# why are non singular curves used in elliptic curve cryptography?

It is not possible to draw tangent at all the points of a singular curve. What is the specialty of this and how it is related to cryptography and elliptic discriminant?

• In ECC we use elliptic curves, where by definition are non-singular. But you can use varieties in cryptography. For instance, you can use Jacobian varieties, because they form a group where dlog is hard. If it occurs non-singular curves to form a group, whee dlog is hard, then they will also used such curves. – 111 Jan 25 '17 at 0:29

The discriminant characterizes all curves which are non-singular. In other words, the curves that are non-singular are exactly those for which the discriminant $\Delta$ is non-zero.