Key Exchange Protocol in Elliptic Curve Cryptography with No Public Point

Abstract

In recent years some cryptographic algorithms have gained popularity due to properties that make them suitable for use in constrained environment like mobile information appliances, where computing resources and power availability are limited. One of these cryptosystems is Elliptic curve which requires less computational power, memory and communication bandwidth compared to other cryptosystem. This makes the elliptic curve cryptography to gain wide acceptance as an alternative to conventional cryptosystems (DSA, RSA, AES, etc.). All existing protocols for elliptic curve cryptosystems that are used for either key exchange or for ciphering, assume that the curve E, the field F_q and a point P on the curve are all public. In this research we propose a modified protocol for elliptic curve key exchange based on elliptic curve over rings, assuming that only the curve E and F_q are public, keeping the base point P secret, which make attacking the cryptosystem harder by the eavesdropper. Also we provide imbedded authentication, so our protocol does not suffer from the man in the middle attack.