| zkVM / Proof System | Architecture | Frontend | Backend | Security Bits |
|---|---|---|---|---|
| RISC Zero | RISC-V | Rust | STARK-based | 96 bits |
| SP1 | RISC-V | Rust | STARK-based | 100 bits |
| OpenVM | RISC-V | Rust | STARK-based | 100 bits |
| Jolt | RISC-V | Rust | Lookup-based | - |
| Stone | Cairo VM | Cairo | STARK-based | 100 bits |
| Stwo | Cairo VM | Cairo | STARK-based | 96 bits |
dynamic
layout with these configurations.* in the tables.x in the tables.Ubuntu 24.04.2 LTS
Architecture: x86_64
CPU(s): 48
Model name: AMD EPYC-Milan Processor
Thread(s) per core: 2
Core(s) per socket: 24
Socket(s): 1
L3 cache: 32 MiB (1 instance)
MemTotal: 193203524 kB
MemFree: 175112252 kB
MemAvailable: 188428420 kB
Buffers: 265828 kB
Cached: 13927620 kB
SwapTotal: 0 kB
SwapFree: 0 kB
Benchmark n Fibonacci iterations.
| n | jolt | sp1 | openvm | r0 | stone | stwo |
|---|---|---|---|---|---|---|
| 4096 | 1.684 | 5.555 | 8.825 | 5.846 | 15.583 | 2.651 |
| 8192 | 2.499 | 6.772 | 10.733 | 11.349 | 22.654 | 2.562 |
| 16384 | 4.2 | 9.153 | 13.421 | 22.472 | 32.151 | 2.739 |
| 32768 | 7.829 | 14.421 | 19.739 | 45.13 | 63.677 | 2.925 |
| 65536 | 14.27 | 26.564 | 37.304 | 89.973 | 103.429 | 3.24 |
| 131072 | 26.79 | 29.536 | 69.569 | 141.097 | * | 3.463 |
| 262144 | 52.224 | 41.88 | 134.757 | 279.451 | * | 4.406 |
| 524288 | 101.165 | 73.689 | 142.485 | 559.176 | * | 6.311 |

| n | jolt | sp1 | openvm | r0 | stone | stwo |
|---|---|---|---|---|---|---|
| 4096 | 86 | 139 | 45 | 21 | 88.0 | 10 |
| 8192 | 66 | 139 | 45 | 20 | 98.0 | 9 |
| 16384 | 41 | 138 | 44 | 20 | 88.0 | 36 |
| 32768 | 83 | 142 | 44 | 20 | 65.0 | 34 |
| 65536 | 43 | 147 | 45 | 25 | 103.0 | 17 |
| 131072 | 56 | 341 | 46 | 48 | * | 10 |
| 262144 | 72 | 543 | 47 | 85 | * | 19 |
| 524288 | 80 | 906 | 87 | 160 | * | 141 |

| n | jolt | sp1 | openvm | r0 | stone | stwo |
|---|---|---|---|---|---|---|
| 4096 | 178.959 | 1799.8 | 770.545 | 244.218 | 106.568 | 711.1 |
| 8192 | 188.727 | 1799.8 | 770.545 | 255.93 | 111.848 | 693.132 |
| 16384 | 198.911 | 1799.8 | 770.545 | 268.154 | 119.528 | 711.368 |
| 32768 | 209.511 | 1875.83 | 770.545 | 281.402 | 126.472 | 720.612 |
| 65536 | 220.527 | 1955.06 | 803.841 | 562.652 | 130.952 | 719.156 |
| 131072 | 231.959 | 4815.17 | 838.481 | 1087.97 | * | 719.236 |
| 262144 | 243.807 | 8108.85 | 874.465 | 1943.43 | * | 707.068 |
| 524288 | 256.071 | 13282.3 | 1599.9 | 3643.15 | * | 723.176 |

| n | jolt | sp1 | r0 | stone | stwo |
|---|---|---|---|---|---|
| 4096 | 99479 | 102986 | 100582 | 24594.0 | 32767 |
| 8192 | 197719 | 201290 | 198886 | 49170.0 | 65535 |
| 16384 | 394406 | 397898 | 395494 | 98322.0 | 131071 |
| 32768 | 787622 | 791114 | 788710 | 196626 | 262143 |
| 65536 | 1574054 | 1577546 | 1575142 | 393234 | 524287 |
| 131072 | 3146918 | 3150410 | 3148006 | * | 1048575 |
| 262144 | 6292646 | 6296138 | 6293734 | * | 2097151 |
| 524288 | 12584102 | 12587594 | 12585190 | * | 4194303 |

