arkworks integration (#13031)

* fix * fix * fix * fix * fix * fix * fix * fix * fix * fix * fix * fix * fix * fix * fix compression * fix compression * fix compression * fix compression * fix compression * fix std leak * fix std leak * fix std leak * merge master * merge master * cargo update * cargo update * cargo update * cargo update * cargo update * use serialize_result * cargo update * cargo update * cargo update * cargo update * reduce boilerplate code * remove host function muls * reduce boilerplate code * remove patches * uuse correct ark-substrate branch * reduce boilerplate code * cleanup * cleanup * proper error handling * derive serialize for error * proper error handling * proper error handling * proper error handling * derive Debug for PairingError * sp-arkworks path * cargo update * adopt tests to error handling * fix tests * cargo update * remove results * deserialize as G2Affine * cargo update * add codex index to PairingError * replace Vec<Vec<u8>> * replace Vec<Vec<u8>> * use into_iter for chunks * use chunks for scalars * fix ersialized_size * use into * collect as vec * collect as vec * no collect Vec * use into_iter * import AffineRepr * fix typo * cargo update * new serialization * fix typo * unwrap results * unwrap results * use correct deserialization * fix bugs, cleanup * correct len * vec without capacity * Revert "vec without capacity" This reverts commit 2b1cd004f9f3f7cb1b0513c794f9ea781bb75ef1. * Revert "correct len" This reverts commit b85de8606364260c310f3c306b0a920e184e7e53. * Revert "fix bugs, cleanup" This reverts commit eef4c77ac99c0ed2e4b4857702e6ab5f1d2ce36c. * Revert "use correct deserialization" This reverts commit 9eacba93150bd41614e198cc6f2838d57d14f8db. * Revert "unwrap results" This reverts commit b0df1e1bdbd2518baa23040e0c6663ca69d2ba25. * Revert "unwrap results" This reverts commit de3cfbd04964dd66faeae5616b5763b1d30520e2. * Revert "fix typo" This reverts commit c12045d78f2468800be30ee1b31b12768aa7a786. * Revert "new serialization" This reverts commit e56a088be7612e4511382817afaf61f65b0c3aca. * Revert "cargo update" This reverts commit 15898da94677a5f19290a7f15fb15cb4cbd8f431. * Revert "fix typo" This reverts commit c89e96331f1d07e3b9b6a00ea9c89896553d67c6. * Revert "import AffineRepr" This reverts commit 5a103ac1b3506736181ddda040d896930bd8f83a. * Revert "use into_iter" This reverts commit 2e31d912bd4103529b40b250410f9f5b1a980ce4. * Revert "no collect Vec" This reverts commit db18dcac34fc3c3ddc20c3b42331f8d5fa7014b5. * Revert "collect as vec" This reverts commit dd3f809e965cec361a0feaab9abfae7115756e2c. * Revert "collect as vec" This reverts commit 9167d5984d8ecc3903d24f96d8c9fcac45c87bf7. * Revert "use into" This reverts commit 344cfffbd38fde130225df35f36259872754bd3a. * Revert "fix ersialized_size" This reverts commit c6a760986551cbbcaa3748564dd5e3c7630209c6. * Revert "use chunks for scalars" This reverts commit 67987ae0bbba7e3963ccba0dd9f1fbaa4c922d4f. * Revert "use into_iter for chunks" This reverts commit 1ddd6b89c2f8fb4e6dd26768be0edaca2d1be3f9. * Revert "replace Vec<Vec<u8>>" This reverts commit 4d3b13c02a9db0ea6bd130bda38c851f2371ec6e. * cargo update * cargo update * Revert "replace Vec<Vec<u8>>" This reverts commit 4389714068d939abc97288c5b06ee23d399a19ad. * cargo update * add error * add error * add error * fix typo * fix imports * import coded * import codec * import PairingError * fix patches * sp-arkworks * sp-arkworks * use random values for multiplications * cargo update * fix imports * fix imports * add host functions * re-add mul impls * cargo update * cargo update * cargo update * cargo update * cargo update * cargo update * cargo update * PairingError -> () * remove PairingError * cargo update * cargo update * cargo update * reduce boilerplate code * cargo update * update comments * cargo update * optimize code quality * use ark_scale (#13954) * use ark_scale * fix tests * fix tests * cleanup & comments * use correct PR branch * hazmat * ed curves, use ArkScaleProjective * Achimcc/arkworks integration remove affine hostcalls (#13971) * remove affine host-calls * remove affine host-call