Method of elliptic curve cryptographic key agreement using coefficient splitting

摘要

A method of generating a cryptographic key in an authenticated manner using coefficient splitting. Select a prime number p and an elliptic curve of either a first class or a second class. Select a point P. The first user generates r_a, w_a, and R_a=r_aP and W_a=w_aP via coefficient splitting. The second user generates r_b, w_b, and R_b=r_bP and W_b=w_bP via coefficient splitting. After the users have exchanged the points R_a, W_a, R_b, W_b, the first user generates c_a, g_a, and c_aW_b, and g_aR_b via coefficient splitting, and the second user generates c_b, g_b, and c_bW_a and g_bR_a via coefficient splitting. Each user then sums the corresponding results to form K and derives the cryptographic key from K in the same user-definable manner. An unauthenticated key exchange method is also presented.