Area Optimized Low Latency Karatsuba Ofman Multiplier Variant for Elliptical Curve Cryptography
Keywords:
ECC, Double Point Multiplication, Karatsuba Ofman multiplication, Area optimizationAbstract
Due to resource constrains, implementation of secure protocols for securing embedded systems has become a challenging task. System designers are advised to design and install area efficient versions of existing, proven security protocols. System designers are finding ways and means to compress existing security protocols without compromising security and without tampering with basic security structure of algorithm. Modular multiplication, point multiplication, point doubling are few critical activities to be carried out in ECC algorithm. By optimizing Modular Multiplier, area efficiency in ECC algorithm can be achieved. In this paper, we propose Area optimized and low latency multiplier that implements the efficient KOA algorithm in altogether novel style to be used in ECC architecture. The proposed algorithm uses a novel technique of splitting input operands based on exponent’s parity and it eventually helps in reducing FPGA footprint and offers low latency by avoiding overlapping, prime concern for any embedded system. The complete modular multiplier and the cryptoprocessor module is synthesized and simulated using Xilinx ISE Design suite 14.4 software. We have investigated area occupancy of proposed multiplier and cryptoprocessor and concluded that proposed scheme occupies relatively reduced percentage area of FPGA as compared to the one using traditional KOA multiplier.
Â
References
C. Paar. A new architecture for a parallel finite field multiplier with low complexity based on composite fields. IEEE Transactions on Computers, 45(7):856– 861, July 1996.
Azarderakhsh. R, Jarvinen K.U and Mozaffari-Kermani. M,“Efficient algorithm and architecture for elliptic curve cryptography for extremely constrained secure applicationsâ€, IEEE Transactions on circuits and systems- I , Vol. 61, No. 4, April 2014.
Hossein Mahdizadeh and Massoud Masoumi, "Novel architecture for efficient FPGA implementation of elliptic curve cryptographic processor over GF(2163)", IEEE Transactions on very large scale integration (vlsi) systems, Vol. 21, NO. 12, pp: 2330- 2333, Dec.2013
Sunil Devidas Bobade and Dr. Vijay R.Mankar,†Low footprint Hybrid Finite field multiplier for Embedded cryptographyâ€, International Journal of Computer Science and Information Security(IJCSIS) , Vol. 13, No. 3, pp: 28- 32,March 2015.
Sunil Devidas Bobade and Dr. Vijay R.Mankar,†Space optimized Multiplier Architecture for Embedded cryptographyâ€, International Journal of Computer and Applications(IJCA) , Vol. 113, No. 14, pp: 26- 32,March 2015.
Roy. S.S, Rebeiro,C and Mukhopadhyay. D, “Theoretical modeling of elliptic curve scalar multiplier on LUT-based FPGAs for area and speedâ€, IEEE Transactions on Very Large Scale Integration (VLSI) systems, Vol. 21, No. 5, May 2013.
Azarderakhsh. R, Jarvinen K.U and Mozaffari-Kermani. M,“Efficient algorithm and architecture for elliptic curve cryptography for extremely constrained secure applicationsâ€, IEEE Transactions on circuits and systems- I , Vol. 61, No. 4, April 2014.
Kazuo Sakiyama, Miroslav Knezevica, Junfeng Fana, , Bart Preneela, and Ingrid Verbauwhedea, “Tripartite modular multiplicationâ€, Integration, the VLSI Journal, Vol. 44, No.4, pp: 259–269, September 2011.
Roy. S.S, Rebeiro,C and Mukhopadhyay. D, “Theoretical modeling of elliptic curve scalar multiplier on LUT-based FPGAs for area and speedâ€, IEEE Transactions on Very Large Scale Integration (VLSI) systems, Vol. 21, No. 5, May 2013.
R. Azarderakhsh and K. Karabina, “ A New Double Point Multiplication Algorithm and its Application to Binary Elliptic Curves with Endomorphismsâ€, IEEE Transactions on Computers, to appear:pp, 2013.
A.Kaleel Rahuman and G.Athisha, “Reconfigurable Architecture for Elliptic Curve Cryptography Using FPGAâ€, Hindawi Publishing Corporation Mathematical Problems in Engineering, 2013.
Downloads
Published
Issue
Section
License
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.
