Architectures for Exponentiation Over GF(2n) Adopted for Smartcard Application

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5 Scopus citations


Two exponentiation circuits over GF(2n) are proposed. Using the fact that squaring is a linear operation over GF(2n), a time-space tradeoff in smartcard-based circuitry is presented. It is further shown how multiplication is performed by a single shift, based on replacing the public key aa ∊ GF(2n) by its minimal polynomial. Other considerations, related to structure regularity and the possible use of dynamic shift registers, are also treated.

Original languageEnglish
Pages (from-to)494-497
Number of pages4
JournalIEEE Transactions on Computers
Issue number4
StatePublished - 1 Jan 1993


  • Cryptography
  • Galois fields
  • VLSI
  • finite field arithmetics
  • modular exponentiation
  • smartcards

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics


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