> ## Documentation Index
> Fetch the complete documentation index at: https://docs.starknet.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Benchmarks Report

* Overview of zkVM and Proof Systems

| zkVM / Proof System                                     | Architecture | Frontend | Backend      | Security Bits |
| :------------------------------------------------------ | :----------- | :------- | :----------- | :------------ |
| [RISC Zero](https://github.com/risc0/risc0)             | RISC-V       | Rust     | STARK-based  | 96 bits       |
| [SP1](https://github.com/succinctlabs/sp1)              | RISC-V       | Rust     | STARK-based  | 100 bits      |
| [OpenVM](https://github.com/openvm-org/openvm)          | RISC-V       | Rust     | STARK-based  | 100 bits      |
| [Jolt](https://github.com/a16z/jolt)                    | RISC-V       | Rust     | Lookup-based | -             |
| [Stone](https://github.com/starkware-libs/stone-prover) | Cairo VM     | Cairo    | STARK-based  | 100 bits      |
| [S-two](https://github.com/starkware-libs/stwo)         | Cairo VM     | Cairo    | STARK-based  | 96 bits       |

* All benchmarks presented here are **CPU-only** and do not utilize any GPU acceleration.
* Stone benchmarks were generated using the `dynamic` layout with these [configurations](https://github.com/zksecurity/zkvm-benchmarks/tree/master/stone/configs).
* The benchmarks for SP1, R0 and OpenVM use compressed or succinct prover type, which aggregates all the STARK proofs into a single STARK proof.
* Benchmarks which run out of memory have been indicated by `💾` and benchmarks which generate errors in proof generation have been indicated by `❌` in the tables.

## Time and Commit Hash

* **Commit Hash**: f27856ec17fbd9e85ec31cba9c2cb9e96d8dd08f
* **Timestamp**: Thursday, July 03, 2025 20:52:50 UTC

## System Information

### OS Version

Ubuntu 24.04.2 LTS

### CPU Info

* **Architecture**: x86\_64

* **CPU(s)**: 48

* **Model name**: AMD EPYC-Rome Processor

* **Thread(s) per core**: 2

* **Core(s) per socket**: 24

* **Socket(s)**: 1

* **L3 cache**: 16 MiB (1 instance)

### Memory Info

* **MemTotal**: 184.25 GB

* **MemFree**: 166.19 GB

* **MemAvailable**: 178.69 GB

## Fibonacci

Benchmark `n` Fibonacci iterations.

### Prover Time (s)

|       n |   jolt |     sp1 |  openvm |      r0 |  stone |   stwo |
| ------: | -----: | ------: | ------: | ------: | -----: | -----: |
|   32768 |  3.208 |  15.003 |  34.291 |  17.128 | 56.325 | 13.198 |
|   65536 |  5.183 |  18.252 |  42.403 |  29.241 | 95.468 | 11.372 |
|  131072 |   9.17 |  24.982 |  57.978 |  52.298 |     💾 | 12.886 |
|  262144 | 15.771 |  39.327 |  92.229 |  86.743 |     💾 | 12.587 |
|  524288 |  28.16 |  54.812 | 158.128 | 167.607 |     💾 | 16.166 |
| 1048576 |  54.42 |  72.028 | 320.082 | 306.386 |     💾 | 18.612 |
| 2097152 | 107.89 | 128.215 | 515.567 |  605.92 |     💾 | 31.047 |
| 4194304 |      ❌ | 222.332 | 1042.58 | 1206.76 |     💾 | 60.939 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/fib_prover_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=235fcfccc18aa0b7f3c77a0d9cd7d9ad" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/fib_prover_time_vs_n.png" />

### Verifier Time (ms)

|       n |  jolt | sp1 | openvm | r0 | stone | stwo |
| ------: | ----: | --: | -----: | -: | ----: | ---: |
|   32768 |  53.0 | 108 |    142 | 23 |  92.0 |   41 |
|   65536 |  77.0 | 107 |    139 | 10 | 113.0 |   16 |
|  131072 |  58.0 | 101 |    140 | 23 |    💾 |   18 |
|  262144 | 103.0 | 100 |    141 | 22 |    💾 |   89 |
|  524288 |  56.0 |  83 |    140 | 24 |    💾 |   14 |
| 1048576 | 104.0 |  83 |     57 | 23 |    💾 |  414 |
| 2097152 |  98.0 |  84 |     57 | 10 |    💾 |  367 |
| 4194304 |     ❌ |  83 |     57 | 23 |    💾 |   10 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/fib_verifier_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=3a873e28e6a33927dbcb37bcd6b63a63" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/fib_verifier_time_vs_n.png" />

### Proof Size (KB)

|       n |    jolt |     sp1 |  openvm |      r0 |   stone |    stwo |
| ------: | ------: | ------: | ------: | ------: | ------: | ------: |
|   32768 | 187.615 | 1315.53 | 1708.31 | 223.234 | 125.608 | 789.578 |
|   65536 | 197.799 | 1315.53 | 1708.31 | 223.234 |   129.8 |  783.63 |
|  131072 | 208.399 | 1315.53 | 1708.31 | 223.234 |      💾 | 783.834 |
|  262144 | 219.415 | 1315.53 | 1708.31 | 223.234 |      💾 | 802.678 |
|  524288 | 230.847 | 1315.53 | 1708.31 | 223.234 |      💾 | 801.194 |
| 1048576 | 242.695 | 1315.53 | 852.937 | 223.234 |      💾 | 808.038 |
| 2097152 | 254.959 | 1315.53 | 852.937 | 223.234 |      💾 | 819.122 |
| 4194304 |       ❌ | 1315.53 | 816.649 | 223.234 |      💾 | 866.882 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/fib_proof_size_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=9b1009988d628e52e83247b8621f4ff2" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/fib_proof_size_vs_n.png" />

### Cycle Count

|       n |     jolt |      sp1 |       r0 |  stone |     stwo |
| ------: | -------: | -------: | -------: | -----: | -------: |
|   32768 |   196974 |   168808 |   166215 | 229390 |   262143 |
|   65536 |   393582 |   332648 |   330055 | 458766 |   524287 |
|  131072 |   786798 |   660328 |   657735 |     💾 |  1048575 |
|  262144 |  1573230 |  1315688 |  1313095 |     💾 |  2097151 |
|  524288 |  3146041 |  2626408 |  2623815 |     💾 |  4194303 |
| 1048576 |  6291822 |  5247848 |  5245255 |     💾 |  8388607 |
| 2097152 | 12583293 | 10490728 | 10488135 |     💾 | 16777215 |
| 4194304 |        ❌ | 20976488 | 20973895 |     💾 | 33554431 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/fib_cycle_count_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=cfb51b349c254b3fc9734748b2877a12" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/fib_cycle_count_vs_n.png" />

### Peak Memory (GB)

|       n |  jolt |   sp1 | openvm |   r0 |  stone |  stwo |
| ------: | ----: | ----: | -----: | ---: | -----: | ----: |
|   32768 |  6.44 |  5.12 |      7 |  2.3 |  59.44 | 11.08 |
|   65536 |  5.83 |  6.42 |   5.43 | 4.58 | 118.54 | 11.46 |
|  131072 |  8.79 |  9.18 |   5.43 | 9.15 |     💾 |  12.2 |
|  262144 | 14.73 |  14.3 |   6.57 | 9.17 |     💾 | 14.01 |
|  524288 | 26.95 | 15.12 |  12.22 | 9.17 |     💾 | 17.57 |
| 1048576 | 50.85 | 25.94 |  12.22 | 9.17 |     💾 | 24.57 |
| 2097152 | 98.93 | 35.61 |  12.42 | 9.18 |     💾 | 38.62 |
| 4194304 |     ❌ | 51.25 |  12.43 | 9.18 |     💾 | 72.26 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/fib_peak_memory_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=0baaadadf2d5ecf57f95539d890c10a9" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/fib_peak_memory_vs_n.png" />

## Sha2

Benchmark Sha256 hash of `n` bytes. For Stone, the [cairo implementation of sha256](https://github.com/cartridge-gg/cairo-sha256) by cartridge was used for benchmarking and for other zkvms [sha2 Rust crate](https://crates.io/crates/sha2) was used for benchmarking.