| n | jolt | sp1 | openvm | r0 | stone | stwo |
|---|---|---|---|---|---|---|
| 4096 | 6.44 | 4.59 | 2.81 | 1.16 | 12.44 | 2.68 |
| 8192 | 4.9 | 5.08 | 1.36 | 2.3 | 15.22 | 2.61 |
| 16384 | 5.89 | 6.37 | 1.54 | 4.58 | 30.06 | 2.68 |
| 32768 | 8.92 | 8.97 | 1.92 | 9.15 | 59.79 | 2.81 |
| 65536 | 15.08 | 13.29 | 3.39 | 9.17 | 119.22 | 3.07 |
| 131072 | 27.63 | 21.56 | 6.19 | 9.17 | * | 3.61 |
| 262144 | 51.94 | 33.34 | 11.83 | 9.17 | * | 4.67 |
| 524288 | 102.01 | 41.06 | 11.83 | 9.18 | * | 7.1 |

Benchmark Sha256 hash of n bytes. For Stone, the cairo implementation
of sha256 by cartridge was used for benchmarking and for other zkvms
sha2 Rust crate was used for
benchmarking.
| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile |
|---|---|---|---|---|---|---|---|---|---|
| 256 | 1.182 | 5.141 | 7.939 | 5.804 | 9.439 | 2.595 | 3.479 | 3.088 | 7.512 |
| 512 | 1.241 | 5.004 | 8.536 | 5.91 | 19.059 | 2.642 | 3.491 | 5.899 | 7.626 |
| 1024 | 1.62 | 5.551 | 9.699 | 11.401 | 29.826 | 2.808 | 3.42 | 5.919 | 7.907 |
| 2048 | 2.444 | 6.463 | 12.55 | 22.586 | 30.702 | 2.829 | 3.541 | 11.432 | 8.386 |
| 4096 | x | 8.358 | 17.567 | 44.8 | 65.437 | 3.07 | 3.818 | 22.628 | 9.649 |
| 8192 | x | 13.682 | 28.314 | 67.908 | 117.676 | 3.275 | 4.912 | 44.997 | 11.681 |
| 16384 | x | 25.896 | 53.536 | 111.825 | * | 3.732 | 7.219 | 89.82 | 16.644 |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile |
|---|---|---|---|---|---|---|---|---|---|
| 256 | 37.0 | 141 | 49 | 21 | 328.0 | 12 | 384 | 19 | 68 |
| 512 | 37.0 | 141 | 50 | 21 | 308.0 | 12 | 385 | 21 | 69 |
| 1024 | 39.0 | 164 | 50 | 21 | 331.0 | 12 | 399 | 20 | 69 |
| 2048 | 68.0 | 162 | 50 | 11 | 322.0 | 12 | 384 | 21 | 68 |
| 4096 | x | 166 | 50 | 19 | 361.0 | 12 | 384 | 19 | 68 |
| 8192 | x | 170 | 49 | 24 | 429.0 | 11 | 388 | 20 | 69 |
| 16384 | x | 171 | 58 | 37 | * | 12 | 407 | 25 | 68 |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile |
|---|---|---|---|---|---|---|---|---|---|
| 256 | 172.143 | 1799.82 | 811.409 | 244.442 | 108.776 | 1017.86 | 5674.59 | 221.402 | 950.873 |
| 512 | 172.143 | 1799.82 | 811.409 | 244.442 | 113.128 | 1012.51 | 5674.59 | 244.442 | 950.873 |
| 1024 | 181.495 | 1799.82 | 811.409 | 256.154 | 118.76 | 1020.16 | 5674.59 | 244.442 | 950.873 |
| 2048 | 191.263 | 1799.82 | 811.409 | 268.378 | 118.248 | 1044.65 | 5674.59 | 256.154 | 950.873 |
| 4096 | x | 1799.82 | 811.409 | 281.626 | 124.296 | 1033.81 | 5674.59 | 268.378 | 950.873 |
| 8192 | x | 1875.85 | 811.409 | 549.628 | 129.512 | 1018.06 | 5674.59 | 281.626 | 950.873 |
| 16384 | x | 1955.08 | 844.705 | 830.878 | * | 1043.84 | 5674.59 | 562.876 | 950.873 |

