What is the best pseudo random number generator (PRNG) for designing RSA cryptosystems. I need it in simulating my program in ModelSim + Quartus. However, if you know how to use the built-in command in VHDL it would be appreciated. Even if it works with only 32-bit.
There is no in-built function in Modelsim, but you can use the standard VHDL packages that contains RNG(Random Number Generator). Refer the IEEE VHDL packages.
Both VHDL and VerilogHDL has built in functions for implementing random number generation. But "the best" term depends on what you mean. For random number generation it depends on the entropy of the generator and i am sure that both HDLs random number generation functions has that parapeter a really good value. But i think this is not what you need. In crypto systems true random number generators (TRNG) are used because it is quite easy to hack PRNGs.
Linear feedback shift register are easy to implement in FPGA and take very few resources. They produce very long sequences with nearly Dirac delta like autocorrelation, and flat frequency spectrum.
In any case there is no "best" pseudo random generator. there are instead some randomness testing procedures based on different criteria to test the RNGs. But at the end the best RNG depends on how and what it will be used for.
A better method is to use a symmetric encryption algorithm, for example AES, in OFB mode of operation. For cleartext can you use the output a LFS.
In this case for cryptography you need a good random number generator. For testing your design you can simply pick any RNG, like VHDL standard RNG.
In case you would need for real life applications, then you need a cryptographic secure RNG.
I suggest reading NIST standard 800-90A and/or BIS standard AIS 31
As suggestion, you can apply a LSFR with a good entropy source, because you need to feed the LSFR with entropy all times.
Another good sugestion is to reuse block ciphers or hashs, since your system will need them if you are thinking in cryptographic applications.
Also, you can investigate stream ciphers, since they are PRNG, like Trivium.
To read the BSI dokument AIS 31 is a good idea. It is to find on the hompage of the BSI (Bundesamt für Sicherheit in der Informationstechnik).
For more details please see following book
http://www.crypto-textbook.com/