Key Exchange Protocol in Elliptic Curve Cryptography with No Public Point

K Kaabneh,H Al-Bdour

doi:10.3844/ajassp.2005.1232.1235

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 Fq 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 Fq 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.

Highlights

With the proliferation of the handheld wireless information appliances, the ability to perform security functions with limited computing resources has become increasingly important
New smaller and faster security algorithms provide part of the solution, the elliptic curve cryptography ECC provides a faster alternative for public key cryptography
The terms elliptic curve cipher and elliptic curve cryptography refers to an existing generic cryptosystem which use numbers generated from an elliptic curve

Summary

INTRODUCTION

With the proliferation of the handheld wireless information appliances, the ability to perform security functions with limited computing resources has become increasingly important. Elliptic curve over a finite field Fp: Using the real numbers for cryptography will cause a problem because it is very hard to store them precisely in computer memory and to predict how much storage we will need for them. ECDH begin by selecting the underlying the public point by both the secret key generated by field GF (P) or GF (2k) , the curve E with parameters a, Alice and Bob Ted has exchanged keys with Bob b and the base point P. The standards often suggest that we select an not authenticated This means that Alice has no way of elliptic curve with prime order and any knowing if bP was sent from Bob. A third party element of the group would be selected and their order Ted could have intercepted the transmission from Bob will be the prime number n.

B receives Ga and computes the point

CONCLUSION