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Galois Fields GF(2m)

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Algebraic Circuits

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 66))

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Abstract

After the presentation of the basic algebraic circuits, this chapter is specifically dedicated to the circuits based on the finite fields GF(2m). Finite fields or Galois fields have a variety of applications in several areas such as cryptography, coding and digital signal processing.

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References

  1. Berlekamp, E.R.: Bit-serial reed-solomon encoders. IEEE Trans. Inf. Theor. IT-28(6), 869–874 (1982)

    Article  Google Scholar 

  2. Brunner, H., Curiger, A., Hofstetter, M.: On computing multiplicative inverses in GF(2m). IEEE Trans. Compt. 42(8), 1010–1015 (1993)

    Article  MathSciNet  Google Scholar 

  3. Hsu, I.S., Troung, T.K., Deutsch, L.J., Reed, I.S.: A comparison of VLSI architecture of finite field multipliers using dual, normal, or standard bases. IEEE Trans. Compt. 37(6), 735–739 (1988)

    Article  Google Scholar 

  4. Itoh, T., Tsujii, S.: A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases. Inf. Comput. 78, 171–177 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  5. Montgomery, P.L.: Modular multiplication without trial division. Math. Comput. 44(170), 519–521 (1985)

    Article  MATH  Google Scholar 

  6. National Institute of Standards and Technology: FIPS 186-4: Digital Signature Standard (DSS), Gaithersburg, July 2013

    Google Scholar 

  7. Savas, E., Koç, Ç.K.: The Montgomery modular inverse-revisited. IEEE Trans. Compt. 49(7), 763–766 (2000)

    Article  Google Scholar 

  8. Wang, C.H., Lin, J.L.: A systolic architecture for computing inverses and división in finite fields GF(2m). IEEE Trans. Compt. 42(9), 1141–1146 (1993)

    Article  Google Scholar 

  9. Wu, H.: Montgomery multiplier and squarer for a class of finite fields. IEEE Trans. Compt. 51(5), 521–529 (2002)

    Article  Google Scholar 

  10. Yeh, C.S., Reed, I.S., Troung, T.K.: Systolic multiplier for finite fields GF(2m). IEEE Trans. Compt. 33(4), 357–360 (1984)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Electrónica y Tecnología de Computadores, Universidad de Granada, Granada, Spain

    Antonio Lloris Ruiz, Encarnación Castillo Morales, Luis Parrilla Roure & Antonio García Ríos

Authors
  1. Antonio Lloris Ruiz
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  2. Encarnación Castillo Morales
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  3. Luis Parrilla Roure
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  4. Antonio García Ríos
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Correspondence to Antonio Lloris Ruiz .

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Lloris Ruiz, A., Castillo Morales, E., Parrilla Roure, L., García Ríos, A. (2014). Galois Fields GF(2m). In: Algebraic Circuits. Intelligent Systems Reference Library, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54649-5_5

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  • DOI: https://doi.org/10.1007/978-3-642-54649-5_5

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  • Print ISBN: 978-3-642-54648-8

  • Online ISBN: 978-3-642-54649-5

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