### Prover Time (s)

|      n |  jolt |     sp1 |  openvm |      r0 |   stone |   stwo | sp1-precompile | r0-precompile | openvm-precompile |
| -----: | ----: | ------: | ------: | ------: | ------: | -----: | -------------: | ------------: | ----------------: |
|    256 | 1.657 |   12.71 |  28.943 |  11.196 |  10.835 | 17.978 |         34.019 |         8.316 |            44.301 |
|    512 | 1.711 |  13.184 |  29.561 |  11.306 |   19.88 | 15.051 |         33.991 |         11.33 |            43.728 |
|   1024 | 2.173 |  13.863 |  30.609 |  17.136 |  31.021 | 16.833 |          33.83 |        11.201 |            44.897 |
|   2048 | 3.324 |  15.021 |  34.184 |  28.934 |  31.294 | 17.726 |         34.531 |        17.174 |            44.683 |
|   4096 |     ❌ |   16.88 |   39.38 |  52.487 |  66.539 | 14.084 |         34.418 |        28.982 |            47.701 |
|   8192 |     ❌ |  24.037 |  50.539 |  86.688 | 116.467 | 14.979 |         35.564 |         52.48 |            48.995 |
|  16384 |     ❌ |  37.958 |  78.057 | 167.856 |      💾 | 21.402 |         38.267 |       110.887 |            52.865 |
|  32768 |     ❌ |  52.566 | 129.842 | 300.572 |      💾 | 16.555 |         46.209 |       184.873 |            60.148 |
|  65536 |     ❌ |  72.136 | 249.403 |  589.84 |      💾 | 18.384 |         60.138 |       357.716 |            79.957 |
| 131072 |     ❌ | 136.592 | 532.796 | 1172.21 |      💾 | 27.871 |          87.29 |       709.726 |           124.996 |
| 262144 |     ❌ |  257.02 | 916.603 | 2338.03 |      💾 | 27.362 |        121.022 |       1415.34 |           219.654 |
| 524288 |     ❌ | 513.726 | 1790.29 | 4673.32 |      💾 | 43.242 |        233.959 |       2825.46 |           393.678 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha2_prover_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=d76af17bfeb4ee3cf47d38dbe1cb135b" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha2_prover_time_vs_n.png" />

### Verifier Time (ms)

|      n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile |
| -----: | ---: | --: | -----: | -: | ----: | ---: | -------------: | ------------: | ----------------: |
|    256 | 50.0 | 108 |    141 | 10 | 428.0 |   10 |             83 |            22 |               142 |
|    512 | 49.0 | 113 |    144 | 20 | 418.0 |   11 |            106 |            23 |               141 |
|   1024 | 49.0 | 102 |    140 | 23 | 426.0 |   11 |             90 |            15 |               141 |
|   2048 | 75.0 |  97 |    140 | 22 | 440.0 |   11 |            109 |            22 |               142 |
|   4096 |    ❌ | 106 |    139 | 22 | 454.0 |   11 |             99 |            23 |               141 |
|   8192 |    ❌ | 109 |    141 | 22 | 525.0 |   11 |             87 |            22 |               142 |
|  16384 |    ❌ |  82 |    144 | 22 |    💾 |   42 |             92 |            23 |               142 |
|  32768 |    ❌ |  94 |    140 | 23 |    💾 |   49 |            102 |            15 |               142 |
|  65536 |    ❌ |  83 |    141 | 23 |    💾 |  143 |             95 |            23 |               141 |
| 131072 |    ❌ |  83 |     57 | 24 |    💾 |  441 |             83 |            24 |               141 |
| 262144 |    ❌ |  83 |     56 | 24 |    💾 |  236 |             83 |            23 |               142 |
| 524288 |    ❌ |  83 |     56 | 23 |    💾 |   12 |             82 |            24 |               141 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha2_verifier_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=3d464d361a76358a65e86bf00d6cb1fd" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha2_verifier_time_vs_n.png" />

### Proof Size (KB)

|      n |    jolt |     sp1 |  openvm |      r0 |   stone |    stwo | sp1-precompile | r0-precompile | openvm-precompile |
| -----: | ------: | ------: | ------: | ------: | ------: | ------: | -------------: | ------------: | ----------------: |
|    256 | 172.143 | 1315.56 | 1708.31 | 223.482 | 104.104 | 986.394 |        1315.56 |       223.482 |           1784.35 |
|    512 | 172.143 | 1315.56 | 1708.31 | 223.482 | 114.152 | 1000.61 |        1315.56 |       223.482 |           1784.35 |
|   1024 | 181.495 | 1315.56 | 1708.31 | 223.482 | 117.224 | 1011.16 |        1315.56 |       223.482 |           1784.35 |
|   2048 | 191.263 | 1315.56 | 1708.31 | 223.482 |  120.04 | 1011.71 |        1315.56 |       223.482 |           1784.35 |
|   4096 |       ❌ | 1315.56 | 1708.31 | 223.482 | 126.632 | 1007.77 |        1315.56 |       223.482 |           1784.35 |
|   8192 |       ❌ | 1315.56 | 1708.31 | 223.482 | 130.824 | 1013.42 |        1315.56 |       223.482 |           1784.35 |
|  16384 |       ❌ | 1315.56 | 1708.31 | 223.482 |      💾 | 1005.31 |        1315.56 |       223.482 |           1784.35 |
|  32768 |       ❌ | 1315.56 | 1708.31 | 223.482 |      💾 | 1018.49 |        1315.56 |       223.482 |           1784.35 |
|  65536 |       ❌ | 1315.56 | 1708.31 | 223.482 |      💾 | 1017.72 |        1315.56 |       223.482 |           1784.35 |
| 131072 |       ❌ | 1315.56 | 852.937 | 223.482 |      💾 | 1037.15 |        1315.56 |       223.482 |           1784.35 |
| 262144 |       ❌ | 1315.56 | 852.937 | 223.482 |      💾 | 1045.93 |        1315.56 |       223.482 |           1784.35 |
| 524288 |       ❌ | 1315.56 | 816.649 | 223.482 |      💾 | 1092.14 |        1315.56 |       223.482 |           1784.35 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha2_proof_size_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=fde7d53297a6e9991d114913df6ebb91" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha2_proof_size_vs_n.png" />

### Cycle Count

|      n |    jolt |      sp1 |       r0 |   stone |     stwo | sp1-precompile | r0-precompile |
| -----: | ------: | -------: | -------: | ------: | -------: | -------------: | ------------: |
|    256 | 35325.0 |    33911 |    51280 | 14791.0 |   131071 |          11492 |         31643 |
|    512 | 60893.0 |    52743 |    90848 | 29233.0 |   131071 |          15820 |         55467 |
|   1024 |  112029 |    90407 |   169984 | 46295.0 |   131071 |          24476 |        103133 |
|   2048 |  214301 |   165735 |   328256 | 80419.0 |   131071 |          41788 |        198463 |
|   4096 |       ❌ |   316391 |   644800 |  160489 |   262143 |          76412 |        389106 |
|   8192 |       ❌ |   617703 |  1277888 |  308807 |   524287 |         145660 |        770392 |
|  16384 |       ❌ |  1220327 |  2544064 |      💾 |  1048575 |         284156 |       1532981 |
|  32768 |       ❌ |  2425575 |  5076416 |      💾 |  2097151 |         561148 |       3058159 |
|  65536 |       ❌ |  4836071 | 10141120 |      💾 |  4194303 |        1115132 |       6108532 |
| 131072 |       ❌ |  9657063 | 20270528 |      💾 |  8388607 |        2223100 |      12209241 |
| 262144 |       ❌ | 19299047 | 40529344 |      💾 | 16777215 |        4439036 |      24410676 |
| 524288 |       ❌ | 38583015 | 81046976 |      💾 | 33554431 |        8870908 |      48813546 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha2_cycle_count_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=751338b8d23acdde28e44739b1854435" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha2_cycle_count_vs_n.png" />

### Peak Memory (GB)

|      n | jolt |   sp1 | openvm |   r0 |  stone |  stwo | sp1-precompile | r0-precompile | openvm-precompile |
| -----: | ---: | ----: | -----: | ---: | -----: | ----: | -------------: | ------------: | ----------------: |
|    256 | 5.09 |  4.29 |   5.45 | 1.43 |   9.63 | 10.79 |           7.84 |          1.43 |              5.44 |
|    512 |  4.9 |  4.42 |   5.44 | 1.42 |   18.9 | 10.82 |           8.18 |          1.42 |              5.45 |
|   1024 |  4.9 |  4.54 |   5.44 |  2.3 |  35.74 | 10.86 |           8.01 |          1.42 |              5.44 |
|   2048 | 4.91 |  5.02 |   5.44 | 4.58 |  35.73 | 10.87 |            8.1 |           2.3 |              5.44 |
|   4096 |    ❌ |  6.28 |   5.44 | 9.15 |  71.46 | 11.03 |           8.29 |          4.59 |              5.44 |
|   8192 |    ❌ |   8.6 |   5.44 | 9.17 | 142.68 | 11.34 |           8.53 |          9.16 |              5.44 |
|  16384 |    ❌ | 13.32 |   5.44 | 9.18 |     💾 | 11.94 |           8.79 |          9.17 |              5.44 |
|  32768 |    ❌ | 15.31 |   8.78 | 9.18 |     💾 | 13.48 |           8.63 |          9.18 |              5.44 |
|  65536 |    ❌ | 29.19 |  16.64 | 9.18 |     💾 | 16.52 |           12.9 |          9.18 |              5.44 |
| 131072 |    ❌ |  35.4 |   21.6 |  9.2 |     💾 |  22.5 |          21.26 |          9.19 |              6.89 |
| 262144 |    ❌ | 45.34 |  22.77 | 9.21 |     💾 | 34.52 |          34.15 |          9.21 |             12.86 |
| 524288 |    ❌ | 54.88 |  25.59 | 9.25 |     💾 | 63.89 |          49.57 |          9.23 |             24.78 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha2_peak_memory_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=c73bf42ac0ea1f7b4688d848d1b1924c" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha2_peak_memory_vs_n.png" />

## Sha2-Chain

Benchmark Sha256 hash of 32 bytes for `n` iteration.

