# Why is a cyclic subgroup chosen in ECDSA?

One thing which I am wondering for a long time and to which I did not find an answer after doing a web search and hope to find an answer here.

When we construct the elliptic curve over a prime field why do we actually select a cyclic subgroup instead of taking the entire group of the elliptic curve?

On a side note the thing that confuses me most about this choice: We know that the cyclic subgroup of prime order `p` is isomorphic to `Z/pZ` and finding the isomorphism would mean solving the discrete log.

Switching to a cyclic group seems actually rather like making the problem easier in comparison to staying with the full elliptic curve.

• You may get better answers on Crypto.SE. Commented Feb 22, 2019 at 19:32
• ah that is a good idea. I will repost it there if no answer comes in here (: Commented Feb 22, 2019 at 19:50

• would still need to know the prime factors of `n` but yeah I see why it makes sense to just take a large (or the largest) cyclic subgroup. thanks a lot! Commented Feb 22, 2019 at 22:17