释义 |
Elliptic Group Modulo p denotes the elliptic Group modulo whose elements are and together with the pairs ofIntegers with satisfying
 | (1) |
with and Integers such that
 | (2) |
Given , define
 | (3) |
The Order of is given by
 | (4) |
where is the Legendre Symbol, although this Formula quickly becomes impractical. However, ithas been proven that
 | (5) |
Furthermore, for a Prime and Integer in the above interval, there exists and such that
 | (6) |
and the orders of elliptic Groups mod are nearly uniformly distributed in the interval.
|