J. K. Omura

Publications (5)3.31 Total impact

• Article: Normal basis of finite field GF(2 super m)

  D. Y. Pei, C. C. Wang, J. K. Omura
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  ABSTRACT: Massey and Omura (1981) recently developed a new multiplication algorithm for Galois fields based on the normal basis representation. This algorithm shows a much simpler way to perform multiplication in finite field than the conventional method. The necessary and sufficient conditions are presented for an element to generate a normal basis in the field GF(2 super m), where m = 2 super k p super n and p super n has two as a primitive root. This result provides a way to find a normal basis in the field.
  04/1986;
• Article: VLSI architectures for computing multiplications and inverses in GF(2m).

  C C Wang, T K Truong, H M Shao, L J Deutsch, J K Omura, I S Reed
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  ABSTRACT: Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that can be easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. In this paper, a pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal basis representation used together with this multiplier, a pipeline architecture is developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable, and therefore, naturally suitable for VLSI implementation.
  IEEE Transactions on Computers 09/1985; C-34(8):709-17. · 1.10 Impact Factor
• Article: VLSI Architectures for Computing Multiplications and Inverses in GF(2^m)

  C. C. Wang, T. K. Troung, H. M. Shao, L. J. Deutsch, J. K. Omura, I.S. Reed
  [show abstract] [hide abstract]
  ABSTRACT: Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that can be easily realized on VLSI chips. Massey and Omura [1] recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. In this paper, a pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable, and therefore, naturally suitable for VLSI implementation.
  IEEE Transactions on Computers 09/1985; C-34(8):709-717. · 1.10 Impact Factor
• Source

  Available from: tmo.jpl.nasa.gov

  Article: VLSI Architectures for Computing Multiplications and Inverses in GF(2^m)

  C.C. Wang, T.K. Troung, H.M. Shao, L.J. Deutsch, J.K. Omura, I.S. Reed
  [show abstract] [hide abstract]
  ABSTRACT: Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that can be easily realized on VLSI chips. Massey and Omura [1] recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. In this paper, a pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable, and therefore, naturally suitable for VLSI implementation.
  IEEE Transactions on Computers 07/1985; 34:709-717. · 1.10 Impact Factor
• Article: VLSI architectures for computing multiplications and inverses in GF(2-m)

  C. C. Wang, T. K. Truong, H. M. Shao, L. J. Deutsch, J. K. Omura, I.S. Reed
  [show abstract] [hide abstract]
  ABSTRACT: Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that are easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. A pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal-basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.
  12/1983;