### Prover Time (s)

|     n |   jolt |     sp1 |  openvm |      r0 |  stone |   stwo | sp1-precompile | r0-precompile | openvm-precompile |
| ----: | -----: | ------: | ------: | ------: | -----: | -----: | -------------: | ------------: | ----------------: |
|     8 |  2.164 |  12.798 |  29.444 |  11.303 | 11.083 | 11.488 |         34.606 |         6.862 |            43.511 |
|    16 |  2.973 |  13.875 |  30.349 |  11.252 | 11.115 | 18.583 |         34.339 |         8.352 |            44.295 |
|    32 |  4.912 |   14.62 |  33.814 |  17.156 | 11.991 | 11.938 |         34.203 |         8.305 |            43.893 |
|    64 |  8.285 |  17.617 |  38.294 |  28.948 | 10.631 | 14.158 |         33.862 |        11.289 |            44.197 |
|   128 | 14.469 |  24.728 |  49.582 |  52.457 | 19.206 | 10.335 |         35.134 |        11.315 |            45.006 |
|   256 | 25.909 |  37.471 |  73.574 |  74.818 | 26.184 | 14.057 |         36.234 |        17.422 |            42.793 |
|   512 | 50.064 |  52.895 | 126.086 | 144.234 | 56.529 | 22.012 |         40.643 |        29.057 |            46.573 |
|  1024 | 96.901 |  71.752 | 231.888 | 285.012 | 95.878 | 20.846 |          50.02 |        52.522 |            52.862 |
|  2048 |      ❌ | 132.275 | 516.789 | 574.819 |     💾 | 14.061 |         77.808 |       110.071 |            61.761 |
|  4096 |      ❌ | 227.325 | 905.706 | 1110.77 |     💾 | 17.799 |        103.011 |       191.208 |            81.617 |
|  8192 |      ❌ | 444.028 | 1814.44 | 2210.89 |     💾 | 18.607 |        193.572 |       365.446 |            122.31 |
| 16384 |      ❌ | 872.638 | 3596.93 | 4404.24 |     💾 | 20.569 |         319.33 |       723.963 |            212.16 |
| 32768 |      ❌ | 1698.85 | 7067.26 | 8791.74 |     💾 | 25.041 |        628.712 |       1443.04 |            388.56 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha2-chain_prover_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=a96d2c21ec52941417a151f023435fef" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha2-chain_prover_time_vs_n.png" />

### Verifier Time (ms)

|     n |  jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile |
| ----: | ----: | --: | -----: | -: | ----: | ---: | -------------: | ------------: | ----------------: |
|     8 |  49.0 |  82 |    140 | 22 | 432.0 |   10 |             83 |            23 |               141 |
|    16 |  55.0 | 101 |    140 | 23 | 398.0 |   10 |             93 |            20 |               142 |
|    32 |  86.0 | 108 |    140 | 22 | 402.0 |   10 |             94 |            21 |               141 |
|    64 | 102.0 |  88 |    140 | 23 | 375.0 |   10 |             87 |            22 |               141 |
|   128 |  78.0 | 108 |    141 | 23 | 413.0 |   10 |             84 |            21 |               141 |
|   256 |  60.0 |  83 |    139 | 22 | 422.0 |   11 |             83 |            23 |               141 |
|   512 |  60.0 |  84 |    140 | 22 | 420.0 |   37 |             83 |            22 |               142 |
|  1024 | 103.0 |  83 |    139 | 23 | 456.0 |   41 |             83 |            22 |               141 |
|  2048 |     ❌ |  83 |     57 | 23 |    💾 |   40 |             83 |            10 |               141 |
|  4096 |     ❌ |  86 |     56 | 22 |    💾 |  119 |             83 |            23 |               141 |
|  8192 |     ❌ |  83 |     56 | 22 |    💾 |  116 |             83 |            10 |               142 |
| 16384 |     ❌ |  84 |     56 | 24 |    💾 |  182 |             86 |            23 |               141 |
| 32768 |     ❌ |  83 |     56 | 24 |    💾 |  262 |             83 |            23 |               141 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha2-chain_verifier_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=d3d2018538aea036a786c9b2c94a577f" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha2-chain_verifier_time_vs_n.png" />

### Proof Size (KB)

|     n |    jolt |     sp1 |  openvm |      r0 |   stone |    stwo | sp1-precompile | r0-precompile | openvm-precompile |
| ----: | ------: | ------: | ------: | ------: | ------: | ------: | -------------: | ------------: | ----------------: |
|     8 | 181.495 | 1315.56 | 1708.31 | 223.482 | 109.544 | 952.094 |        1315.56 |       223.482 |           1784.35 |
|    16 | 191.263 | 1315.56 | 1708.31 | 223.482 | 106.728 | 971.154 |        1315.56 |       223.482 |           1784.35 |
|    32 | 201.447 | 1315.56 | 1708.31 | 223.482 | 108.776 | 955.554 |        1315.56 |       223.482 |           1784.35 |
|    64 | 212.047 | 1315.56 | 1708.31 | 223.482 | 106.568 | 962.798 |        1315.56 |       223.482 |           1784.35 |
|   128 | 223.063 | 1315.56 | 1708.31 | 223.482 |  112.36 | 946.158 |        1315.56 |       223.482 |           1784.35 |
|   256 | 234.495 | 1315.56 | 1708.31 | 223.482 | 117.992 | 969.698 |        1315.56 |       223.482 |           1784.35 |
|   512 | 246.343 | 1315.56 | 1708.31 | 223.482 | 124.168 | 947.738 |        1315.56 |       223.482 |           1784.35 |
|  1024 | 258.607 | 1315.56 | 1708.31 | 223.482 | 129.512 | 948.874 |        1315.56 |       223.482 |           1784.35 |
|  2048 |       ❌ | 1315.56 | 852.937 | 223.482 |      💾 | 959.414 |        1315.56 |       223.482 |           1784.35 |
|  4096 |       ❌ | 1315.56 | 852.937 | 223.482 |      💾 | 966.074 |        1315.56 |       223.482 |           1784.35 |
|  8192 |       ❌ | 1315.56 | 816.649 | 223.482 |      💾 | 976.142 |        1315.56 |       223.482 |           1784.35 |
| 16384 |       ❌ | 1315.56 | 816.649 | 223.482 |      💾 | 986.186 |        1315.56 |       223.482 |           1784.35 |
| 32768 |       ❌ | 1315.56 | 852.937 | 223.482 |      💾 | 1001.51 |        1315.56 |       223.482 |           1784.35 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha2-chain_proof_size_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=61690ff88273b0fe970c56d9624d00db" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha2-chain_proof_size_vs_n.png" />

### Cycle Count

|     n |    jolt |       sp1 |        r0 |   stone |     stwo | sp1-precompile | r0-precompile |
| ----: | ------: | --------: | --------: | ------: | -------: | -------------: | ------------: |
|     8 | 69290.0 |     48118 |     45952 |  3008.0 |    65535 |          13495 |         14624 |
|    16 |  136282 |     85686 |     83432 |  5872.0 |    65535 |          20287 |         20776 |
|    32 |  270266 |    160822 |    158392 | 11600.0 |    65535 |          33871 |         33080 |
|    64 |  538234 |    311094 |    308312 | 23056.0 |    65535 |          61039 |         57688 |
|   128 | 1074187 |    611638 |    608152 | 45968.0 |    65535 |         115375 |        106904 |
|   256 | 2146059 |   1212726 |   1207832 | 91792.0 |   131071 |         224047 |        205336 |
|   512 | 4289803 |   2414902 |   2407192 |  183440 |   262143 |         441391 |        402200 |
|  1024 | 8577291 |   4819254 |   4805912 |  366736 |   524287 |         876079 |        795928 |
|  2048 |       ❌ |   9627958 |   9603352 |      💾 |  1048575 |        1745455 |       1583384 |
|  4096 |       ❌ |  19245366 |  19198232 |      💾 |  2097151 |        3484207 |       3158296 |
|  8192 |       ❌ |  38480182 |  38387992 |      💾 |  4194303 |        6961711 |       6308120 |
| 16384 |       ❌ |  76949814 |  76767512 |      💾 |  8388607 |       13916719 |      12607768 |
| 32768 |       ❌ | 153889078 | 153526552 |      💾 | 16777215 |       27826735 |      25207064 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha2-chain_cycle_count_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=fbd376d54e8bdfd5ba8b7479de0740d8" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha2-chain_cycle_count_vs_n.png" />

