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varunthakore committed Oct 22, 2023
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# Nova-SHA512

The repository includes a benchmarking of the SHA-512 hash function based on [Nova](https://github.com/microsoft/Nova). This requires a gadget for the SHA-512 compression function, which is obtained from the [SHA-512 circuit](https://github.com/varunthakore/bellperson-sha512) implemented using [bellperson](https://github.com/filecoin-project/bellperson).
The repository includes a benchmarking of the SHA-512 hash function based on [Nova](https://github.com/microsoft/Nova). This requires a gadget for the SHA-512 compression function, which is obtained from the [SHA-512 circuit](https://github.com/lurk-lab/bellpepper-gadgets/tree/main/crates/sha512) implemented using [bellpepper](https://github.com/lurk-lab/bellpepper).

The SHA-512 compression function is represented as the step function $F$ within the Nova computation. It follows the format $z_{i+1} = F(z_i)$, where $z_0$ is a fixed initial value, denoted as $IV$.

## Running the example
Run the following commands.
```
cargo build --release
cargo run -r --example sha512 6
cargo run --release --example sha512 6
```
In the above case, The input message to SHA-512 will be $2^6$ zero bytes. The output will look like the following.
```
Nova-based SHA512 compression function iterations
=========================================================
Producing public parameters...
PublicParams::setup, took 5.919208353s
PublicParams::setup, took 5.414872083s
Number of constraints per step (primary circuit): 78415
Number of constraints per step (secondary circuit): 10347
Number of variables per step (primary circuit): 78331
Number of variables per step (secondary circuit): 10329
Generating a RecursiveSNARK...
RecursiveSNARK::prove_step 0: true, took 121.632004ms
Total time taken by RecursiveSNARK::prove_steps: 121.645998ms
RecursiveSNARK::prove_step 0: true, took 4.333µs
Total time taken by RecursiveSNARK::prove_steps: 27.458µs
Verifying a RecursiveSNARK...
RecursiveSNARK::verify: true, took 80.677392ms
RecursiveSNARK::verify: true, took 49.15675ms
Generating a CompressedSNARK using Spartan with IPA-PC...
CompressedSNARK::prove: true, took 6.328847634s
Total proving time is 8.185695442s
CompressedSNARK::len 9924 bytes
CompressedSNARK::prove: true, took 7.57205325s
Total proving time is 8.230779375s
CompressedSNARK::len 9913 bytes
Verifying a CompressedSNARK...
CompressedSNARK::verify: true, took 268.03797ms
CompressedSNARK::verify: true, took 309.657833ms
=========================================================
Public parameters generation time: 5.919208353s
Total proving time (excl pp generation): 8.185695442s
Total verification time: 268.03797ms
Public parameters generation time: 5.414872083s
Total proving time (excl pp generation): 8.230779375s
Total verification time: 309.657833ms
=========================================================
Expected value of final hash = "7be9fda48f4179e611c698a73cff09faf72869431efee6eaad14de0cb44bbf66503f752b7a8eb17083355f3ce6eb7d2806f236b25af96a24e22b887405c20081"
Actual value of final hash = "7be9fda48f4179e611c698a73cff09faf72869431efee6eaad14de0cb44bbf66503f752b7a8eb17083355f3ce6eb7d2806f236b25af96a24e22b887405c20081"
```

To change the input length to 64 KB ($2^{16}$ bytes), run the following command. The input is again all zero bytes.
```
cargo run -r --example sha512 16
cargo run --release --example sha512 16
```

