[feature] integrate zeknox GPU-acceleration library into gnark

[dloghin]

Description

This PR aims to integrate zeknox GPU-acceleration library into gnark. Specifically, this PR targets the GPU (NVIDIA CUDA) acceleration of groth16 backend over BN254. In addition, this PR adds a new example consisting of proving/verifying a batch of secp256r1 (P256) signatures. Our benchmarking shows 1.54-1.57X speedup of the CPU+GPU execution (with zeknox) compared to the default CPU-only execution.

In summary, we did the following addition:

• accelerated groth16 over BN254 with zeknox under backend/groth16/bn254/zeknox folder.
• timing in backend/groth16/bn254/prove.go printed in debug mode.
• a code example of proving/verifying a batch of secp256r1 (P256) signatures under examples/p256.
• instructions in README.md on how to run gnark with zeknox.

Type of change

• New feature (non-breaking change which adds functionality)
• This change requires a documentation update

How has this been tested?

We wrote new tests under backend/groth16/bn254/zeknox and examples/p256. In addition, we also run tests under backend/groth16/bn254.

• Test A: backend/groth16/bn254

cd backend/groth16/bn254
go test
go test -tags zeknox

• Test B: backend/groth16/bn254/zeknox

cd backend/groth16/bn254/zeknox
go test
go test -tags zeknox

• Test C: examples/p256

cd examples/p256
go test
go test -tags zeknox

• Test D: examples/mimc

cd examples/mimc
go test
go test -tags zeknox

How has this been benchmarked?

• Benchmark A

We ran the P256 example to prove/verify a batch of 10 secp256r1 keys. The steps to run:

cd examples
go build -tags zeknox
./examples

• Platform A: on Google Cloud Platform g2-standard-32 instance with 32 vCPU (cores) of Intel Xeon type, one NVIDIA L4 GPU, and 128 GB RAM.
• Platform B: on a x86-64 AMD Ryzen 9 5950X CPU with 16 cores (32 threads), one NVIDIA RTX 4080 GPU, and 128 GB RAM.

Results

The times below represent the proving time (in milliseconds) for 10 secp256r1 keys.

Platform	CPU-only	CPU+GPU (zeknox)	Speedup
Platform A	5840.96 ms	3792.48 ms	1.54 X
Platform B	4066.95 ms	2588.51 ms	1.57 X

Checklist:

• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• I have added tests that prove my fix is effective or that my feature works
• I did not modify files generated from templates
• golangci-lint does not output errors locally
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules

[doutv]

@ivokub need your help and review!

[ivokub]

@ivokub need your help and review!

On it. Would it be possible to allow adding commits directly to the branch for easier review?

[doutv]

@ivokub need your help and review!

On it. Would it be possible to allow adding commits directly to the branch for easier review?

Sure, I've add grant you push permission in https://github.com/okx/gnark/invitations

Let me delete those examples to keep the PR clean

[ivokub]

I'm not able to create a proof for now, in the debug logs I see the last action is:

�[90m14:05:05�[0m DBG Bs.MultiExp done �[36mMSMG2 5 took=�[0m0.86421 �[36macceleration=�[0mzeknox �[36mbackend=�[0mgroth16 �[36mcurve=�[0mbn254 �[36mnbConstraints=�[0m6

I guess it is probably some deadlock somewhere. Have you been able to run end-to-end prover?