### Peak Memory (GB)

|     n |  jolt |   sp1 | openvm |   r0 |  stone |  stwo | sp1-precompile | r0-precompile | openvm-precompile |
| ----: | ----: | ----: | -----: | ---: | -----: | ----: | -------------: | ------------: | ----------------: |
|     8 |   5.1 |  4.31 |   5.44 | 1.42 |    9.1 | 10.74 |           7.81 |          1.44 |              5.44 |
|    16 |  4.91 |  4.54 |   5.44 | 1.42 |   9.04 | 10.74 |           8.04 |          1.43 |              5.44 |
|    32 |  5.92 |  4.98 |   5.44 |  2.3 |   9.04 | 10.75 |            8.5 |          1.43 |              5.44 |
|    64 |  8.69 |  6.19 |   5.44 | 4.58 |   9.05 | 10.77 |           8.05 |          1.42 |              5.44 |
|   128 | 14.39 |  8.81 |   5.44 | 9.14 |  17.87 | 10.78 |           8.29 |          1.42 |              5.44 |
|   256 | 26.36 | 13.27 |   5.44 | 9.17 |  29.66 | 10.83 |           8.52 |           2.3 |              5.44 |
|   512 | 48.32 |  14.7 |   8.57 | 9.17 |  59.33 | 10.95 |           8.63 |          4.59 |              5.44 |
|  1024 | 93.03 |  27.2 |  16.24 | 9.17 | 118.62 | 11.18 |          11.08 |          9.15 |              5.44 |
|  2048 |     ❌ |  40.4 |  20.59 | 9.18 |     💾 | 11.64 |          18.61 |          9.17 |              5.44 |
|  4096 |     ❌ | 44.04 |   20.6 | 9.19 |     💾 | 12.88 |          35.18 |          9.17 |              5.44 |
|  8192 |     ❌ | 55.14 |  20.62 |  9.2 |     💾 | 15.31 |           53.3 |          9.17 |              6.64 |
| 16384 |     ❌ | 58.47 |  20.66 |  9.2 |     💾 | 20.08 |          52.23 |          9.18 |             12.34 |
| 32768 |     ❌ | 60.22 |   20.8 | 9.27 |     💾 | 29.71 |          63.03 |          9.18 |             23.74 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha2-chain_peak_memory_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=7f21b799be4f2f42f1a1c6ae89467ce8" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha2-chain_peak_memory_vs_n.png" />

## Sha3

Benchmark Keccak256 hash of `n` bytes. For Stone, the implementation of Keccak256 from stdlib as well as builtin was benchmarked.

### Prover Time (s)

|      n |  jolt |     sp1 |  openvm |      r0 |   stone |    stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-precompile |
| -----: | ----: | ------: | ------: | ------: | ------: | ------: | -------------: | ------------: | ----------------: | ---------------: |
|    256 | 1.719 |  13.328 |  31.471 |  11.348 |  20.266 |  19.743 |         60.343 |          33.9 |            57.925 |           18.361 |
|    512 | 2.109 |  13.627 |  32.773 |  17.205 |  30.972 |  10.897 |         60.387 |        36.853 |            59.354 |            17.21 |
|   1024 |  3.15 |  15.275 |  34.777 |  17.179 |  65.925 |  23.258 |         60.193 |        42.789 |            58.748 |           18.037 |
|   2048 | 4.924 |  17.564 |  39.929 |  29.094 | 115.746 |  16.661 |         60.696 |        43.047 |            59.419 |            16.58 |
|   4096 |     ❌ |  24.096 |  45.142 |   52.54 |      💾 |  11.693 |         60.073 |        54.792 |            61.503 |           27.567 |
|   8192 |     ❌ |  37.851 |  60.927 |  110.08 |      💾 |  16.392 |         61.477 |        78.203 |            63.798 |           43.043 |
|  16384 |     ❌ |  50.158 |   94.74 | 225.876 |      💾 |  15.422 |         63.416 |       136.103 |            70.003 |           86.217 |
|  32768 |     ❌ |  66.943 | 165.212 | 422.471 |      💾 |  16.528 |         70.234 |       251.263 |             79.62 |          151.873 |
|  65536 |     ❌ | 109.098 | 308.693 | 841.045 |      💾 |  21.269 |         84.047 |       437.697 |           102.599 |               💾 |
| 131072 |     ❌ | 207.231 | 753.494 | 1671.26 |      💾 |  32.631 |         96.357 |       856.136 |           151.591 |               💾 |
| 262144 |     ❌ | 367.867 | 1526.34 |  3310.6 |      💾 |  59.078 |         133.31 |       1691.49 |           252.934 |               💾 |
| 524288 |     ❌ |  701.99 | 3048.73 | 6615.82 |      💾 | 106.153 |        191.352 |       3376.32 |           454.067 |               💾 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha3_prover_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=3572e3d8949071c1fd39b36796ab9d92" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha3_prover_time_vs_n.png" />

### Verifier Time (ms)

|      n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-precompile |
| -----: | ---: | --: | -----: | -: | ----: | ---: | -------------: | ------------: | ----------------: | ---------------: |
|    256 | 77.0 | 107 |    139 | 23 | 505.0 |   11 |            116 |            24 |               141 |            269.0 |
|    512 | 66.0 | 107 |    139 | 23 | 494.0 |   11 |            108 |            23 |               141 |            213.0 |
|   1024 | 58.0 |  84 |    139 | 22 | 495.0 |   11 |             88 |            23 |               141 |            244.0 |
|   2048 | 61.0 | 109 |    140 | 24 | 544.0 |   11 |            104 |            22 |               141 |            217.0 |
|   4096 |    ❌ | 110 |    140 | 22 |    💾 |   11 |            114 |            22 |               142 |            229.0 |
|   8192 |    ❌ | 108 |    139 | 23 |    💾 |   11 |             89 |            22 |               142 |            254.0 |
|  16384 |    ❌ |  83 |    140 | 24 |    💾 |   38 |             91 |            23 |               142 |            262.0 |
|  32768 |    ❌ |  83 |    140 | 24 |    💾 |  139 |             88 |            22 |               141 |            273.0 |
|  65536 |    ❌ |  82 |    140 | 24 |    💾 |  198 |            111 |            23 |               141 |               💾 |
| 131072 |    ❌ |  83 |     57 | 24 |    💾 |  201 |             88 |            22 |               141 |               💾 |
| 262144 |    ❌ |  83 |     56 | 23 |    💾 |  631 |             88 |            23 |               141 |               💾 |
| 524288 |    ❌ |  83 |     56 | 22 |    💾 |  191 |             88 |            23 |               141 |               💾 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha3_verifier_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=31ed10afad5b4b16a2d59059def4f408" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha3_verifier_time_vs_n.png" />

### Proof Size (KB)

|      n |    jolt |     sp1 |  openvm |      r0 |   stone |    stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-precompile |
| -----: | ------: | ------: | ------: | ------: | ------: | ------: | -------------: | ------------: | ----------------: | ---------------: |
|    256 | 170.823 | 1315.56 | 1708.31 | 223.482 |  113.64 | 1002.79 |        1477.23 |       223.482 |           1787.55 |          108.008 |
|    512 | 180.175 | 1315.56 | 1708.31 | 223.482 | 119.272 | 991.494 |        1477.23 |       223.482 |           1787.55 |          107.752 |
|   1024 | 189.943 | 1315.56 | 1708.31 | 223.482 |  126.92 | 1001.15 |        1477.23 |       223.482 |           1787.55 |          110.312 |
|   2048 | 200.127 | 1315.56 | 1708.31 | 223.482 | 130.536 |  1001.4 |        1477.23 |       223.482 |           1787.55 |          110.056 |
|   4096 |       ❌ | 1315.56 | 1708.31 | 223.482 |      💾 | 1016.95 |        1477.23 |       223.482 |           1787.55 |           114.92 |
|   8192 |       ❌ | 1315.56 | 1708.31 | 223.482 |      💾 | 1012.45 |        1477.23 |       223.482 |           1787.55 |          119.848 |
|  16384 |       ❌ | 1315.56 | 1708.31 | 223.482 |      💾 |  1027.4 |        1477.23 |       223.482 |           1787.55 |          126.088 |
|  32768 |       ❌ | 1315.56 | 1708.31 | 223.482 |      💾 | 1014.61 |        1477.23 |       223.482 |           1787.55 |          132.872 |
|  65536 |       ❌ | 1315.56 | 1708.31 | 223.482 |      💾 | 1037.78 |        1477.23 |       223.482 |           1787.55 |               💾 |
| 131072 |       ❌ | 1315.56 | 852.937 | 223.482 |      💾 | 1073.61 |        1477.23 |       223.482 |           1787.55 |               💾 |
| 262144 |       ❌ | 1315.56 | 816.649 | 223.482 |      💾 | 1154.34 |        1477.23 |       223.482 |           1787.55 |               💾 |
| 524288 |       ❌ | 1315.56 | 852.937 | 223.482 |      💾 | 1179.28 |        1477.23 |       223.482 |           1787.55 |               💾 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha3_proof_size_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=1314e7726f60cdb10048b83624e63f01" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha3_proof_size_vs_n.png" />