## Generating the benchmarks
Expand All @@ -61,91 +61,91 @@ To generate the logs for a particular length, you can run the `genlog.sh` script
./genlog.sh 10
```
## Existing benchmarks
The existing files in the `logs` directory were generated on a Dell Inspiron laptop with a [7th Gen Intel i7-7700 CPU](https://www.intel.in/content/www/in/en/products/sku/97128/intel-core-i77700-processor-8m-cache-up-to-4-20-ghz/specifications.html) and 8 GB of RAM. The CPU has 4 cores with 2 threads per core.
The existing files in the `logs` directory were generated on Apple Macbook Air M1 with 8GB RAM.
- For all lengths
- The peak memory usage was about 430 MB.
- Verification time was less than 322 milliseconds.
- The peak memory usage was about 522 MB.
- Verification time was less than 260 milliseconds.
- Proof size was about 10,000 bytes.
- Public parameter generation time was about 7.3 seconds
- The proving time for 64KB input was just over 2 minutes. Proving times for other lengths are shown below.
- Public parameter generation time was about 5.3 seconds
- The proving time for 64KB input was just over 100s. Proving times for other lengths are shown below.

### Proving times
```bash
$ grep "Total proving time is" $(ls logs/output_* -rt)
logs/output_65536.txt:Total proving time is 125.664165914s
logs/output_32768.txt:Total proving time is 60.092193749s
logs/output_16384.txt:Total proving time is 34.509046982s
logs/output_8192.txt:Total proving time is 21.062932541s
logs/output_4096.txt:Total proving time is 14.233733443s
logs/output_2048.txt:Total proving time is 11.400438599s
logs/output_1024.txt:Total proving time is 9.740290095s
logs/output_512.txt:Total proving time is 9.408122565s
logs/output_256.txt:Total proving time is 9.446057425s
logs/output_128.txt:Total proving time is 8.835119723s
logs/output_64.txt:Total proving time is 7.969319354s
$ grep "Total proving time is" $(ls -rt logs/output_*)
logs/output_65536.txt:Total proving time is 104.831938083s
logs/output_32768.txt:Total proving time is 59.466137458s
logs/output_16384.txt:Total proving time is 31.542905375s
logs/output_8192.txt:Total proving time is 19.869245042s
logs/output_4096.txt:Total proving time is 14.004221375s
logs/output_2048.txt:Total proving time is 11.19301675s
logs/output_1024.txt:Total proving time is 9.965042583s
logs/output_512.txt:Total proving time is 10.307841959s
logs/output_256.txt:Total proving time is 10.498092333s
logs/output_128.txt:Total proving time is 8.687329542s
logs/output_64.txt:Total proving time is 8.20162325s
```

### Verification times
```bash
$ grep "CompressedSNARK::verify" $(ls logs/output_* -rt)
logs/output_65536.txt:CompressedSNARK::verify: true, took 237.246422ms
logs/output_32768.txt:CompressedSNARK::verify: true, took 263.331711ms
logs/output_16384.txt:CompressedSNARK::verify: true, took 241.443806ms
logs/output_8192.txt:CompressedSNARK::verify: true, took 321.000251ms
logs/output_4096.txt:CompressedSNARK::verify: true, took 213.370396ms
logs/output_2048.txt:CompressedSNARK::verify: true, took 214.010385ms
logs/output_1024.txt:CompressedSNARK::verify: true, took 235.100483ms
logs/output_512.txt:CompressedSNARK::verify: true, took 228.78052ms
logs/output_256.txt:CompressedSNARK::verify: true, took 255.712681ms
logs/output_128.txt:CompressedSNARK::verify: true, took 274.365492ms
logs/output_64.txt:CompressedSNARK::verify: true, took 231.26493ms
$ grep "CompressedSNARK::verify" $(ls -rt logs/output_*)
logs/output_65536.txt:CompressedSNARK::verify: true, took 248.697125ms
logs/output_32768.txt:CompressedSNARK::verify: true, took 266.471667ms
logs/output_16384.txt:CompressedSNARK::verify: true, took 248.045542ms
logs/output_8192.txt:CompressedSNARK::verify: true, took 247.234416ms
logs/output_4096.txt:CompressedSNARK::verify: true, took 249.306458ms
logs/output_2048.txt:CompressedSNARK::verify: true, took 246.204209ms
logs/output_1024.txt:CompressedSNARK::verify: true, took 286.810875ms
logs/output_512.txt:CompressedSNARK::verify: true, took 294.566292ms
logs/output_256.txt:CompressedSNARK::verify: true, took 256.616ms
logs/output_128.txt:CompressedSNARK::verify: true, took 249.140125ms
logs/output_64.txt:CompressedSNARK::verify: true, took 259.960375ms
```

### Proof sizes
```bash
$ grep "len" $(ls logs/output_* -rt)
logs/output_65536.txt:CompressedSNARK::len 10401 bytes
logs/output_32768.txt:CompressedSNARK::len 10399 bytes
logs/output_16384.txt:CompressedSNARK::len 10408 bytes
logs/output_8192.txt:CompressedSNARK::len 10409 bytes
logs/output_4096.txt:CompressedSNARK::len 10400 bytes
