Patent ID: 6212279
Filing Date: 2001-04-03
Classification: H04L

Abstract:
A method of cryptographic key exchange, comprising the steps of:a) agreeing upon an elliptic curve between a first user and a second user, where the elliptic curve is of the form y.sup.2 +xy=x.sup.3 +ax.sup.2 +1, where ""a"" is a member of a field F.sub.2, where the elliptic curve is defined over a field F.sub.2 m, where m is an integer;b) agreeing upon a point G as the base point of the elliptic curve, where the point G is of order q, and where q is an integer;c) generating a private integer x.sub.A by the first user;d) reducing x.sub.A by mod (.tau..sup.m -1) in the form of w+z.tau. by the first user;e) generating a base tau expansion, in non-adjacent form, of the result of step (d) by the first user;f) multiplying G by the result of step (e) by the first user;g) transmitting, by the first user, the result of step (f) to the second user;h) receiving, by the first user, a value y.sub.B from the second user that is based on a private integer x.sub.B of the second user, where the received value is computed in a similar manner as was the result of step (f);i) multiplying, by the first user, x.sub.A by the value received fiom the second user in order to form a common secret point;j) multiplying, by the second user, x.sub.B by the value received from the first user in order to form the common secret point; andk) deriving the cryptographic key from the common secret point by the first user and the second user.