### Cycle Count

|      n |    jolt |      sp1 |        r0 |   stone |     stwo | sp1-precompile | r0-precompile | stone-precompile |
| -----: | ------: | -------: | --------: | ------: | -------: | -------------: | ------------: | ---------------: |
|    256 | 46732.0 |    47653 |     63651 | 19431.0 |   131071 |          15337 |         36390 |            998.0 |
|    512 | 90274.0 |    84714 |    121925 | 38611.0 |   131071 |          20082 |         63910 |           1762.0 |
|   1024 |  177358 |   158823 |    238473 | 59058.0 |   262143 |          29559 |        118950 |           3286.0 |
|   2048 |  351574 |   307036 |    471569 |  117859 |   524287 |          48508 |        229030 |           6334.0 |
|   4096 |       ❌ |   586913 |    921296 |      💾 |  1048575 |          86015 |        448102 |          12241.0 |
|   8192 |       ❌ |  1146654 |   1820750 |      💾 |  2097151 |         161016 |        886246 |          24055.0 |
|  16384 |       ❌ |  2266147 |   3619658 |      💾 |  2097151 |         311029 |       1762534 |          47683.0 |
|  32768 |       ❌ |  4505110 |   7217474 |      💾 |  4194303 |         611032 |       3515110 |          94930.0 |
|  65536 |       ❌ |  8999653 |  14429571 |      💾 |  8388607 |        1211497 |       7021350 |               💾 |
| 131072 |       ❌ | 17988714 |  28853765 |      💾 | 16777215 |        2412402 |      14038604 |               💾 |
| 262144 |       ❌ | 35966823 |  57702153 |      💾 | 33554431 |        4814199 |      28068169 |               💾 |
| 524288 |       ❌ | 71923036 | 115398929 |      💾 | 67108863 |        9617788 |      56132428 |               💾 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha3_cycle_count_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=6e347370228a5cd01c95ad2054921947" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha3_cycle_count_vs_n.png" />

### Peak Memory (GB)

|      n | jolt |   sp1 | openvm |   r0 |  stone |   stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-precompile |
| -----: | ---: | ----: | -----: | ---: | -----: | -----: | -------------: | ------------: | ----------------: | ---------------: |
|    256 | 5.43 |   4.5 |   5.44 | 1.42 |  19.02 |  10.82 |          11.56 |          3.46 |              5.49 |            11.13 |
|    512 |  4.9 |  4.54 |   5.44 |  2.3 |  35.74 |  10.85 |          11.59 |          3.45 |              5.49 |            11.07 |
|   1024 |  4.9 |  5.01 |   5.44 |  2.3 |  71.41 |  10.97 |          11.55 |          3.45 |              5.49 |            11.07 |
|   2048 |  5.8 |  6.16 |   5.44 | 4.59 | 142.54 |  11.21 |          11.62 |          3.45 |              5.49 |            11.07 |
|   4096 |    ❌ |   8.7 |   5.44 | 9.17 |     💾 |   11.9 |          11.79 |          4.59 |              5.49 |            21.97 |
|   8192 |    ❌ | 13.65 |   5.44 | 9.17 |     💾 |  13.19 |          11.96 |          9.16 |              5.49 |            43.91 |
|  16384 |    ❌ | 12.24 |   5.85 | 9.18 |     💾 |  13.73 |          11.87 |          9.17 |              5.49 |            87.17 |
|  32768 |    ❌ | 24.03 |  10.77 | 9.18 |     💾 |     17 |          12.23 |          9.17 |              5.48 |           174.24 |
|  65536 |    ❌ |    39 |  20.53 | 9.19 |     💾 |  23.54 |          12.22 |          9.18 |              5.49 |               💾 |
| 131072 |    ❌ | 52.23 |  21.23 |  9.2 |     💾 |  42.08 |          17.09 |          9.18 |              8.19 |               💾 |
| 262144 |    ❌ | 52.28 |  22.77 |  9.2 |     💾 |  78.97 |          27.25 |          9.21 |             15.42 |               💾 |
| 524288 |    ❌ | 57.67 |  22.93 | 9.27 |     💾 | 151.16 |          55.68 |          9.22 |             29.87 |               💾 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha3_peak_memory_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=88ee4e69417027d86aa0755d2c3ced5e" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha3_peak_memory_vs_n.png" />

## Sha3-Chain

Benchmark Keccak256 hash of 32 bytes for `n` iteration.

### Prover Time (s)

|     n |    jolt |     sp1 |  openvm |      r0 |  stone |   stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-precompile |
| ----: | ------: | ------: | ------: | ------: | -----: | -----: | -------------: | ------------: | ----------------: | ---------------: |
|     8 |   3.151 |  14.691 |  31.427 |    17.2 | 66.291 | 13.552 |         59.266 |        34.114 |            58.806 |           16.827 |
|    16 |   5.142 |  17.431 |  34.818 |  28.941 | 115.28 |  18.47 |         60.353 |        37.322 |            59.329 |           18.279 |
|    32 |    8.57 |  23.603 |  43.135 |  52.437 |     💾 | 13.475 |         60.409 |        36.973 |            58.913 |           27.208 |
|    64 |  15.082 |  37.422 |  57.017 |  74.883 |     💾 |  14.55 |         60.377 |        42.978 |            59.971 |           43.739 |
|   128 |   29.25 |  50.151 |  90.378 | 132.931 |     💾 | 18.699 |         59.433 |        54.814 |            61.487 |           85.956 |
|   256 |  55.496 |  66.364 | 156.377 | 261.039 |     💾 | 22.329 |         61.843 |        78.503 |            65.217 |          151.067 |
|   512 | 105.689 | 104.036 | 297.659 | 515.447 |     💾 | 29.078 |         65.634 |        92.151 |            72.255 |               💾 |
|  1024 |       ❌ | 192.377 | 715.326 | 1037.74 |     💾 |  52.14 |           73.4 |       176.441 |            88.201 |               💾 |
|  2048 |       ❌ | 357.885 | 1474.13 | 2034.16 |     💾 | 94.358 |         91.595 |       348.058 |           115.792 |               💾 |
|  4096 |       ❌ | 681.138 | 2909.76 | 4083.82 |     💾 |      ❌ |        109.247 |       665.897 |           171.808 |               💾 |
|  8192 |       ❌ | 1316.41 | 5795.09 | 8122.75 |     💾 |      ❌ |         183.78 |        1286.1 |           510.264 |               💾 |
| 16384 |       ❌ | 2597.86 | 11684.6 | 16241.2 |     💾 |      ❌ |        353.935 |       2565.25 |           870.635 |               💾 |
| 32768 |       ❌ | 5192.04 | 23068.5 | 32449.9 |     💾 |      ❌ |        657.383 |       5090.45 |           1712.06 |               💾 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha3-chain_prover_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=a6bf031c90e6f80054d7200adb14a161" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha3-chain_prover_time_vs_n.png" />

### Verifier Time (ms)

|     n |  jolt | sp1 | openvm | r0 | stone |  stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-precompile |
| ----: | ----: | --: | -----: | -: | ----: | ----: | -------------: | ------------: | ----------------: | ---------------: |
|     8 |  83.0 | 107 |    139 | 23 | 526.0 |  11.0 |            122 |            20 |               142 |            252.0 |
|    16 | 114.0 |  86 |    139 | 23 | 555.0 |  11.0 |            116 |            23 |               142 |            254.0 |
|    32 |  75.0 | 111 |    139 | 23 |    💾 |  11.0 |             88 |            23 |               142 |            256.0 |
|    64 |  79.0 | 102 |    139 | 23 |    💾 |  11.0 |            116 |            23 |               142 |            265.0 |
|   128 |  57.0 |  99 |    139 | 23 |    💾 |  11.0 |             99 |            22 |               141 |            270.0 |
|   256 |  64.0 |  83 |    139 | 22 |    💾 |  42.0 |             90 |            20 |               141 |            288.0 |
|   512 | 118.0 |  83 |    139 | 23 |    💾 |  44.0 |            103 |            23 |               141 |               💾 |
|  1024 |     ❌ |  83 |     56 | 23 |    💾 |  49.0 |            106 |            23 |               144 |               💾 |
|  2048 |     ❌ |  84 |     56 | 23 |    💾 | 572.0 |             88 |            24 |               142 |               💾 |
|  4096 |     ❌ |  83 |     56 | 23 |    💾 |     ❌ |             88 |            23 |               141 |               💾 |
|  8192 |     ❌ |  84 |     56 | 23 |    💾 |     ❌ |             87 |            22 |                56 |               💾 |
| 16384 |     ❌ |  83 |     55 | 20 |    💾 |     ❌ |             88 |            24 |                57 |               💾 |
| 32768 |     ❌ |  84 |     57 | 23 |    💾 |     ❌ |             88 |            22 |                55 |               💾 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha3-chain_verifier_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=44a742b80f220d808126fba211abfccd" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha3-chain_verifier_time_vs_n.png" />