| n | jolt | sp1 | r0 | stone | stwo | sp1-precompile | r0-precompile |
|---|---|---|---|---|---|---|---|
| 256 | 35403.0 | 33132 | 48398 | 14780.0 | 131071 | 11763 | 29627 |
| 512 | 60971.0 | 52288 | 87266 | 29222.0 | 131071 | 17115 | 53451 |
| 1024 | 112107 | 90600 | 165002 | 46284.0 | 131071 | 27819 | 101117 |
| 2048 | 214379 | 167224 | 320474 | 80408.0 | 131071 | 49227 | 196447 |
| 4096 | x | 320472 | 631418 | 160478 | 262143 | 92043 | 387090 |
| 8192 | x | 626968 | 1253306 | 308796 | 524287 | 177675 | 768376 |
| 16384 | x | 1239960 | 2497082 | * | 1048575 | 348939 | 1530965 |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile |
|---|---|---|---|---|---|---|---|---|---|
| 256 | 5.09 | 4.31 | 1.22 | 1.15 | 9.63 | 2.66 | 4.4 | 0.58 | 1.18 |
| 512 | 4.91 | 4.29 | 1.25 | 1.16 | 18.94 | 2.65 | 4.4 | 1.15 | 1.19 |
| 1024 | 4.9 | 4.57 | 1.33 | 2.3 | 35.74 | 2.7 | 4.42 | 1.16 | 1.21 |
| 2048 | 4.9 | 5.01 | 1.5 | 4.59 | 35.75 | 2.71 | 4.65 | 2.3 | 1.24 |
| 4096 | x | 6.09 | 1.82 | 9.15 | 71.57 | 2.87 | 4.73 | 4.59 | 1.32 |
| 8192 | x | 8.26 | 2.46 | 9.18 | 142.77 | 3.17 | 5.44 | 9.16 | 1.46 |
| 16384 | x | 12.96 | 4.41 | 9.18 | * | 3.76 | 6.89 | 9.18 | 1.76 |

