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Efficient Inversion Algorithm for Optimal Normal Bases Type II

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Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2667))

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Abstract

In this paper, we propose an efficient inversion algorithm for optimal normal bases type II. The efficiency of the arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis. An inversion algorithm based on reduced multiplication for optimal normal basis is studied. The combination of optimal normal basis and shifted form of the canonical basis is also employed. It is shown that the suggested inversion algorithm reduces the computation time to 45 ∼ 60 % of the simple algorithm. The algorithm is very effective in composite numbers in which have optimal normal basis type II.

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References

  1. R. Lidl and H. Niederreiter, Introduction to finite fields and their applications, Cambridge University Press, Cambridge, 1986

    MATH  Google Scholar 

  2. R. C. Mullin, I. M. Onyszchuk and S. A. Vanstone, “Optimal normal bases in GF (pn)*,” Discrete Applied Mathematics, 22, 149–161, 1988

    Article  MathSciNet  Google Scholar 

  3. T. Itoh and S. Tsujii, “A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases,” 78, 171–177, 1988

    MATH  MathSciNet  Google Scholar 

  4. J. Juajardo and C. Paar, “Itoh-Tsujii inversion in standard basis and its application in cryptography and codes,” 25, 207–216, 2002

    Google Scholar 

  5. R. Schroeppel, H. Orman, S. O. Malley and O. Spatscheck, “Fast key exchange with elliptic curve systems,” CRYPTO’ 95, LNCS 963, 43–56, 1995

    Google Scholar 

  6. E. De Win, A. Bosselaers, S. Vandenberghe, P. D. Gersem and J. Vanderwalle, “A fast software implementation for arithmetic operations in GF(2k),” ASIACRYPT’ 96, LNCS 1233, 65–76, 1996

    Google Scholar 

  7. C. K. Koç and T. Acar, “Montgomery multiplication in GF(2k),” Design, Codes and Cryptography, 14,1, 57–69, 1998

    Article  MATH  Google Scholar 

  8. B. Sunar and C. K. Koç, “An efficient optimal normal basis type II multiplier,” IEEE Trans. on Computers, 50,1, 83–87, 2001

    Article  Google Scholar 

  9. D. V. Bailey and C. Paar, “Optimal extension fields for fast arithmetic in public-key algorithms,” CRYPTO’ 98, LNCS 1462, 472–485, 1998

    Google Scholar 

  10. M. Rosing, Implementing elliptic curve cryptography, Manning Publ. Co., Greenwich, CT, 1999

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Inha University, Incheon, 402-751, Korea

    Hyeong Seon Yoo & Eui Sun Kim

Authors
  1. Hyeong Seon Yoo
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  2. Eui Sun Kim
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8 Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. Département d’informatique et de recherche opérationelle, Université de Montréal, Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

  5. Department of Computer Science and Engineering, University of Minessota, MN, 55455, USA

    Vipin Kumar

  6. The Queen’s University of Belfast, School of Computer Science, Belfast BT7 1NN, Northern Ireland, UK

    Chih Jeng Kenneth Tan

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© 2003 Springer-Verlag Berlin Heidelberg

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Yoo, H.S., Kim, E.S. (2003). Efficient Inversion Algorithm for Optimal Normal Bases Type II. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44839-X_36

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  • DOI: https://doi.org/10.1007/3-540-44839-X_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40155-1

  • Online ISBN: 978-3-540-44839-6

  • eBook Packages: Springer Book Archive

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