### Proof Size (KB)

|     n |    jolt |     sp1 |  openvm |      r0 |   stone |     stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-precompile |
| ----: | ------: | ------: | ------: | ------: | ------: | -------: | -------------: | ------------: | ----------------: | ---------------: |
|     8 | 191.263 | 1315.56 | 1708.31 | 223.482 | 124.616 |  995.554 |        1477.23 |       223.482 |           1787.55 |            109.8 |
|    16 | 201.447 | 1315.56 | 1708.31 | 223.482 |  129.96 | 1006.302 |        1477.23 |       223.482 |           1787.55 |          108.264 |
|    32 | 212.047 | 1315.56 | 1708.31 | 223.482 |      💾 | 1028.558 |        1477.23 |       223.482 |           1787.55 |          115.944 |
|    64 | 223.063 | 1315.56 | 1708.31 | 223.482 |      💾 | 1023.458 |        1477.23 |       223.482 |           1787.55 |          122.856 |
|   128 | 234.495 | 1315.56 | 1708.31 | 223.482 |      💾 | 1032.058 |        1477.23 |       223.482 |           1787.55 |          123.304 |
|   256 | 246.343 | 1315.56 | 1708.31 | 223.482 |      💾 |  1031.81 |        1477.23 |       223.482 |           1787.55 |          131.944 |
|   512 | 258.607 | 1315.56 | 1708.31 | 223.482 |      💾 | 1084.746 |        1477.23 |       223.482 |           1787.55 |               💾 |
|  1024 |       ❌ | 1315.56 | 852.937 | 223.482 |      💾 | 1155.054 |        1477.23 |       223.482 |           1787.55 |               💾 |
|  2048 |       ❌ | 1315.56 | 816.649 | 223.482 |      💾 | 1182.062 |        1477.23 |       223.482 |           1787.55 |               💾 |
|  4096 |       ❌ | 1315.56 | 852.937 | 223.482 |      💾 |        ❌ |        1477.23 |       223.482 |           1787.55 |               💾 |
|  8192 |       ❌ | 1315.56 | 816.649 | 223.482 |      💾 |        ❌ |        1477.23 |       223.482 |           852.937 |               💾 |
| 16384 |       ❌ | 1315.56 | 816.649 | 223.482 |      💾 |        ❌ |        1477.23 |       223.482 |           852.937 |               💾 |
| 32768 |       ❌ | 1315.56 | 852.937 | 223.482 |      💾 |        ❌ |        1477.23 |       223.482 |           816.649 |               💾 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha3-chain_proof_size_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=bd10e81a3af21051745411bc9a0d220f" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha3-chain_proof_size_vs_n.png" />

### Cycle Count

|     n |     jolt |       sp1 |        r0 |   stone |     stwo | sp1-precompile | r0-precompile | stone-precompile |
| ----: | -------: | --------: | --------: | ------: | -------: | -------------: | ------------: | ---------------: |
|     8 |   203331 |    147841 |    147328 | 57648.0 |   262143 |          18577 |         27805 |           3480.0 |
|    16 |   404363 |    284353 |    286232 |  115185 |   524287 |          25825 |         43693 |           6904.0 |
|    32 |   806427 |    557377 |    564040 |      💾 |  1048575 |          40321 |         75469 |          13752.0 |
|    64 |  1610555 |   1103425 |   1119656 |      💾 |  2097151 |          69313 |        139021 |          27448.0 |
|   128 |  3218828 |   2195521 |   2230888 |      💾 |  4194303 |         127297 |        266125 |          54840.0 |
|   256 |  6435340 |   4379713 |   4453352 |      💾 |  8388607 |         243265 |        520333 |           109624 |
|   512 | 12868364 |   8748097 |   8898280 |      💾 | 16777215 |         475201 |       1028749 |               💾 |
|  1024 |        ❌ |  17484865 |  17788136 |      💾 | 33554431 |         939073 |       2050355 |               💾 |
|  2048 |        ❌ |  34958401 |  35567848 |      💾 | 67108863 |        1866817 |       4093575 |               💾 |
|  4096 |        ❌ |  69905473 |  71127272 |      💾 |        ❌ |        3722305 |       8174812 |               💾 |
|  8192 |        ❌ | 139799617 | 142246120 |      💾 |        ❌ |        7433281 |      16338156 |               💾 |
| 16384 |        ❌ | 279587905 | 284483816 |      💾 |        ❌ |       14855233 |      32669621 |               💾 |
| 32768 |        ❌ | 559164481 | 568959208 |      💾 |        ❌ |       29699137 |      65327886 |               💾 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha3-chain_cycle_count_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=efd02254a5f4f620662c42994164930e" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha3-chain_cycle_count_vs_n.png" />

### Peak Memory (GB)

|     n |  jolt |   sp1 | openvm |   r0 |  stone |   stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-precompile |
| ----: | ----: | ----: | -----: | ---: | -----: | -----: | -------------: | ------------: | ----------------: | ---------------: |
|     8 |  5.09 |  5.14 |   5.44 |  2.3 |  71.49 |  10.95 |          11.61 |          3.45 |              5.49 |            11.07 |
|    16 |  5.85 |  6.23 |   5.44 | 4.58 | 142.53 |  11.14 |          11.43 |          3.45 |              5.49 |            11.07 |
|    32 |  8.88 |  9.03 |   5.44 | 9.14 |     💾 |  11.83 |          11.95 |          3.45 |              5.49 |            21.98 |
|    64 | 14.89 | 13.13 |   5.44 | 9.17 |     💾 |   13.2 |           11.6 |          3.45 |              5.49 |            43.91 |
|   128 | 27.13 | 12.02 |    5.7 | 9.18 |     💾 |   15.6 |          11.49 |          4.57 |              5.49 |            87.26 |
|   256 | 51.24 | 21.98 |  10.48 | 9.18 |     💾 |  20.66 |          11.14 |          9.13 |              5.49 |           174.37 |
|   512 | 100.0 | 39.84 |  19.95 | 9.18 |     💾 |  36.36 |          11.92 |          9.16 |              5.49 |               💾 |
|  1024 |     ❌ | 41.18 |  19.95 | 9.19 |     💾 |  67.57 |          11.24 |          9.16 |              5.49 |               💾 |
|  2048 |     ❌ |  47.4 |  19.96 |  9.2 |     💾 | 128.39 |          14.17 |          9.16 |              6.28 |               💾 |
|  4096 |     ❌ | 59.51 |  20.31 | 9.22 |     💾 |      ❌ |           30.3 |          9.17 |             11.39 |               💾 |
|  8192 |     ❌ | 61.16 |   20.5 | 9.26 |     💾 |      ❌ |          53.85 |          9.18 |             20.72 |               💾 |
| 16384 |     ❌ | 61.43 |  20.75 | 9.34 |     💾 |      ❌ |          57.23 |           9.2 |              20.8 |               💾 |
| 32768 |     ❌ | 63.58 |  20.93 | 9.49 |     💾 |      ❌ |          63.67 |          9.22 |             20.87 |               💾 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/sha3-chain_peak_memory_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=91f392b1d4b09132757c966a72cbbd88" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/sha3-chain_peak_memory_vs_n.png" />

## BLAKE

Benchmark Blake2s256 hash of `n` bytes. For the **S-two** benchmarks, a dedicated opcode for BLAKE was used, as illustrated in [this Cairo source file](https://github.com/starkware-libs/cairo-lang/blob/ab8be40403a7634ba296c467b26b8bd945ba5cfa/src/starkware/cairo/common/cairo_blake2s/blake2s.cairo#L671). **SP1** and **R0** do not support precompiles for BLAKE.

