I have a Pollard Rho code in GMP for Elliptic Curve Discrete logarithmic problem (ECDLP) which I wanted to parallelize using MPI. Kindly guide me whether it is possible to use both libraries simultaneous in the same C code OR do I have to convert my entire code into MPI syntax.
GMP is a multi-precision arithmetic library.
MPI's a library and set of tools that enables you to run your code in different processes (though some versions of MPI used threads, this is not common).
Since processes do not share memory, anything you're doing with GMP in one process will not affect another.
Your only worry is that GMP is doing some kind of internal multithreading to speed things up (I don't think it does). If so, allocate fewer processes in MPI than you otherwise might or disable GMP's multithreading.