Is there a floating point CSPRNG? Is there a floating-point CSPRNG that operates, natively, using floating point operations?  

Looking for a CSPRNG that's very fast on GPUs, and would be hard for a CPU to beat.

EDIT: Floating point doesn't matter too much.   Specifically, I'm looking for something for which GPUs or FPUs are, by far, the optimal hardware to use: as opposed to custom hardware, because the operations used are already heavily optimized on GPU.

My understanding is that floating-point-operations (FLOPS) are probably the best candidate here.    (It seems to me that most chaotic attractors can be trivially run using FLOPS.)
Are you sure?

Float operations are very hard to reproduce in diverse environments.

Do you round towards positive, negative or zero? Do you handle denormals or just treat them as zero? What about dividing by zero?

I'm sure we would love to have that problem with every cipher we implement.


  Looking for a CSPRNG that's very fast on GPUs, and would be hard for a CPU or FPGA to beat.


To beat FPGA... don't do anything. There are problems that are slow on CPUs &amp; GPUs, but otherwise you won't have as big FPGA that can reach nearly same frequency. If that wasn't case we wouldn't have processors, just builtin FPGAs that switch between GPUs and CPUs...

To beat CPU... just use something that uses a lot of simple math... +,-,xor,ror,rol etc. This doesn't have to be on floats, ints will suffice. Chacha20 might work well on GPUs. Note that this won't be slow on CPUs, it will just be faster on GPUs because it parallelizes well (and this is always case, because CPUs are complex beasts that can do more than GPU, except there just isn't enough of it for raw number crunching at that speed).

Honestly, most cryptographic primitives will be faster on GPUs because they frequently rely on number crunching, and rarely do any significant memory access and/or branching.

Just remember that there are still ASICs that will always win against you, because they are exceptionally good at number crunching (and if you are looking to outrun them, argon2 and CPU are your friends).