A new aspect of dual basis for efficient field arithmetic

Chang Hyi Lee, Jong In Lim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

In this paper we consider a special type of dual basis for finite fields, GF(2m), where the variants of m are presented in section 2. We introduce our field representing method for efficient field arithmetic(such as field multiplication and field inversion). It reveals a very effective role for both software and hardware(VLSI) implementations, but the aspect of hardware design of its structure is out of this manuscript and so, here, we deal only the case of its software implementation(the efficiency of hardware implementation is appeared in another article submitted to IEEE Transactions on Computers). A brief description of several advantageous characteristics of our method is that (1) the field multiplication in GF(2m) can be constructed only by m + 1 vector rotations and the same amount of vector XOR operations, (2) there is required no additional work load such as basis changing(from standard to dual basis or from dual basis to standard basis as the conventional dual based arithmetic does), (3) the field squaring is only bit-by-bit permutation and it has a good regularity for its implementation, and (4) the field inversion process is available to both cases of its implementation using Fermat’s Theorem and using almost inverse algorithm[14], especially the case of using the almost inverse algorithm has an additional advantage in find- ing(computing) its complete inverse element(i.e., there is required no pre-computed table of the values, x-k, k = 1, 2,…).

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages12-28
Number of pages17
Volume1560
ISBN (Print)3540656448, 9783540656449
Publication statusPublished - 1999
Event2nd International Workshop on Practice and Theory in Public Key Cryptography, PKC 1999 - Kamakura, Japan
Duration: 1999 Mar 11999 Mar 3

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1560
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other2nd International Workshop on Practice and Theory in Public Key Cryptography, PKC 1999
CountryJapan
CityKamakura
Period99/3/199/3/3

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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  • Cite this

    Lee, C. H., & Lim, J. I. (1999). A new aspect of dual basis for efficient field arithmetic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1560, pp. 12-28). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1560). Springer Verlag.