application to ECC Designs‖,2007 EDAA

[15] Prof.Rahila Bilal Dr.M.Rajaram, ―High Speed and Low Space Complexity FPGA Based ECC Processor‖,International Journal of Computer Applications (0975 – 8887) ,Volume 8–No.3, October 2010.

[16] Maurice Keller, Andrew Byrne and William P. Marnane, ―Elliptic Curve Cryptography on FPGA for LowPower Applications‖, ACM Transactions on Reconfigurable Technology and Systems, Vol. 2, No. 1, Article 2, Pub. date: March 2009.

[17] Lo’ai Ali Tawalbeh& Abidalrahman Mohammad & Adnan Abdul-Aziz Gutub, ―Efficient FPGA Implementation of a Programmable Architecture for GF(p) Elliptic Curve Crypto Computations‖, 59:233-244 DOI 10.1007/s11265-009-037-x,Springer,2010.

[18]J. Lo´ pez, R. Dahab, ―Fast multiplication on elliptic curves over GF(2m), in: Cryptographic Hardware and Embedded Systems (CHES)‖, LNCS 1717, 1999, pp. 316 -327

[19] RALF LAUE AND SORIN A. HUSS, ―Parallel Memory Architecture for Elliptic Curve Cryptography over GF(P) Aimed at Efficient FPGA Implementation‖, Journal of Signal Processing Systems 51, 39–55, Springer Science + Business Media, 2008.

[20]Kazuo Sakiyama,LejlaBatina , Bart Preneel, Ingrid Verbauwhede, ―High-performance Public-key Cryptoprocessor for Wireless Mobile Applications‖, Published online: 3 October 2007, Springer Science + Business Media,

[21]Aaron E. Cohen , Keshab K. Parhi,‖Fast Reconfigurable Elliptic Curve Cryptography Acceleration for GF(2m) on 32 bit Processors‖, Published online: 1 July 2009, Springer Science + Business Media.

[22]SantoshGhosh, MonjurAlam, Dipanwita Roy Chowdhury and IndranilSenGupta,‖A GF(p) Elliptic Curve Group Operator Resistant Against Side Channel Attacks‖, GLSVLSI’08, May 4–6, 2008, Orlando, Florida, USA,ACM 978-1-59593-999-9/08/05

[23] MiaoqingHuang,Krisgaj,Tarek El-Ghazawi, ―New Hardware Architecture for Montgomery Modular Multiplication Algorithm‖,IEEE Transactions on Computers, VOL,60,NO.7,JULY 2011,DOI NO. 10.1109/TC.2010.247

[24] SıddıkaBernaOrs, LejlaBatina, Bart Prenee, JoosVandewalle, ―Hardware Implementation of an Elliptic Curve Processor over GF(p)‖, Proceedings of the Application-Specific Systems, Architectures, and Processors (ASAP’03), 2003 IEEE.

[25] Nils Gura, Hans Eberle, Chang Shantz,‖ Generic Implementations of Elliptic Curve Cryptography using Partial Reduction‖, NOV18-22, 2002,Washington, DC, USA.ACM 1-58113-612-9./02/0011

[26] M. Sudhakar& R. V. Kamala &M. B. Srinivas, ―New and Improved Architectures for Montgomery Modular Multiplication‖,Springer Science + Business Media, 2007 .

[27] Yi Wang,DouglasL.Maskell, JussipekkaLeiwo,‖A Unified Architecture for a Public Key Cryptographic Coprocessor‖ .JSA 2008,Elsevier

[28]Hao Li a,*, Jian Huang b, Philip Sweany a, Dijiang Huang c, ―FPGA implementations of elliptic curve cryptography and Tate pairing over a binary field‖, Journal of Systems Architecture 54 ,2008, 1077–1088,Elsevier

[29] Yu Zhang, Dongdong Chen, Younhee Choi, Li Chen, Seok-Bum Ko, ―A high performance ECC hardware implementation with instruction-level parallelism over GF(2163)‖, Elsevier B.V,doi:10.1016/j.micpro.2010.04.006

[30]SantoshGhosh *, MonjurAlam, Dipanwita Roy Chowdhury, IndranilSenGupta, ―Parallel crypto-devices for GF(p) elliptic curve multiplication resistant against side channel attacks‖,2009,Elsevier Ltd,doi:10.1016/j.compleceng.2008.06.09

[31] Chang Hoon Kim, Soonhak Kwon, Chun Pyo Hong ,‖FPGA implementation of high performance elliptic curve cryptographic processor over GF(2163)‖,Journal of Systems Architecture 54 ,2008 893–900, Elsevier B.V.,

[32]GashawSassaw, Carlos J. Jimenez, Manuel Valencia, ―High Radix Implementation of Montgomery Multipliers with CSA‖, 22nd International Conference on Microelectronics (ICM 2010),2009 IEEE

[33]R.Dhanagopal, B.Manivasakam, ―FPGA implementation of public keyprocessor for network security‖, 2010 IEEE

[34] B.MuthuKumar, S.Jeevananthan,‖High Speed Hardware Implementation of an EllipticCurve Cryptography (ECC) Co-Processor‖, 2010 IEEE

[35] A.Kaleel Rahuman, Dr. G.Athisha, ―Reconfigurable Architecture for Elliptic CurveCryptography‖,Proceedings of the International Conference on Communication and Computational Intelligence – 2010, Kongu Engineering College, Perundurai, Erode, T.N.,India.27 – 29 December,2010.

