Java Card: can this operations be implemented?

I'm new to Smart Cards and Java Card. I'm planning to implement a variation of the ElGamal key generation algorithm. It's not easy to find information, so is it possible to calculate this steps on a Java Card?

1. Find smallest prime number greater than a number x (about 2048 bit)
2. Determine if a number g is a primitive root mod p
3. Modular exponentation, arithmetic on big numbers (about 2048 bit)

I know that the RSA key generation is possible on a Smart Card, but are the individual steps of the generation (like finding a prime number) also possible? If not, are there other kinds of security tokens that can do this? I'm planning to use the NXP J3D081 Card.

The El gamal algorithm itself is not implemented on any card as far as i know. The requiured cryptographic primitives are not available in java card. Manual implementations are too slow as well