How fast we can run 128-bit LCG generator? Let's consider some 128-bit LCG generator mod $2^{128}$, with some random 128-bit multiplier and increment. How fast we can run it using the same tricks like in AES:
https://crypto.stackexchange.com/questions/44927/how-long-does-a-good-aes-encryption-take
They use there some hardware instruction/hardware acceleration and it is absurdly fast. Can we do the same thing with LCG? If we run pure LCG in C it could be several dozen of GB/s. But can we do it faster in some easy way?
If you have a linear congruential random number generator X, then applying X say 8 times is another LCG whose constants are easy to find. If X calculated a series a0, A1.a2 etc. then you can calculate a0 to a7, and then apply Y to all 8 numbers in parallel, assuming this takes a lot less than eight times the effort.
I hope you know how to calculate the same LCG many times without divisions.