Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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FAST OPERATION METHOD IN GF$(2^n)$

  • Park, Il-Whan (Electronics and Telecommunications Research Institute) ;
  • Jung, Seok-Won (Electronics and Telecommunications Research Institute) ;
  • Kim, Hee-Jean (Electronics and Telecommunications Research Institute) ;
  • Lim, Jong-In (Department of Mathematics Korea University)
  • Published : 1997.07.01
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Abstract

In this paper, we show how to construct an optimal normal basis over finite field of high degree and compare two methods for fast operations in some finite field $GF(2^n)$. The first method is to use an optimal normal basis of $GF(2^n)$ over $GF(2)$. In case of n = st where s and t are relatively primes, the second method which regards the finite field $GF(2^n)$ as an extension field of $GF(2^s)$ and $GF(2^t)$ is to use an optimal normal basis of $GF(2^t)$ over $GF(2)$. In section 4, we tabulate implementation result of two methods.

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References

  1. Design. Coded and Cryptography v.2 Optimal Normal Bases S. Gao;H. Lenstra
  2. Advances in Cryptology - Eurocrypt'92, LNCS 658 Public-key Cryptosystems with very small key lenghths G. Harper;A. Menezes;S. Vanstone
  3. Finite Fields R. Lidl;H. Niederreiter
  4. Patent Application of Computational Method and Apparatus for Finite Field Arithmetic J. L. Massey;J. K. Omura
  5. Applications of Finite Fields A. J. Menezes
  6. Discrete Applied Math. v.22 Optimal Normal Bases in GF($p^n$ R. C. Mullin;I. M. Onyszchuk;S. A. Vanstone;R. M. Wilson
  7. Univ. of California, Ph. D. Exponentiation in Finite Fields C. C. Wang