### Prover Time (s)

|      n |     sp1 |      r0 | stwo-precompile |
| -----: | ------: | ------: | --------------: |
|   2048 |  14.272 |  28.817 |          35.206 |
|   4096 |  14.773 |   52.33 |          34.752 |
|   8192 |  17.678 |   65.67 |          30.911 |
|  16384 |  24.308 | 126.219 |          32.214 |
|  32768 |  37.485 | 240.843 |          30.324 |
|  65536 |  55.119 | 476.273 |          38.614 |
| 131072 | 101.786 | 947.306 |          35.269 |
| 262144 | 162.863 | 1888.15 |          33.434 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/blake_prover_time_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=18c5c24e6dbf9fe866b06a7cab97b1eb" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/blake_prover_time_vs_n.png" />

### Verifier Time (ms)

|      n | sp1 | r0 | stwo-precompile |
| -----: | --: | -: | --------------: |
|   2048 | 102 | 10 |              11 |
|   4096 | 105 | 23 |              11 |
|   8192 | 111 | 22 |              11 |
|  16384 |  99 | 24 |              11 |
|  32768 | 104 | 23 |              12 |
|  65536 |  81 | 22 |              12 |
| 131072 |  81 | 23 |              37 |
| 262144 |  81 | 22 |              48 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/blake_verifier_time_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=2cc47eb60d9c44d8bae331c3cc231373" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/blake_verifier_time_vs_n.png" />

### Proof Size (KB)

|      n |     sp1 |      r0 | stwo-precompile |
| -----: | ------: | ------: | --------------: |
|   2048 | 1315.56 | 223.482 |         1117.14 |
|   4096 | 1315.56 | 223.482 |         1138.83 |
|   8192 | 1315.56 | 223.482 |         1134.37 |
|  16384 | 1315.56 | 223.482 |         1121.81 |
|  32768 | 1315.56 | 223.482 |         1144.87 |
|  65536 | 1315.56 | 223.482 |         1158.19 |
| 131072 | 1315.56 | 223.482 |         1141.67 |
| 262144 | 1315.56 | 223.482 |         1148.66 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/blake_proof_size_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=b3cf12fd9b8b4705a9b32edab6987e43" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/blake_proof_size_vs_n.png" />

### Cycle Count

|      n |      sp1 |       r0 | stwo-precompile |
| -----: | -------: | -------: | --------------: |
|   2048 |   100997 |   264515 |           65535 |
|   4096 |   193061 |   521763 |           65535 |
|   8192 |   377189 |  1036259 |           65535 |
|  16384 |   745445 |  2065251 |           65535 |
|  32768 |  1481957 |  4123235 |          131071 |
|  65536 |  2954981 |  8239203 |          262143 |
| 131072 |  5901029 | 16471139 |          524287 |
| 262144 | 11793125 | 32935011 |         1048575 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/blake_cycle_count_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=3316ce9f76e587edc6eb93a20381f337" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/blake_cycle_count_vs_n.png" />

### Peak Memory (GB)

|      n |   sp1 |   r0 | stwo-precompile |
| -----: | ----: | ---: | --------------: |
|   2048 |  4.55 | 4.58 |           19.98 |
|   4096 |     5 | 9.14 |           19.94 |
|   8192 |  6.09 | 9.17 |           19.98 |
|  16384 |  8.83 | 9.18 |           20.02 |
|  32768 | 13.83 | 9.18 |           20.17 |
|  65536 | 16.59 | 9.18 |            20.5 |
| 131072 |    38 | 9.19 |           20.88 |
| 262144 | 45.31 | 9.19 |           21.97 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/blake_peak_memory_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=2fa0af585079702f2f152f82c8b8b5ec" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/blake_peak_memory_vs_n.png" />

## BLAKE-Chain

Benchmark Blake2s256 hash of 32 bytes for `n` iteration. For the **S-two** benchmarks, a dedicated opcode for BLAKE was used, as illustrated in [this Cairo source file](https://github.com/starkware-libs/cairo-lang/blob/ab8be40403a7634ba296c467b26b8bd945ba5cfa/src/starkware/cairo/common/cairo_blake2s/blake2s.cairo#L671). **SP1** and **R0** do not support precompiles for BLAKE.

### Prover Time (s)

|     n |     sp1 |      r0 | stwo-precompile |
| ----: | ------: | ------: | --------------: |
|   128 |  17.319 |   28.76 |          30.885 |
|   256 |  24.279 |  52.074 |          32.974 |
|   512 |    38.5 |  86.181 |           33.26 |
|  1024 |  53.129 | 166.706 |          30.723 |
|  2048 |  89.423 | 316.029 |          38.153 |
|  4096 | 145.299 | 628.118 |          31.717 |
|  8192 |  259.23 | 1260.14 |          37.422 |
| 16384 | 495.878 | 2521.17 |           35.82 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/blake-chain_prover_time_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=f08ac483e720b064d5af7fe9e4b89aea" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/blake-chain_prover_time_vs_n.png" />

### Verifier Time (ms)

|     n | sp1 | r0 | stwo-precompile |
| ----: | --: | -: | --------------: |
|   128 | 105 | 22 |              11 |
|   256 | 104 | 22 |              11 |
|   512 | 108 | 23 |              11 |
|  1024 |  84 | 23 |              11 |
|  2048 |  81 | 23 |              41 |
|  4096 |  85 | 23 |              40 |
|  8192 |  81 | 23 |              49 |
| 16384 |  81 | 22 |              39 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/blake-chain_verifier_time_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=7b241c88bab672de9df7b4d2635fd107" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/blake-chain_verifier_time_vs_n.png" />

### Proof Size (KB)

|     n |     sp1 |      r0 | stwo-precompile |
| ----: | ------: | ------: | --------------: |
|   128 | 1315.56 | 223.482 |         1119.07 |
|   256 | 1315.56 | 223.482 |         1121.09 |
|   512 | 1315.56 | 223.482 |         1128.54 |
|  1024 | 1315.56 | 223.482 |         1119.77 |
|  2048 | 1315.56 | 223.482 |         1127.81 |
|  4096 | 1315.56 | 223.482 |         1127.26 |
|  8192 | 1315.56 | 223.482 |            1134 |
| 16384 | 1315.56 | 223.482 |         1143.83 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/blake-chain_proof_size_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=2e0edb7efef4325e54a2ed0ea6a8a223" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/blake-chain_proof_size_vs_n.png" />

### Cycle Count

|     n |      sp1 |       r0 | stwo-precompile |
| ----: | -------: | -------: | --------------: |
|   128 |   376249 |   356507 |           65535 |
|   256 |   742841 |   702491 |           65535 |
|   512 |  1476025 |  1394459 |          131071 |
|  1024 |  2942393 |  2778395 |          262143 |
|  2048 |  5875129 |  5546267 |          524287 |
|  4096 | 11740601 | 11082011 |         1048575 |
|  8192 | 23471545 | 22153499 |         2097151 |
| 16384 | 46933433 | 44296475 |         4194303 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/blake-chain_cycle_count_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=5797de97eb588bfb3382403f31bb6ee6" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/blake-chain_cycle_count_vs_n.png" />

### Peak Memory (GB)

|     n |   sp1 |   r0 | stwo-precompile |
| ----: | ----: | ---: | --------------: |
|   128 |  6.16 | 4.58 |           19.99 |
|   256 |  9.12 | 9.15 |           20.01 |
|   512 | 13.17 | 9.17 |           20.13 |
|  1024 | 15.96 | 9.17 |           20.39 |
|  2048 | 32.88 | 9.17 |           20.72 |
|  4096 |  44.6 | 9.19 |           21.54 |
|  8192 | 50.57 | 9.19 |           23.31 |
| 16384 | 53.25 | 9.21 |           27.19 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/blake-chain_peak_memory_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=728c9d553265bb81abcc18b20a61aed4" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/blake-chain_peak_memory_vs_n.png" />

## Matrix Multiplication

Benchmark multiplication of two matrices of size n x n.

### Prover Time (s)

|   n |   jolt |     sp1 |  openvm |      r0 |  stone |   stwo |
| --: | -----: | ------: | ------: | ------: | -----: | -----: |
|   4 |  1.196 |  13.179 |  29.508 |   6.763 | 10.922 |  12.72 |
|   8 |  1.648 |  12.862 |  30.119 |    8.21 |  9.879 | 19.566 |
|  16 |  4.979 |  15.252 |  33.467 |  17.135 | 26.384 | 16.531 |
|  32 | 27.702 |  26.491 |  58.102 |  65.806 |     💾 | 14.655 |
|  64 |      ❌ | 135.352 | 292.125 | 480.724 |     💾 | 21.199 |
| 128 |      ❌ |  881.29 | 2671.68 | 3809.76 |     💾 | 76.061 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/mat-mul_prover_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=cf5b54f415c8fc2319b944e370debbd6" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/mat-mul_prover_time_vs_n.png" />

### Verifier Time (ms)

|   n | jolt | sp1 | openvm | r0 | stone | stwo |
| --: | ---: | --: | -----: | -: | ----: | ---: |
|   4 | 44.0 | 110 |    140 | 23 | 111.0 |   10 |
|   8 | 51.0 | 110 |    140 | 22 | 120.0 |   10 |
|  16 | 86.0 | 102 |    139 | 23 | 139.0 |   10 |
|  32 | 84.0 | 109 |    140 | 25 |    💾 |   18 |
|  64 |    ❌ |  85 |    140 | 22 |    💾 |   41 |
| 128 |    ❌ |  84 |     56 | 23 |    💾 |   45 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/mat-mul_verifier_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=d5702caf479503469ca29b6b68e82276" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/mat-mul_verifier_time_vs_n.png" />

