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Efficient Linear Array for Multiplication over NIST Recommended Binary Fields

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Fuzzy Logic and Applications (WILF 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3849))

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Abstract

We propose a new linear array for multiplication in GF(2m) which outperforms most of the existing linear multipliers in terms of the area and time complexity. Moreover we will give a very detailed comparison of our array with other existing architectures for the five binary fields GF(2m), m = 163,233,283,409,571, recommended by NIST for elliptic curve cryptography.

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References

  1. Massy, J.L., Omura, J.K.: Computational method and apparatus for finite field arithmetic. US Patent No. 4587627 (1986)

    Google Scholar 

  2. Agnew, G.B., Mullin, R.C., Onyszchuk, I., Vanstone, S.A.: An implementation for a fast public key cryptosystem. J. Cryptology 3, 63–79 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kwon, S., Gaj, K., Kim, C., Hong, C.: Efficient linear array for multiplication in GF(2m) using a normal basis for elliptic curve cryptography. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 76–91. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Berlekamp, E.R.: Bit-serial Reed-Solomon encoders. IEEE Trans. Inform. Theory 28, 869–874 (1982)

    Article  MATH  Google Scholar 

  5. Wang, M., Blake, I.F.: Bit serial multiplication in finite fields. SIAM J. Disc. Math. 3, 140–148 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  6. Morii, M., Kasahara, M., Whiting, D.L.: Efficient bit-serial multiplication and the discrete-time Wiener-Hopf equation over finite fields. IEEE Trans. Inform. Theory 35, 1177–1183 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  7. Lee, C.Y., Lu, Y.C., Lu, E.H.: Low complexity systolic multiplier over GF(2m) using weakly dual basis. In: APCCAS 2002: Asia Pacific Conference on Circuits and Systems, vol. 1, pp. 367–372 (2002)

    Google Scholar 

  8. Stinson, D.R.: On bit-serial multiplication and dual bases in GF(2m). IEEE Trans. Inform. Theory 37, 1733–1736 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  9. NIST, Digital Signature Standard, FIPS Publication, 186-2 (February 2000)

    Google Scholar 

  10. Hankerson, D., Menezes, A.J., Vanstone, S.A.: Guide to Elliptic Curve Cryptography. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  11. Song, L., Parhi, K.K.: Efficient finite field serial/parallel multiplication. In: International Conference on Application Specific Systems, Architectures and Processors, pp. 19–21 (1996)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Inst. of Basic Science and Dept. of Mathematics, Sungkyunkwan University, Suwon, 440-746, Korea

    Soonhak Kwon

  2. School of Computer Engineering, Sejong University, Seoul, 143-747, Korea

    Taekyoung Kwon

  3. Dept. of Information Security, Sejong Cyber University, Seoul, 143-747, Korea

    Young-Ho Park

Authors
  1. Soonhak Kwon
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  2. Taekyoung Kwon
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  3. Young-Ho Park
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Editor information

Editors and Affiliations

  1. Dept. TSI, CNRS UMR 5141 LTCI, ENST (Télécom ParisTech), Paris, France

    Isabelle Bloch

  2. Centro Direzionale, DSA, University of Naples, Parthenope, Isola C/4, 80143, Naples, Italy

    Alfredo Petrosino

  3. Dipartimento di Tecnologie dell’Informazione, Università di Milano Crema,  

    Andrea G. B. Tettamanzi

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© 2006 Springer-Verlag Berlin Heidelberg

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Kwon, S., Kwon, T., Park, YH. (2006). Efficient Linear Array for Multiplication over NIST Recommended Binary Fields. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds) Fuzzy Logic and Applications. WILF 2005. Lecture Notes in Computer Science(), vol 3849. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11676935_53

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  • DOI: https://doi.org/10.1007/11676935_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32529-1

  • Online ISBN: 978-3-540-32530-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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