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Which tool is the best one for accesing large bit numbers for testing Crypto systems..either GMP library or JAVA big integers..?? in terms of speed, memory, functions, flexibility towards crptosystems(mathematical functions like invert,pwm..etc).

+3  A: 

The question makes little sense because if you are using Java, then you cannot use GMP, and if you are not using Java, then you cannot use Java's BigInteger.

It is possible to do cryptography with both (I do that for a living). Java's big integers are decent but not very fast (they are "fast enough for most purposes"). For instance, I get 300 RSA signatures per second with Java, while GMP would yield more than 1000 per second on the same system.

However, Java comes with a garbage collector, and that's good.

Thomas Pornin