You work modulo p, yes, but the group is the set of points of the curve. The qubit bottleneck seems to be the Extended Euclidean Algorithm to perform modular di

You work modulo p, yes, but the group is the set of points of the curve. The qubit bottleneck seems to be the Extended Euclidean Algorithm to perform modular divisions, which requires the greatest amount of space. Check [1, §6.2] for details. [1] http://arxiv.org/abs/quantph/0301141 http://arxiv.org/abs/quantph/0301141