Benchmark Sha256 hash of 32 bytes for n iteration.
| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile |
|---|---|---|---|---|---|---|---|---|---|
| 8 | 1.526 | 4.993 | 8.724 | 5.882 | 9.362 | 2.868 | 3.436 | 3.033 | 7.384 |
| 16 | 2.192 | 5.659 | 9.671 | 5.865 | 9.795 | 2.722 | 3.397 | 3.073 | 7.579 |
| 32 | 3.871 | 6.422 | 12.364 | 11.369 | 9.745 | 2.579 | 3.538 | 3.013 | 7.581 |
| 64 | 7.105 | 8.312 | 17.268 | 22.614 | 9.575 | 2.886 | 3.571 | 5.859 | 8.041 |
| 128 | 12.614 | 13.641 | 27.652 | 45.159 | 18.25 | 2.725 | 3.937 | 5.894 | 8.501 |
| 256 | 25.265 | 25.991 | 52.698 | 57.442 | 25.371 | 2.755 | 5.485 | 11.462 | 9.964 |
| 512 | 47.808 | 25.239 | 102.218 | 112.223 | 56.474 | 2.828 | 8.775 | 22.608 | 12.352 |
| 1024 | 92.338 | 36.896 | 203.878 | 225.054 | 94.504 | 3.083 | 15.985 | 45.164 | 17.401 |
| 2048 | x | 70.326 | 329.925 | 417.449 | * | 3.685 | 31.189 | 90.441 | 28.385 |
| 4096 | x | 124.759 | 656.719 | 832.116 | * | 4.458 | 54.085 | 146.118 | 49.37 |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile |
|---|---|---|---|---|---|---|---|---|---|
| 8 | 37.0 | 141 | 50 | 21 | 338.0 | 11 | 384 | 20 | 64 |
| 16 | 39.0 | 139 | 50 | 21 | 323.0 | 11 | 383 | 21 | 64 |
| 32 | 78.0 | 159 | 50 | 20 | 315.0 | 11 | 391 | 20 | 63 |
| 64 | 40.0 | 139 | 49 | 20 | 317.0 | 11 | 397 | 20 | 64 |
| 128 | 42.0 | 142 | 50 | 17 | 303.0 | 11 | 385 | 10 | 64 |
| 256 | 74.0 | 144 | 50 | 23 | 335.0 | 11 | 383 | 20 | 64 |
| 512 | 104.0 | 316 | 51 | 36 | 330.0 | 11 | 384 | 12 | 64 |
| 1024 | 58.0 | 448 | 52 | 65 | 347.0 | 11 | 409 | 19 | 63 |
| 2048 | x | 787 | 100 | 124 | * | 36 | 503 | 25 | 64 |
| 4096 | x | 1339 | 151 | 238 | * | 44 | 629 | 49 | 63 |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile |
|---|---|---|---|---|---|---|---|---|---|
| 8 | 181.495 | 1799.82 | 811.409 | 244.442 | 106.696 | 907.708 | 5674.59 | 221.402 | 911.697 |
| 16 | 191.263 | 1799.82 | 811.409 | 244.442 | 107.176 | 919.924 | 5674.59 | 221.402 | 911.697 |
| 32 | 201.447 | 1799.82 | 811.409 | 256.154 | 108.776 | 916.9 | 5674.59 | 221.402 | 911.697 |
| 64 | 212.047 | 1799.82 | 811.409 | 268.378 | 106.216 | 962.184 | 5674.59 | 244.442 | 911.697 |
| 128 | 223.063 | 1875.85 | 811.409 | 281.626 | 111.592 | 942.304 | 5674.59 | 244.442 | 911.697 |
| 256 | 234.495 | 1955.08 | 844.705 | 537.404 | 114.792 | 934.536 | 5674.59 | 256.154 | 911.697 |
| 512 | 246.343 | 4735.95 | 879.345 | 830.878 | 123.304 | 930.336 | 5674.59 | 268.378 | 911.697 |
| 1024 | 258.607 | 6539.66 | 915.329 | 1406.63 | 130.088 | 940.264 | 5750.62 | 281.626 | 911.697 |
| 2048 | x | 11633.8 | 1742.7 | 2787.4 | * | 941.284 | 7449.63 | 562.876 | 911.697 |
| 4096 | x | 20335.4 | 2675.33 | 5330.88 | * | 962.028 | 9452.77 | 1099.9 | 911.697 |

| n | jolt | sp1 | r0 | stone | stwo | sp1-precompile | r0-precompile |
|---|---|---|---|---|---|---|---|
| 8 | 69356.0 | 47296 | 44730 | 2997.0 | 65535 | 14248 | 14778 |
| 16 | 136412 | 83672 | 80858 | 5861.0 | 65535 | 21248 | 20954 |
| 32 | 270524 | 156424 | 153114 | 11589.0 | 65535 | 35248 | 33306 |
| 64 | 538748 | 301928 | 297626 | 23045.0 | 65535 | 63248 | 58010 |
| 128 | 1075213 | 592936 | 586650 | 45957.0 | 65535 | 119248 | 107418 |
| 256 | 2148109 | 1174952 | 1164698 | 91781.0 | 131071 | 231248 | 206234 |
| 512 | 4293901 | 2338984 | 2320794 | 183429 | 262143 | 455248 | 403866 |
| 1024 | 8585485 | 4667048 | 4632986 | 366725 | 524287 | 903248 | 799130 |
| 2048 | x | 9323176 | 9257370 | * | 1048575 | 1799248 | 1589658 |
| 4096 | x | 18635432 | 18506138 | * | 2097151 | 3591248 | 3170714 |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile |
|---|---|---|---|---|---|---|---|---|---|
| 8 | 5.09 | 4.31 | 1.25 | 1.15 | 9.1 | 2.57 | 4.39 | 0.58 | 1.18 |
| 16 | 4.9 | 4.57 | 1.32 | 1.16 | 9.04 | 2.58 | 4.46 | 0.58 | 1.18 |
| 32 | 5.79 | 5.03 | 1.49 | 2.3 | 9.04 | 2.58 | 4.56 | 0.58 | 1.19 |
| 64 | 8.67 | 6.12 | 1.79 | 4.58 | 9.04 | 2.6 | 4.56 | 1.15 | 1.21 |
| 128 | 14.46 | 8.13 | 2.4 | 9.14 | 17.88 | 2.61 | 5.06 | 1.16 | 1.25 |
| 256 | 26.21 | 13.35 | 4.3 | 9.17 | 29.73 | 2.67 | 6.2 | 2.3 | 1.33 |
| 512 | 48.55 | 14.86 | 8.13 | 9.17 | 59.33 | 2.79 | 7.42 | 4.59 | 1.49 |
| 1024 | 93.08 | 26.98 | 15.8 | 9.17 | 118.82 | 3.02 | 11.13 | 9.15 | 1.81 |
| 2048 | x | 44.18 | 20.15 | 9.18 | * | 3.48 | 19.53 | 9.17 | 2.47 |
| 4096 | x | 44.15 | 20.16 | 9.18 | * | 4.7 | 33.89 | 9.17 | 3.75 |

