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Add host function calls for elliptic curve arithmetic to Polkadot #8

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Add host function calls for elliptic curve arithmetic to Polkadot #8

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update benchmark result table
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Achim Schneider committed Mar 14, 2023
commit 0a433984b02ddf0bf4252104ac9d32669cc6cb9e
92 changes: 47 additions & 45 deletions proposals/0000-arkworks-integration.md
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Expand Up @@ -34,56 +34,58 @@ Example implementations and benchmarks for the code can be found under: https://
The following comparison table of benchmarking results should justify the introduction of the new host functions:


| extrinsic | normal(µs)[^1] |optimized(µs)[^2]| dummy(µs)[^3] | wasm(µs)[^4] | native(µs)[^5] |
| ------------------------------------------- | --------------- | --------------- | --------------- | --------------- | --------------- |
| groth16_verification (bls12_381) | 26535.30 | 8244.31 | 5800.99 | 45070 | 4040 |
| bls12_381_pairing | 8257.70 | 1448.53 | 448.97 | 14140 | 1350 |
| bls12_381_msm_g1, 10 arguments | 16932.20 | 6869.28 | 87.63 | 24650 | 600.44 |
| bls12_381_msm_g1, 1000 arguments | 1313899.30 | 653168.11 | 6486.63 | 191000 | 11160 |
| bls12_381_msm_g2, 10 arguments | 115465.19 | 23583.63 | 10738.18 | 185240 | 1660 |
| bls12_381_msm_g2, 1000 arguments | 10668568.36 | 2458212.20 | 9896.67 | 14850000 | 33420 |
| bls12_381_mul_projective_g1[^*] | 8.00 | 21.96 | 12.13 | 19.85 | 0.45 |
| bls12_381_mul_affine_g1[^*] | 8.56 | 21.74 | 9.74 | 39.70 | 0.45 |
| bls12_381_mul_projective_g2[^*] | 16.88 | 27.87 | 18.22 | 37.74 | 1.18 |
| bls12_381_mul_affine_g2[^*] | 15.87 | 27.71 | 16.41 | 34.40 | 1.19 |
| bls12_377_pairing | 10963.00 | 1889.50 | 16.64 | 15160 | 1520 |
| bls12_377_msm_g1, 10 arguments | 20745.06 | 9270.83 | 51.48 | 28620 | 559.16 |
| bls12_377_msm_g1, 1000 arguments | 1287941.57 | 831275.64 | 4484.67 | 1920000 | 11160 |
| bls12_377_msm_g2, 10 arguments | 131852.78 | 34796.36 | 89.93 | 162870 | 2020 |
| bls12_377_msm_g2, 1000 arguments | 10196159.70 | 2781007.89 | 7948.46 | 14570000 | 40410 |
| bls12_377_mul_projective_g1[^*] | 6.87 | 17.36 | 11.42 | 19.38 | 0.44 |
| bls12_377_mul_affine_g1[^*] | 6.76 | 16.57 | 11.11 | 24.49 | 0.45 |
| bls12_377_mul_projective_g2[^*] | 13.80 | 22.24 | 16.64 | 28.26 | 1.42 |
| bls12_377_mul_affine_g2[^*] | 13.60 | 22.49 | 17.18 | 38.94 | 1.46 |
| bw6_761_pairing | 44374.64 | 6002.54 | 844.10 | 55440 | 6940 |
| bw6_761_msm_g1, 10 arguments | 155393.79 | 53231.17 | 161.28 | 206610 | 3490 |
| bw6_761_msm_g1, 1000 arguments | 13384952.55 | 5070669.53 | 13526.84 | 18010000 | 75270 |
| bw6_761_msm_g2, 10 arguments | 141484.94 | 39324.56 | 161.92 | 212280 | 3430 |
| bw6_761_msm_g2, 1000 arguments | 12528071.10 | 4732393.47 | 13633.30 | 18020000 | 75330 |
| bw6_761_mul_projective_g1[^*] | 17.05 | 53.83 | 21.99 | 34.82 | 1.79 |
| bw6_761_mul_affine_g1[^*] | 18.47 | 55.10 | 21.35 | 35.64 | 1.77 |
| bw6_761_mul_projective_g2[^*] | 17.45 | 53.65 | 21.64 | 35.42 | 1.78 |
| bw6_761_mul_affine_g2[^*] | 17.55 | 54.28 | 21.57 | 34.68 | 1.78 |
| ed_on_bls12_381_msm_sw, 10 arguments | 6663.28 | 3686.07 | 36.30 | 8610 | 376.61 |
| ed_on_bls12_381_msm_sw, 1000 arguments | 296140.25 | 215932.66 | 2465.60 | 430700 | 6010 |
| ed_on_bls12_381_mul_projective_sw[^*] | 5.57 | 10.08 | 6.69 | 24.89 | 0.36 |
| ed_on_bls12_381_mul_affine_sw[^*] | 5.51 | 10.12 | 6.17 | 36.63 | 0.36 |
| ed_on_bls12_381_msm_te, 10 arguments | 7813.27 | 3207.47 | 35.21 | 12470 | 560.82 |
| ed_on_bls12_381_msm_te, 1000 arguments | 334199.35 | 242277.02 | 2391.21 | 533490 | 7890 |
| ed_on_bls12_381_mul_projective_te[^*] | 9.13 | 10.60 | 7.69 | 22.37 | 0.83 |
| ed_on_bls12_381_mul_affine_te[^*] | 5.59 | 10.07 | 7.61 | 17.25 | 0.37 |
| ed_on_bls12_377_msm, 10 arguments | 7768.41 | 3192.99 | 43.24 | 10060 | 553.69 |
| ed_on_bls12_377_msm, 1000 arguments | 357890.37 | 267844.08 | 2465.60 | 537810 | 7680 |
| ed_on_bls12_377_mul_projective[^*] | 9.41 | 10.32 | 7.00 | 22.48 | 0.89 |
| ed_on_bls12_377_mul_affine[^*] | 8.84 | 442.80 | 8.47 | 22.34 | 0.86 |
| extrinsic | normal(µs)[^1] |optimized(µs)[^2]| speedup[^3] | dummy(µs)[^4] | wasm(µs)[^5] | native(µs)[^6] |
