If \mathbb{F}_q is a finite field and the elliptic curve E is defined over finite field \mathbb{F}_p such that ECDLP is hard in E(\mathbb{F}_p), where q, p are prime and q \ll p. Let T \in E(\mathbb{F}_p) with mT= \mathcal{O}. My question is in finite field \mathbb{F}_q, $1=q+1$. It follows that T=(q+1)T. Does it imply m have to be divided by q? Is there any other possibility? Thank you~