Benchmark Keccak256 hash of n bytes. For Stone, the
implementation of Keccak256 from stdlib as well as builtin was
benchmarked.
| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-builtin |
|---|---|---|---|---|---|---|---|---|---|---|
| 256 | 1.166 | 5.181 | 8.632 | 5.814 | 19.131 | 2.6 | 3.234 | 24.073 | 7.575 | 15.781 |
| 512 | 1.513 | 5.646 | 9.602 | 11.397 | 31.922 | 2.646 | 3.379 | 26.09 | 7.671 | 16.317 |
| 1024 | 2.402 | 6.661 | 12.433 | 11.413 | 67.444 | 2.817 | 3.237 | 32.07 | 8.146 | 16.891 |
| 2048 | 4.167 | 8.282 | 17.16 | 22.414 | 117.651 | 3.073 | 3.356 | 32.132 | 8.619 | 15.829 |
| 4096 | x | 13.843 | 21.932 | 44.79 | * | 3.682 | 3.555 | 43.796 | 9.856 | 25.902 |
| 8192 | x | 25.786 | 37.391 | 89.998 | * | 4.499 | 4.46 | 65.887 | 12.613 | 41.13 |
| 16384 | x | 23.059 | 70.308 | 179.33 | * | 4.809 | 6.791 | 111.091 | 18.053 | 83.958 |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-builtin |
|---|---|---|---|---|---|---|---|---|---|---|
| 256 | 51.0 | 140 | 53 | 20 | 401.0 | 11 | 531 | 20 | 155 | 220 |
| 512 | 43.0 | 139 | 52 | 20 | 400.0 | 11 | 531 | 20 | 156 | 201 |
| 1024 | 71.0 | 141 | 52 | 20 | 403.0 | 11 | 530 | 21 | 156 | 203 |
| 2048 | 55.0 | 166 | 53 | 12 | 439.0 | 11 | 531 | 21 | 156 | 199 |
| 4096 | x | 169 | 52 | 19 | * | 11 | 530 | 22 | 156 | 193 |
| 8192 | x | 162 | 52 | 25 | * | 12 | 531 | 22 | 156 | 208 |
| 16384 | x | 310 | 53 | 49 | * | 11 | 550 | 34 | 156 | 216 |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-builtin |
|---|---|---|---|---|---|---|---|---|---|---|
| 256 | 170.823 | 1799.82 | 832.297 | 244.442 | 116.2 | 974.964 | 5785.69 | 444.535 | 1556.5 | 108.008 |
| 512 | 180.175 | 1799.82 | 832.297 | 256.154 | 119.272 | 973.56 | 5785.69 | 467.575 | 1556.5 | 107.752 |
| 1024 | 189.943 | 1799.82 | 832.297 | 256.154 | 126.056 | 968.968 | 5785.69 | 479.287 | 1556.5 | 110.312 |
| 2048 | 200.127 | 1799.82 | 832.297 | 268.378 | 132.84 | 975.608 | 5785.69 | 479.287 | 1556.5 | 110.056 |
| 4096 | x | 1875.85 | 832.297 | 281.626 | * | 991.06 | 5785.69 | 491.511 | 1556.5 | 114.92 |
| 8192 | x | 1955.08 | 832.297 | 562.876 | * | 1008.38 | 5785.69 | 504.759 | 1556.5 | 119.848 |
| 16384 | x | 4659.92 | 865.593 | 1125.38 | * | 1003.53 | 5785.69 | 786.009 | 1556.5 | 126.088 |