### Proof Size (KB)

|   n |    jolt |     sp1 |  openvm |      r0 |   stone |    stwo |
| --: | ------: | ------: | ------: | ------: | ------: | ------: |
|   4 | 144.647 | 1315.53 | 1708.31 | 223.234 | 109.032 | 815.674 |
|   8 | 169.607 | 1315.53 | 1708.31 | 223.234 |  108.52 | 833.086 |
|  16 | 198.911 | 1315.53 | 1708.31 | 223.234 | 116.456 | 844.238 |
|  32 | 233.591 | 1315.53 | 1708.31 | 223.234 |      💾 | 844.914 |
|  64 |       ❌ | 1315.53 | 1708.31 | 223.234 |      💾 | 876.354 |
| 128 |       ❌ | 1315.53 | 852.937 | 223.234 |      💾 | 981.178 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/mat-mul_proof_size_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=767e2469d6f443405ba0765b3f64a9bf" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/mat-mul_proof_size_vs_n.png" />

### Cycle Count

|   n |    jolt |      sp1 |       r0 |   stone |     stwo |
| --: | ------: | -------: | -------: | ------: | -------: |
|   4 |  7181.0 |     8430 |     5820 |  2181.0 |    32767 |
|   8 | 42753.0 |    23951 |    21352 | 13521.0 |    32767 |
|  16 |  314782 |   139844 |   137280 | 94569.0 |   131071 |
|  32 | 2457710 |  1044394 |  1041904 |      💾 |  1048575 |
|  64 |       ❌ |  8211062 |  8208720 |      💾 |  8388607 |
| 128 |       ❌ | 65306638 | 65304592 |      💾 | 67108863 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/mat-mul_cycle_count_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=2ab22e88f83e77ea6711e61781a38586" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/mat-mul_cycle_count_vs_n.png" />

### Peak Memory (GB)

|   n |  jolt |   sp1 | openvm |   r0 | stone |  stwo |
| --: | ----: | ----: | -----: | ---: | ----: | ----: |
|   4 |  5.43 |  4.45 |   5.43 | 1.42 |  9.09 | 10.73 |
|   8 |  4.91 |  4.29 |   5.43 | 1.43 |  9.03 | 10.73 |
|  16 |   5.8 |  5.12 |   5.43 | 2.29 | 29.68 | 10.82 |
|  32 | 26.45 | 10.34 |   5.43 | 9.17 |    💾 | 11.61 |
|  64 |     ❌ | 39.28 |  19.69 | 9.17 |    💾 | 19.92 |
| 128 |     ❌ | 60.01 |  20.09 | 9.19 |    💾 | 101.6 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/mat-mul_peak_memory_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=2c2ab51212923eb630994ae1baf74a56" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/mat-mul_peak_memory_vs_n.png" />

## Elliptic Curve Addition

Benchmark n point doubling for secp256k1.

### Prover Time (s)

|     n |   jolt |     sp1 |  openvm |       r0 |   stone |   stwo |
| ----: | -----: | ------: | ------: | -------: | ------: | -----: |
|   256 |  50.41 |  70.731 | 158.631 |  283.941 |  18.869 | 11.993 |
|   512 | 96.814 |  116.11 | 292.691 |  531.309 |  30.529 | 19.268 |
|  1024 |      ❌ | 211.962 | 582.356 |  1037.16 |  65.693 | 15.356 |
|  2048 |      ❌ | 394.022 | 1048.01 | 2072.757 | 114.312 | 14.318 |
|  4096 |      ❌ | 741.169 | 2029.72 | 4079.796 |      💾 | 14.407 |
|  8192 |      ❌ | 1426.64 | 4046.32 | 8181.789 |      💾 | 16.635 |
| 16384 |      ❌ | 2844.32 | 7953.88 |        ❌ |      💾 | 24.382 |
| 32768 |      ❌ | 5628.39 | 15793.7 |        ❌ |      💾 | 28.304 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/ec_prover_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=ae86f1ffd0e018eda7afaf00b8d70ce1" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/ec_prover_time_vs_n.png" />

### Verifier Time (ms)

|     n | jolt | sp1 | openvm |   r0 | stone | stwo |
| ----: | ---: | --: | -----: | ---: | ----: | ---: |
|   256 | 67.0 |  83 |    140 | 22.0 | 188.0 |   10 |
|   512 | 60.0 |  83 |    140 | 23.0 | 181.0 |   10 |
|  1024 |    ❌ |  83 |     56 | 23.0 | 187.0 |   34 |
|  2048 |    ❌ |  83 |     56 | 25.0 | 238.0 |   39 |
|  4096 |    ❌ |  83 |     57 | 23.0 |    💾 |   41 |
|  8192 |    ❌ |  83 |     56 | 11.0 |    💾 |   36 |
| 16384 |    ❌ |  83 |     56 |    ❌ |    💾 |  130 |
| 32768 |    ❌ |  83 |     55 |    ❌ |    💾 |   15 |

<img src="https://mintcdn.com/starkware-9575960b/BUFxFaR8oUcVXr6h/learn/S-two-book/benchmarks/plots/ec_verifier_time_vs_n.png?fit=max&auto=format&n=BUFxFaR8oUcVXr6h&q=85&s=c6fbe1352cc4fe7cb6908641cb430982" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/ec_verifier_time_vs_n.png" />

### Proof Size (KB)

|     n |    jolt |     sp1 |  openvm |      r0 |   stone |    stwo |
| ----: | ------: | ------: | ------: | ------: | ------: | ------: |
|   256 | 249.399 | 1315.56 | 1708.31 | 223.482 | 111.592 |  918.41 |
|   512 | 261.663 | 1315.56 | 1708.31 | 223.482 |  120.04 | 897.182 |
|  1024 |       ❌ | 1315.56 | 852.937 | 223.482 | 127.784 |  889.49 |
|  2048 |       ❌ | 1315.56 | 852.937 | 223.482 | 131.976 |  896.15 |
|  4096 |       ❌ | 1315.56 | 816.649 | 223.482 |      💾 | 901.758 |
|  8192 |       ❌ | 1315.56 | 816.649 | 223.482 |      💾 | 910.154 |
| 16384 |       ❌ | 1315.56 | 852.937 |       ❌ |      💾 | 929.282 |
| 32768 |       ❌ | 1315.56 | 816.649 |       ❌ |      💾 | 931.042 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/ec_proof_size_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=fc5cbe1a5af019120844175d66d3f655" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/ec_proof_size_vs_n.png" />

### Cycle Count

|     n |    jolt |       sp1 |        r0 |   stone |    stwo |
| ----: | ------: | --------: | --------: | ------: | ------: |
|   256 | 4760760 |   4715656 |   4711913 | 59936.0 |  131071 |
|   512 | 9290168 |   9169544 |   9165801 |  119840 |  262143 |
|  1024 |       ❌ |  18077320 |  18073577 |  239648 |  262143 |
|  2048 |       ❌ |  35892872 |  35889129 |  479264 |  524287 |
|  4096 |       ❌ |  71523976 |  71520233 |      💾 | 1048575 |
|  8192 |       ❌ | 142786184 | 142782441 |      💾 | 2097151 |
| 16384 |       ❌ | 285310600 |         ❌ |      💾 | 4194303 |
| 32768 |       ❌ | 570359432 |         ❌ |      💾 | 8388607 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/ec_cycle_count_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=01258613e1533af305ee208c3cf5ae7a" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/ec_cycle_count_vs_n.png" />

### Peak Memory (GB)

|     n |  jolt |   sp1 | openvm |   r0 |  stone |  stwo |
| ----: | ----: | ----: | -----: | ---: | -----: | ----: |
|   256 | 48.62 |  23.6 |  10.37 | 9.18 |  17.93 |  10.9 |
|   512 |  93.9 | 47.38 |   19.8 | 9.19 |   35.7 | 11.08 |
|  1024 |     ❌ | 44.31 |  19.83 | 9.19 |  71.47 | 11.27 |
|  2048 |     ❌ | 55.82 |  19.84 | 9.19 | 142.68 | 11.81 |
|  4096 |     ❌ | 62.49 |  19.86 | 9.22 |     💾 | 13.22 |
|  8192 |     ❌ | 63.14 |  19.94 | 9.26 |     💾 | 16.01 |
| 16384 |     ❌ | 66.48 |  19.95 |    ❌ |     💾 | 21.62 |
| 32768 |     ❌ | 66.97 |  19.96 |    ❌ |     💾 | 32.64 |

<img src="https://mintcdn.com/starkware-9575960b/hiq-8JmrXhru12SS/learn/S-two-book/benchmarks/plots/ec_peak_memory_vs_n.png?fit=max&auto=format&n=hiq-8JmrXhru12SS&q=85&s=d919c7c31687a227519fcf5509da72cb" alt="" width="2400" height="1800" data-path="learn/S-two-book/benchmarks/plots/ec_peak_memory_vs_n.png" />