P-adic numbers applied on an elliptic curve cryptography

cryptography

This paper use the group of -rational points of elliptic curve over p-adic numbers field in cryptography. Since this group is an abelian group and can be made cyclic, « addition » on this group have also important geometrical interpretation We introduice some notations in section 1 and review some properties of a p-adic numbers. In section 2, we review group structure of elliptic curves over the field of p-adic numbers.In section 3 we show one possibility to apply the group of -rational points on an elliptic curve in cryptography.In sectio 4, we give an example of cryptosystem based on the key exchange of Diffie-HellmanThe section 5 is reserved for the conclusion.

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