| n | jolt | sp1 | r0 | stone | stwo | sp1-precompile | r0-precompile | stone-builtin |
|---|---|---|---|---|---|---|---|---|
| 256 | 46856.0 | 46003 | 63303 | 19420.0 | 131071 | 13765 | 36501 | 998 |
| 512 | 90422.0 | 83242 | 121245 | 38600.0 | 131071 | 18766 | 64021 | 1762 |
| 1024 | 177554 | 157707 | 237129 | 59047.0 | 262143 | 28755 | 119061 | 3286 |
| 2048 | 351866 | 306632 | 468897 | 117848 | 524287 | 48728 | 229141 | 6334 |
| 4096 | x | 587972 | 916134 | * | 1048575 | 88283 | 448213 | 12241 |
| 8192 | x | 1150639 | 1810608 | * | 2097151 | 167380 | 886357 | 24055 |
| 16384 | x | 2275984 | 3599556 | * | 2097151 | 325585 | 1762645 | 47683 |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-builtin |
|---|---|---|---|---|---|---|---|---|---|---|
| 256 | 5.09 | 4.3 | 1.25 | 1.15 | 19.03 | 2.65 | 4.12 | 3.45 | 1.23 | 11.07 |
| 512 | 4.9 | 4.59 | 1.32 | 2.3 | 35.78 | 2.69 | 4 | 3.45 | 1.24 | 11.07 |
| 1024 | 4.9 | 5.04 | 1.48 | 2.3 | 71.55 | 2.8 | 4.05 | 3.45 | 1.26 | 11.07 |
| 2048 | 5.82 | 6.15 | 1.78 | 4.59 | 142.74 | 3.03 | 4.16 | 3.45 | 1.31 | 11.07 |
| 4096 | x | 8.54 | 2.07 | 9.17 | * | 3.68 | 4.39 | 4.59 | 1.4 | 21.97 |
| 8192 | x | 12.9 | 2.94 | 9.17 | * | 4.92 | 4.7 | 9.16 | 1.58 | 43.9 |
| 16384 | x | 11.99 | 5.4 | 9.18 | * | 5.36 | 5.91 | 9.17 | 1.96 | 87.23 |

