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.
Bibliographical noteFunding Information:
The author was supported by grant no. R06-2002-012-0100-0 from the research program of KOSEF.
- Bilinear pairing map
- Elliptic curves
- Free modules