| --------------------------------------- | --------------- | --------------- | --------------- | --------------- | --------------- | --------------- |
| groth16_verification (bls12_381) | 26535.30 | 8244.31 |${\color{green}\bf 3.22 \boldsymbol{\times}}$| 5800.99 | 45070 | 4040 |
| bls12_381_pairing | 8257.70 | 1448.53 |${\color{green}\bf 5.70 \boldsymbol{\times}}$| 448.97 | 14140 | 1350 |
| bls12_381_msm_g1, 10 arguments | 16932.20 | 6869.28 |${\color{green}\bf 2.46 \boldsymbol{\times}}$| 87.63 | 24650 | 600.44 |
| bls12_381_msm_g1, 1000 arguments | 1313899.30 | 653168.11 |${\color{green}\bf 2.01 \boldsymbol{\times}}$| 6486.63 | 191000 | 11160 |
| bls12_381_msm_g2, 10 arguments | 115465.19 | 23583.63 |${\color{green}\bf 4.90 \boldsymbol{\times}}$| 10738.18 | 185240 | 1660 |
| bls12_381_msm_g2, 1000 arguments | 10668568.36 | 2458212.20 |${\color{green}\bf 4.34 \boldsymbol{\times}}$| 9896.67 | 14850000 | 33420 |
| bls12_381_mul_projective_g1[^*] | 8.00 | 21.96 | - | 12.13 | 19.85 | 0.45 |
| bls12_381_mul_affine_g1[^*] | 8.56 | 21.74 | - | 9.74 | 39.70 | 0.45 |
| bls12_381_mul_projective_g2[^*] | 16.88 | 27.87 | - | 18.22 | 37.74 | 1.18 |
| bls12_381_mul_affine_g2[^*] | 15.87 | 27.71 | - | 16.41 | 34.40 | 1.19 |
| bls12_377_pairing | 10963.00 | 1889.50 |${\color{green}\bf 10.57 \boldsymbol{\times}}$| 16.64 | 15160 | 1520 |
| bls12_377_msm_g1, 10 arguments | 20745.06 | 9270.83 |${\color{green}\bf 2.24 \boldsymbol{\times}}$| 51.48 | 28620 | 559.16 |
| bls12_377_msm_g1, 1000 arguments | 1287941.57 | 831275.64 |${\color{green}\bf 1.55 \boldsymbol{\times}}$| 4484.67 | 1920000 | 11160 |
| bls12_377_msm_g2, 10 arguments | 131852.78 | 34796.36 |${\color{green}\bf 3.79 \boldsymbol{\times}}$| 89.93 | 162870 | 2020 |
| bls12_377_msm_g2, 1000 arguments | 10196159.70 | 2781007.89 |${\color{green}\bf 3.67 \boldsymbol{\times}}$| 7948.46 | 14570000 | 40410 |
| bls12_377_mul_projective_g1[^*] | 6.87 | 17.36 | - | 11.42 | 19.38 | 0.44 |
| bls12_377_mul_affine_g1[^*] | 6.76 | 16.57 | - | 11.11 | 24.49 | 0.45 |
| bls12_377_mul_projective_g2[^*] | 13.80 | 22.24 | - | 16.64 | 28.26 | 1.42 |
| bls12_377_mul_affine_g2[^*] | 13.60 | 22.49 | - | 17.18 | 38.94 | 1.46 |
| bw6_761_pairing | 44374.64 | 6002.54 |${\color{green}\bf 7.39 \boldsymbol{\times}}$| 844.10 | 55440 | 6940 |
| bw6_761_msm_g1, 10 arguments | 155393.79 | 53231.17 |${\color{green}\bf 2.92 \boldsymbol{\times}}$| 161.28 | 206610 | 3490 |
| bw6_761_msm_g1, 1000 arguments | 13384952.55 | 5070669.53 |${\color{green}\bf 2.64 \boldsymbol{\times}}$| 13526.84 | 18010000 | 75270 |
| bw6_761_msm_g2, 10 arguments | 141484.94 | 39324.56 |${\color{green}\bf 3.60 \boldsymbol{\times}}$| 161.92 | 212280 | 3430 |
| bw6_761_msm_g2, 1000 arguments | 12528071.10 | 4732393.47 |${\color{green}\bf 2.65 \boldsymbol{\times}}$| 13633.30 | 18020000 | 75330 |
| bw6_761_mul_projective_g1[^*] | 17.05 | 53.83 | - | 21.99 | 34.82 | 1.79 |
| bw6_761_mul_affine_g1[^*] | 18.47 | 55.10 | - | 21.35 | 35.64 | 1.77 |
| bw6_761_mul_projective_g2[^*] | 17.45 | 53.65 | - | 21.64 | 35.42 | 1.78 |
| bw6_761_mul_affine_g2[^*] | 17.55 | 54.28 | - | 21.57 | 34.68 | 1.78 |
| ed_on_bls12_381_msm_sw, 10 arguments | 6663.28 | 3686.07 |${\color{green}\bf 1.81 \boldsymbol{\times}}$| 36.30 | 8610 | 376.61 |
| ed_on_bls12_381_msm_sw, 1000 arguments | 296140.25 | 215932.66 |${\color{green}\bf 1.37 \boldsymbol{\times}}$| 2465.60 | 430700 | 6010 |
| ed_on_bls12_381_mul_projective_sw[^*] | 5.57 | 10.08 | - | 6.69 | 24.89 | 0.36 |
| ed_on_bls12_381_mul_affine_sw[^*] | 5.51 | 10.12 | - | 6.17 | 36.63 | 0.36 |
| ed_on_bls12_381_msm_te, 10 arguments | 7813.27 | 3207.47 |${\color{green}\bf 2.44 \boldsymbol{\times}}$| 35.21 | 12470 | 560.82 |
| ed_on_bls12_381_msm_te, 1000 arguments | 334199.35 | 242277.02 |${\color{green}\bf 1.38 \boldsymbol{\times}}$| 2391.21 | 533490 | 7890 |
| ed_on_bls12_381_mul_projective_te[^*] | 9.13 | 10.60 | - | 7.69 | 22.37 | 0.83 |
| ed_on_bls12_381_mul_affine_te[^*] | 5.59 | 10.07 | - | 7.61 | 17.25 | 0.37 |
| ed_on_bls12_377_msm, 10 arguments | 7768.41 | 3192.99 |${\color{green}\bf 2.43 \boldsymbol{\times}}$| 43.24 | 10060 | 553.69 |
| ed_on_bls12_377_msm, 1000 arguments | 357890.37 | 267844.08 |${\color{green}\bf 1.34 \boldsymbol{\times}}$| 2465.60 | 537810 | 7680 |
| ed_on_bls12_377_mul_projective[^*] | 9.41 | 10.32 | - | 7.00 | 22.48 | 0.89 |
| ed_on_bls12_377_mul_affine[^*] | 8.84 | 442.80 | - | 8.47 | 22.34 | 0.86 |