Benchmark Keccak256 hash of 32 bytes for n
iteration.
| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-builtin |
|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 2.481 | 6.533 | 10.602 | 11.387 | 67.345 | 2.846 | 3.365 | 23.298 | 7.626 | 15.826 |
| 16 | 3.99 | 8.432 | 14.158 | 22.633 | 118.349 | 3.133 | 3.35 | 26.373 | 7.68 | 15.734 |
| 32 | 7.522 | 13.789 | 21.259 | 45.054 | * | 3.626 | 3.326 | 27.072 | 8.236 | 25.707 |
| 64 | 13.651 | 25.796 | 35.504 | 50.801 | * | 4.585 | 3.392 | 31.977 | 9.126 | 41.801 |
| 128 | 26.783 | 22.814 | 68.366 | 102.685 | * | 7.879 | 3.766 | 42.572 | 10.783 | 83.978 |
| 256 | 50.965 | 30.845 | 136.042 | 202.335 | * | 14.139 | 5.169 | 65.942 | 14.402 | 146.807 |
| 512 | 100.764 | 53.405 | 267.191 | 405.196 | * | x | 8.137 | 68.989 | 21.452 | * |
| 1024 | x | 99.244 | 546.345 | 793.753 | * | x | 14.137 | 139.083 | 36.416 | * |
| 2048 | x | 196.044 | 1066.58 | 1576.58 | * | x | 27.559 | 280.385 | 64.867 | * |
| 4096 | x | 360.793 | 2124.01 | 3136.24 | * | x | 42.007 | 546.264 | 123.191 | * |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-builtin |
|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 57.0 | 139 | 49 | 11 | 414.0 | 11.0 | 544 | 20 | 153 | 209.0 |
| 16 | 45.0 | 160 | 49 | 21 | 443.0 | 11.0 | 549 | 20 | 155 | 209.0 |
| 32 | 75.0 | 142 | 49 | 19 | * | 12.0 | 531 | 20 | 154 | 213.0 |
| 64 | 63.0 | 145 | 50 | 23 | * | 12.0 | 530 | 21 | 153 | 218.0 |
| 128 | 93.0 | 314 | 50 | 36 | * | 12.0 | 531 | 21 | 153 | 224.0 |
| 256 | 47.0 | 442 | 51 | 63 | * | 13.0 | 532 | 23 | 155 | 246.0 |
| 512 | 91.0 | 645 | 52 | 112 | * | x | 536 | 32 | 154 | * |
| 1024 | x | 1100 | 102 | 224 | * | x | 562 | 44 | 153 | * |
| 2048 | x | 1990 | 203 | 432 | * | x | 563 | 69 | 153 | * |
| 4096 | x | 3904 | 403 | 883 | * | x | 684 | 120 | 154 | * |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-builtin |
|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 191.263 | 1799.82 | 811.409 | 256.154 | 124.904 | 993.304 | 5785.69 | 444.535 | 1538.61 | 109.8 |
| 16 | 201.447 | 1799.82 | 811.409 | 268.378 | 131.112 | 1017.196 | 5785.69 | 467.575 | 1538.61 | 108.264 |
| 32 | 212.047 | 1875.85 | 811.409 | 281.626 | * | 1034.616 | 5785.69 | 467.575 | 1538.61 | 115.944 |
| 64 | 223.063 | 1955.08 | 811.409 | 525.692 | * | 1042.476 | 5785.69 | 479.287 | 1538.61 | 122.856 |
| 128 | 234.495 | 4659.92 | 844.705 | 818.654 | * | 1091.6 | 5785.69 | 491.511 | 1538.61 | 123.304 |
| 256 | 246.343 | 6384.39 | 879.345 | 1393.38 | * | 1131.464 | 5785.69 | 504.759 | 1538.61 | 131.944 |
| 512 | 258.607 | 9833.33 | 915.329 | 2531.63 | * | x | 5785.69 | 725.785 | 1538.61 | * |
| 1024 | x | 16807.3 | 1813.32 | 5049.63 | * | x | 5861.73 | 1007.03 | 1538.61 | * |
| 2048 | x | 30682.3 | 3609.31 | 9844.13 | * | x | 5940.96 | 1569.54 | 1538.61 | * |
| 4096 | x | 59843 | 7201.28 | 19674.6 | * | x | 7716 | 2717.57 | 1538.61 | * |

| n | jolt | sp1 | r0 | stone | stwo | sp1-precompile | r0-precompile | stone-builtin |
|---|---|---|---|---|---|---|---|---|
| 8 | 203610 | 145819 | 145881 | 57637.0 | 262143 | 16867 | 27813 | 3480.0 |
| 16 | 404922 | 281235 | 283329 | 115174 | 524287 | 23331 | 43573 | 6904.0 |
| 32 | 807546 | 552067 | 558225 | * | 1048575 | 36259 | 75093 | 13752.0 |
| 64 | 1612794 | 1093731 | 1108017 | * | 2097151 | 62115 | 138133 | 27448.0 |
| 128 | 3223307 | 2177059 | 2207601 | * | 4194303 | 113827 | 264213 | 54840.0 |
| 256 | 6444299 | 4343715 | 4406769 | * | 8388607 | 217251 | 516373 | 109624 |
| 512 | 12886283 | 8677027 | 8805105 | * | x | 424099 | 1020693 | * |
| 1024 | x | 17343651 | 17601777 | * | x | 837795 | 2034194 | * |
| 2048 | x | 34676899 | 35195121 | * | x | 1665187 | 4061208 | * |
| 4096 | x | 69343395 | 70381809 | * | x | 3319971 | 8110124 | * |

