| 摘要 |
A method of cryptographic key exchange by two users agreeing on an elliptic curve of the form y2+xy=x3+ax2+1, where "a" is a member of a field F2, where the elliptic curve is defined over a field F2m, where m is an integer; agreeing on 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; generating a private integer xA by a first user; reducing xA by mod (&tgr;m-1) in the form of w+z&tgr; by the first user; generating a base tau expansion, in non-adjacent form, of the modular reduced xA by the first user; multiplying G by the base tau expansion of the modular reduced xA; transmitting the product to the second user; receiving, by the first user, a value yB from the second user that is based on a private integer xB of the second user, where the received value is computed in a similar manner as was the product transmitted to the second user; multiplying, by the first user, xA by the value received from the second user in order to form a common secret point; multiplying, by the second user, xB by the value received from the first user in order to form the common secret point; and the two users each deriving the same cryptographic key from the common secret point.
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