[^1]: implemented in a Substrate pallet with [arkworks](https://github.com/arkworks-rs/) library by this repo: https://github.com/achimcc/substrate-arkworks-examples
[^2]: implemented in a Substrate pallet with [ark-substrate](https://github.com/paritytech/ark-substrate) library, executed through host-function call, computed by this repo: https://github.com/achimcc/substrate-arkworks-examples
[^3]: These extrinsics just receive the arguemnts, deserialize them without using them and then take a generator or zero element of the expected return group, serizlize it and return it. **Calling a host call through a extrinsic which does nothing has been benchmarked with 3.98µs**. Implementation in: https://github.com/achimcc/substrate-arkworks-examples/tree/dummy-calls
[^4]: executed through wasmtime by this repo: [https://github.com/achimcc/native-bench-arkworks](https://github.com/achimcc/wasm-bench-arkworks)
[^5]: native execution, computed by this repo: https://github.com/achimcc/native-bench-arkworks
[^3]: speedup by using ark-substrate and host calls, compared to native speed
[^4]: These extrinsics just receive the arguemnts, deserialize them without using them and then take a generator or zero element of the expected return group, serizlize it and return it. **Calling a host call through a extrinsic which does nothing has been benchmarked with 3.98µs**. Implementation in: https://github.com/achimcc/substrate-arkworks-examples/tree/dummy-calls
[^5]: executed through wasmtime by this repo: [https://github.com/achimcc/native-bench-arkworks](https://github.com/achimcc/wasm-bench-arkworks)
[^6]: native execution, computed by this repo: https://github.com/achimcc/native-bench-arkworks
[^*]: we removed these host calls in the final ark-substrate implementation, since they didn't yield a performance improvement. Implementations can be found in the branches: https://github.com/paritytech/ark-substrate/tree/arkworks-host-function-mul and https://github.com/paritytech/substrate/tree/arkworks-host-function-mul


## Security considerations
The implementations should be as secure as the arkworks library itself, since all implementations are extensively tested through the same macros from the arkworks testing macro library.

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