| 摘要 |
<p>Methods and apparatus to construct finite fields over which efficient elliptic curve cryptosystems can be set up. Given a security parameter k, the said methods and apparatus consist of devices for carrying out operations in a small k0-bit field k0 and methods to successively build extension fields K1 ; K2, ..., Kt, where the extension K1/K0 has degree 2 or 3 and the other extensions Ki/KI-1 are quadratic, Kt is the final field over which elliptic curves are defined, and Kt has size ko2t or 3k¿02?t-1 just exceeding the said security parameter k.</p> |
