타원곡선
Elliptic curves over finite fields are notably applied in cryptography and for the factorization of large integers. These algorithms often make use of the group structure on the points of "E". Algorithms that are applicable to general groups, for example the group of invertible elements in finite fields, F*"q", can thus be applied to the group of points on an elliptic curve. For example, the discrete logarithm is such an algorithm. The interest in this is that choosing an elliptic curve allows for more flexibility than choosing "q" (and thus the group of units in F"q"). Also, the group structure of elliptic curves is generally more complicated.