[36]Prabhat Chandra Shrivastava, Rupesh Kumar, Arvind Kumar, SanjeevRai,‖ High-Speed and Low Power Unified Dual-Field Multiplier in GF (P) and GF (2m)‖,2010 IEEE

[37] H. Eberle, N. Gura, S. Chang-Shantz, ―A cryptographic processor for arbitrary elliptic curves over GF(2m)‖, in: Application-Specific Systems, Architectures, and Processors,(ASAP), 2003,

[38]Jun-Hong Chen, Ming-Der Shieh and Chien-Ming Wu,Concurrent Algorithm for High-Speed Point Multiplicationin Elliptic Curve Cryptography, 2005 IEEE

[39] Ray C. C. Cheung, Nicolas Jean-baptisteTelle, Wayne Luk, Peter Y. K. Cheung,‖ Customizable Elliptic Curve Cryptosystems‖, IEEE transactions on very large scale integration (VLSI) systems, vol. 13, no. 9, September 2005.

[40] Osama Al-Khaleel, KiamalPekmestzi, ―FPGA-based Design of a Large Moduli Multiplierfor Public-Key Cryptographic Systems‖, 2006 IEEE

[41] Mohamed A. Fayed, M. Watheq El-Kharashi, Fayez Gebali, ―A High-Speed, High-Radix, Processor Array Architecture for Real-Time Elliptic Curve Cryptography Over GF(2m)‖, 2007 IEEE

[42] Xu Huang, Pritam Gajkumar Shah, Dharmendra Sharma, ―Fast Scalar Multiplication for Elliptic Curve Cryptography in Sensor Networks with Hidden Generator Point‖, International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery, 2010 IEEE

[43] William N. Chelton, Mohammed Benaissa,‖Fast Elliptic Curve Cryptography on FPGA‖,IEEE Transactions on VLSI system, 2007 IEEE

[44] Nazar A. Saqib, Francisco Rodr´ıguez-Henriquez and Arturo D´ıaz-P´erez, ―A Parallel Architecture for Computing Scalar Multiplication on Hessian Elliptic Curves‖, Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC’04)2004 IEEE

[45] B. Ansari, M. Anwar Hasan, ―High performance architecture of elliptic curve scalar multiplication‖, Tech. Report CACR 2006-01, 2006.

[46] F. Crowe, A. Daly, W. Marnane, ―A scalable dual mode arithmetic unit for publickey cryptosystems‖, in: International Conference on Information Technology:Coding and Computing ITCC’05,IEEE

[47] Miguel Morales-Sandoval ,Claudia Feregrino-Uribe,on the ―Hardware Design of an Elliptic Curve Cryptosystem‖, Proceedings of the Fifth Mexican International Conference in Computer Science, 2004 IEEE.

[48] G. Orlando, C. Paar, A Scalable GF(p),‖ Elliptic Curve Processor Architecture forProgrammable Hardware‖, CHES 2001, LNCS 2162, Springer-Verlag, 2001.

[49] W. Shuhua and Z. Yuefei, ―A Timing and Area Tradeoff GF(p) Elliptic Curve Processor Architecture for FPGA‖, ICCCAS’05, pp. 1308–1312, IEEE

[50] A. Daly, W. Marnane, T. Kerins and E. Popovici, ―An FPGA Implementation of a GF(p) ALU for Encryption Processors‖, Microprocessors and Microsystems, Vol. 28, pages 253–260, ,2004 Elsevier

[51] ] K. Ja¨rvinen, M. Tommiska, J. Skytta¨, ―A scalable architecture for elliptic curve point multiplication‖, in: IEEE Field-Programmable Technology (FPT), 2004

[52] C. Grabbe, M. Bednara, J. von zurGathen, J. Shokrollahi, J. Teich,‖ A high performance vliw processor for finite field arithmetic‖, in: Reconfigurable Architectures Workshop (RAW), 2003.

[53] A. Cilardo, A. Mazzeo, N. Mazzocca, L. Romano, ―A novel unified architecture forpublic key cryptography‖, in: IEEE Proceeding of the Design, Automation andTest in Europe Conference and Exhibition, vol. 3, 2005.

[54] C. McIvor, M. McLoone, J. McCanny, ―An FPGA ellipticcurve cryptographic accelerator over GF(p)‖, in: Irish Signalsand Systems Conference (ISSC), 2004

[55] N. Gura, S.C. Shantz, H. Eberle, S. Gupta, V. Gupta, D. Finchelstein, E. Goupy, D.Stebila, ―An end-to-end systems approach to elliptic curve cryptography‖, in:CHES 2002, Lecture Notes in Computer Science.

[56] C. Shu, K. Gaj, T. El-Ghazawi, ―Low latency elliptic curve cryptography accelerators for NIST curves on binary fields‖, in: IEEE Field-Programmable Technology (FPT), 2005.

[57].Montgomery,P.‖Modular Multiplication without trial division‖.Mathematics on Computation, 1985.

[58] M. Benaissa, W.M. Lim, ―Design of flexible GF(2m) elliptic curve cryptographyprocessors‖, IEEE Transactions on VLSI System 2006.

[59] M. Morales-Sandoval, C. Feregrino-Uribe2,⋄ , R. Cumplido and I. Algredo-Badillo , ‖A Reconfigurable GF(2m) Elliptic Curve Cryptographic Coprocessor‖, 2011,IEEE

[60] Yi Wang and Renfa Li,‖ A Unified Architecture for Supporting Operations of AES and ECC‖,2011, IEEE

[61].VirtexTM-E 1.8V ―Field Programmable Gate Arrays‖,http://www.xilinx.com/bvdocs/publications/ds0 22.pdf

[62].Virtex-II Pro and Virtex-II Pro X Platform FPGAs:Complete Data Sheet http:// www.xilinx.xom/ bvdocs/publications/ds083.pdf

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