| n | jolt | sp1 | openvm | r0 | stone | stwo | sp1-precompile | r0-precompile | openvm-precompile | stone-builtin |
|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 5.09 | 5.01 | 1.38 | 2.3 | 71.67 | 2.77 | 3.97 | 3.45 | 1.23 | 11.07 |
| 16 | 5.82 | 6.11 | 1.61 | 4.58 | 142.67 | 2.96 | 4.03 | 3.45 | 1.25 | 11.07 |
| 32 | 8.81 | 8.48 | 2.03 | 9.14 | * | 3.61 | 4.26 | 3.45 | 1.29 | 21.98 |
| 64 | 14.81 | 12.71 | 2.87 | 9.17 | * | 4.92 | 4.34 | 3.45 | 1.36 | 43.91 |
| 128 | 26.85 | 11.53 | 5.26 | 9.18 | * | 8.49 | 4.41 | 4.57 | 1.5 | 87.27 |
| 256 | 50.41 | 20.45 | 10.04 | 9.18 | * | 16.07 | 5.28 | 9.13 | 1.79 | 174.41 |
| 512 | 98.74 | 43.45 | 19.51 | 9.18 | * | x | 7.25 | 9.16 | 2.36 | * |
| 1024 | x | 45.25 | 19.52 | 9.19 | * | x | 8.86 | 9.16 | 3.5 | * |
| 2048 | x | 55.71 | 19.52 | 9.2 | * | x | 13.97 | 9.16 | 5.78 | * |
| 4096 | x | 55.17 | 19.95 | 9.22 | * | x | 33.84 | 9.17 | 10.78 | * |

Benchmark multiplication of two matrices of size n x n.
| n | jolt | sp1 | openvm | r0 | stone | stwo |
|---|---|---|---|---|---|---|
| 4 | 0.922 | 5.141 | 7.378 | 1.618 | 15.487 | 2.59 |
| 8 | 1.227 | 5.152 | 7.883 | 3.019 | 24.453 | 2.616 |
| 16 | 4.108 | 6.501 | 10.673 | 11.438 | 70.538 | 3.337 |
| 32 | 26.037 | 25.405 | 36.508 | 58.826 | * | 4.287 |
| 64 | x | 75.756 | 277.29 | 404.705 | * | 18.777 |

| n | jolt | sp1 | openvm | r0 | stone | stwo |
|---|---|---|---|---|---|---|
| 4 | 37.0 | 140 | 52 | 15 | 311.0 | 10 |
| 8 | 36.0 | 139 | 52 | 19 | 306.0 | 10 |
| 16 | 45.0 | 140 | 52 | 20 | 356.0 | 10 |
| 32 | 64.0 | 170 | 52 | 23 | * | 45 |
| 64 | x | 762 | 55 | 115 | * | 17 |

| n | jolt | sp1 | openvm | r0 | stone | stwo |
|---|---|---|---|---|---|---|
| 4 | 153.767 | 1799.79 | 829.609 | 209.506 | 104.68 | 817.692 |
| 8 | 170.823 | 1799.79 | 829.609 | 221.154 | 111.08 | 832.348 |
| 16 | 200.127 | 1799.79 | 829.609 | 255.906 | 124.04 | 850.28 |
| 32 | 234.807 | 1955.05 | 829.609 | 537.156 | * | 843.452 |
| 64 | x | 11713 | 933.529 | 2531.38 | * | 906.636 |

| n | jolt | sp1 | r0 | stone | stwo |
|---|---|---|---|---|---|
| 4 | 9107.0 | 8489 | 6033 | 6371.0 | 131071 |
| 8 | 56283.0 | 25474 | 23029 | 37627.0 | 131071 |
| 16 | 419008 | 152551 | 150141 | 259691 | 524287 |
| 32 | 3282080 | 1144749 | 1142413 | * | 2097151 |
| 64 | x | 9005881 | 9003693 | * | 16777215 |

| n | jolt | sp1 | openvm | r0 | stone | stwo |
|---|---|---|---|---|---|---|
| 4 | 5.09 | 4.26 | 1.16 | 0.3 | 9.56 | 2.59 |
| 8 | 4.9 | 4.33 | 1.2 | 0.58 | 18.22 | 2.61 |
| 16 | 5.87 | 5.07 | 1.39 | 2.29 | 71.91 | 2.94 |
| 32 | 27.18 | 13.11 | 2.94 | 9.17 | * | 4.47 |
| 64 | x | 38.98 | 20.11 | 9.17 | * | 21.94 |
