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FPGA Implementation of Elliptic Curve Point Multiplication over GF(2191)

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Advances in Information Security and Assurance (ISA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5576))

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Abstract

Hardware acceleration of cryptographic algorithms is beneficial because considerable performance improvements can be attained compared to software implementations. Thus, hardware implementations can be used in critical applications requiring high encryption or decryption speeds. Parallel architecture with efficient hardware implementation of Galois field arithmetic operations is used to produce high speed computation time for the scalar multiplication operation which is the main operation in Elliptic Curve Cryptography (ECC) system. This work proposed a modification in karatsuba-ofman algorithm which is one of the best algorithms used to perform multiplication operation over Galois field. The modification contrasted on truncating karatsuba-ofman algorithm in a low level and using the classic polynomial multiplication algorithm. In addition, this work proposed architecture for implementing ECC on hardware using Montgomery algorithm in projective coordinates. The results show that the proposed architecture is able to compute GF(2^191) elliptic curve scalar multiplication operations in 72.939 μs on Xilinx Virtex-II XC2V6000 FPGA device and 100.68 μs on Xilinx VirtexE 2600. Also, the proposed architecture can be changed to be suitable for any arbitrary Galois field size with little modifications.

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Author information

Authors and Affiliations

  1. Computer science department, faculty of computers and information, Menoufiya University, Shebin Elkom, 32511, Egypt

    Sameh m. Shohdy, Ashraf b. El-sisi & Nabil Ismail

Authors
  1. Sameh m. Shohdy
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  2. Ashraf b. El-sisi
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  3. Nabil Ismail
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Editor information

Editors and Affiliations

  1. Computer Engineering Department, Kyungnam University, 449, Wolyong-dong, 631-701, Kyungnam, Masan, Korea

    Jong Hyuk Park

  2. Institute of Communications Engineering, National Sun Yat-Sen University, Kaohsiung City, Taiwan

    Hsiao-Hwa Chen

  3. School of Computer Science,, University of Oklahoma, 200 Felgar Street, 73019, P.O. Box, Norman, OK, USA

    Mohammed Atiquzzaman

  4. School of Computer Engineering, Hanshin University, Kyeong-Gi, Osan, Korea

    Changhoon Lee

  5. Division of Multimedia, Hannam University, Daejeon, Korea

    Tai-hoon Kim

  6. Division of Computer Engineering, Mokwon University, Daejeon, Korea

    Sang-Soo Yeo

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© 2009 Springer-Verlag Berlin Heidelberg

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Shohdy, S.m., El-sisi, A.b., Ismail, N. (2009). FPGA Implementation of Elliptic Curve Point Multiplication over GF(2191). In: Park, J.H., Chen, HH., Atiquzzaman, M., Lee, C., Kim, Th., Yeo, SS. (eds) Advances in Information Security and Assurance. ISA 2009. Lecture Notes in Computer Science, vol 5576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02617-1_63

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  • DOI: https://doi.org/10.1007/978-3-642-02617-1_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02616-4

  • Online ISBN: 978-3-642-02617-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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