A self-pairing map and its applications to cryptography

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In this paper, we propose a bilinear pairing map on finitely generated free R-modules with rank two where R is a commutative ring with 1, and apply this pairing to elliptic curves over fields. We also verify the pairing on elliptic curves can be applicable to the current cryptographic schemes.

Original languageEnglish
Pages (from-to)671-678
Number of pages8
JournalApplied Mathematics and Computation
Issue number3
StatePublished - 15 Apr 2004


  • Bilinear pairing map
  • Cryptography
  • Elliptic curves
  • Free modules


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