I would like to program my cryptographic scheme which uses some computations on elliptic curves. I coded it using sagemath package, which is a python library. It is simple but very slow. I need to deal with very large numbers (like 256 bit integers). Computations on such large numbers are slow in sagmath.
Please suggest some libraries that are fast and simple to use for computations on elliptic curves. I would like to have a library that supports generating elliptic curves, sampling a random generator of an elliptic curve, computing group operations on elliptic curves etc.,