logs/output_2048.txt:CompressedSNARK::len 10399 bytes
logs/output_1024.txt:CompressedSNARK::len 10401 bytes
logs/output_512.txt:CompressedSNARK::len 10400 bytes
logs/output_256.txt:CompressedSNARK::len 10403 bytes
logs/output_128.txt:CompressedSNARK::len 10370 bytes
logs/output_64.txt:CompressedSNARK::len 9924 bytes
$ grep "len" $(ls -rt logs/output_*)
logs/output_65536.txt:CompressedSNARK::len 10297 bytes
logs/output_32768.txt:CompressedSNARK::len 10302 bytes
logs/output_16384.txt:CompressedSNARK::len 10302 bytes
logs/output_8192.txt:CompressedSNARK::len 10303 bytes
logs/output_4096.txt:CompressedSNARK::len 10298 bytes
logs/output_2048.txt:CompressedSNARK::len 10302 bytes
logs/output_1024.txt:CompressedSNARK::len 10300 bytes
logs/output_512.txt:CompressedSNARK::len 10303 bytes
logs/output_256.txt:CompressedSNARK::len 10296 bytes
logs/output_128.txt:CompressedSNARK::len 10263 bytes
logs/output_64.txt:CompressedSNARK::len 9913 bytes
```

### Peak memory usage
### Peak memory usage in bytes
```bash
$ grep "Maximum resident set size" $(ls logs/time_output_* -rt)
logs/time_output_65536.txt: Maximum resident set size (kbytes): 404060
logs/time_output_32768.txt: Maximum resident set size (kbytes): 414268
logs/time_output_16384.txt: Maximum resident set size (kbytes): 396884
logs/time_output_8192.txt: Maximum resident set size (kbytes): 429176
logs/time_output_4096.txt: Maximum resident set size (kbytes): 418536
logs/time_output_2048.txt: Maximum resident set size (kbytes): 410128
logs/time_output_1024.txt: Maximum resident set size (kbytes): 412428
logs/time_output_512.txt: Maximum resident set size (kbytes): 412584
logs/time_output_256.txt: Maximum resident set size (kbytes): 401256
logs/time_output_128.txt: Maximum resident set size (kbytes): 412600
logs/time_output_64.txt: Maximum resident set size (kbytes): 407776
$ grep "maximum resident set size" $(ls -rt logs/time_output_*)
logs/time_output_65536.txt: 401932288 maximum resident set size
logs/time_output_32768.txt: 425590784 maximum resident set size
logs/time_output_16384.txt: 422412288 maximum resident set size
logs/time_output_8192.txt: 460095488 maximum resident set size
logs/time_output_4096.txt: 460521472 maximum resident set size
logs/time_output_2048.txt: 460259328 maximum resident set size
logs/time_output_1024.txt: 474382336 maximum resident set size
logs/time_output_512.txt: 418037760 maximum resident set size
logs/time_output_256.txt: 413073408 maximum resident set size
logs/time_output_128.txt: 521895936 maximum resident set size
logs/time_output_64.txt: 499105792 maximum resident set size
```
### Public parameter generation time
```bash
$ grep "Public parameters" $(ls logs/output_* -rt)
logs/output_65536.txt:Public parameters generation time: 7.328006108s
logs/output_32768.txt:Public parameters generation time: 6.055087751s
logs/output_16384.txt:Public parameters generation time: 5.959388904s
logs/output_8192.txt:Public parameters generation time: 5.740550812s
logs/output_4096.txt:Public parameters generation time: 5.601547852s
logs/output_2048.txt:Public parameters generation time: 5.579313352s
logs/output_1024.txt:Public parameters generation time: 5.649952591s
logs/output_512.txt:Public parameters generation time: 5.907281543s
logs/output_256.txt:Public parameters generation time: 5.831920632s
logs/output_128.txt:Public parameters generation time: 5.878975833s
logs/output_64.txt:Public parameters generation time: 5.576295279s
$ grep "Public parameters" $(ls -rt logs/output_*)
logs/output_65536.txt:Public parameters generation time: 5.272849542s
logs/output_32768.txt:Public parameters generation time: 5.451450625s
logs/output_16384.txt:Public parameters generation time: 5.496126208s
logs/output_8192.txt:Public parameters generation time: 5.288794292s
logs/output_4096.txt:Public parameters generation time: 5.308094333s
logs/output_2048.txt:Public parameters generation time: 5.298190833s
logs/output_1024.txt:Public parameters generation time: 5.320729542s
logs/output_512.txt:Public parameters generation time: 5.725966625s
logs/output_256.txt:Public parameters generation time: 5.858633417s
logs/output_128.txt:Public parameters generation time: 5.33493275s
logs/output_64.txt:Public parameters generation time: 5.343597s
```

This project was part of the submission for [ZK MOOC Hackathon](https://zk-hacking.org/) for [zk-Circuits Track](https://zk-hacking.org/tracks/zk_circuit_track/) and it was selected as one of the winners for *Category 2: Circuits/R1CSs for recursive SNARKs*.
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