impls, also in tests * cargo update * ark-substrate: use main branch * cargo update * Achimcc/arkworks integration bandersnatch (#13977) * use bandersnatch * bandersnatch * add abndersnatch sw msm * use correct PR branch * cargo update * cargo update * fix tests * cleanup * cleanup * fix tests * refactor tests * cargo update * cargo update * cargo update * refactor tests * cleanup & update tests * upgrade arkworks/algebra * cargo update * adopt tests * versioning ark-substrate * cargo update * remove patched deps * bump ark-scale * use crates-io deps * fix doc comments * Cargo.toml, linebreaks at end * reorgainze tests * sp-arkworks -> sp-crypto-ec-utils * move host functions to crypto-ec-utils * fmt * remove sp-ec-crypto-utils from io * remove unwrap from te msm * remove elliptic_curves references in test * elliptic_curves references in test * update doc comments * remove warn missing docs * fmt * cargo update * update doc comments * cargo update * cargo update, bump arkworks, codec versions * bump runtime version in sp-crypto-ec-utils * remove feature flag ec-utils-experimental * crypto-ec-utils -> crypto/ec-utils * tests/ -> test-data/ * update doc comments for signatures * update comments * update doc comments for signatures * fix doc comments * fix doc comments * fix doc comments * fix doc comments * fix doc comments * cleanup * fix doc comments * cargo update * fix doc comments * cargo update
2026-04-26 07:37:57 +00:00 · 2023-06-06 12:23:07 +02:00
parent 35cc4162df
commit 03490d5dd0
14 changed files with 1530 additions and 285 deletions
@@ -0,0 +1,103 @@
+// This file is part of Substrate.
+
+// Copyright (C) 2017-2022 Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Support functions for bls12_377 to improve the performance of
+//! multi_miller_loop, final_exponentiation, msm's and projective
+//! multiplications by host function calls
+
+use crate::utils::{
+	final_exponentiation_generic, msm_sw_generic, mul_projective_generic, multi_miller_loop_generic,
+};
+use ark_bls12_377::{g1, g2, Bls12_377};
+use sp_std::vec::Vec;
+
+/// Compute a multi miller loop through arkworks
+pub fn multi_miller_loop(a: Vec<u8>, b: Vec<u8>) -> Result<Vec<u8>, ()> {
+	multi_miller_loop_generic::<Bls12_377>(a, b)
+}
+
+/// Compute a final exponentiation through arkworks
+pub fn final_exponentiation(target: Vec<u8>) -> Result<Vec<u8>, ()> {
+	final_exponentiation_generic::<Bls12_377>(target)
+}
+
+/// Compute a multi scalar multiplication for short_weierstrass through
+/// arkworks on G1.
+pub fn msm_g1(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+	msm_sw_generic::<g1::Config>(bases, scalars)
+}
+
+/// Compute a multi scalar multiplication for short_weierstrass through
+/// arkworks on G2.
+pub fn msm_g2(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+	msm_sw_generic::<g2::Config>(bases, scalars)
+}
+
+/// Compute a projective scalar multiplication for short_weierstrass
+/// through arkworks on G1.
+pub fn mul_projective_g1(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+	mul_projective_generic::<g1::Config>(base, scalar)
+}
+
+/// Compute a projective scalar multiplication for short_weierstrass
+/// through arkworks on G2.
+pub fn mul_projective_g2(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+	mul_projective_generic::<g2::Config>(base, scalar)
+}
+
+#[cfg(test)]
+mod tests {
+	use super::*;
+	use ark_algebra_test_templates::*;
+	use sp_ark_bls12_377::{
+		Bls12_377 as Bls12_377Host, G1Projective as G1ProjectiveHost,
+		G2Projective as G2ProjectiveHost, HostFunctions,
+	};
+
+	#[derive(PartialEq, Eq)]
+	struct Host;
+
+	impl HostFunctions for Host {
+		fn bls12_377_multi_miller_loop(a: Vec<u8>, b: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_377_multi_miller_loop(a, b)
+		}
+		fn bls12_377_final_exponentiation(f12: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_377_final_exponentiation(f12)
+		}
+		fn bls12_377_msm_g1(bases: Vec<u8>, bigints: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_377_msm_g1(bases, bigints)
+		}
+		fn bls12_377_msm_g2(bases: Vec<u8>, bigints: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_377_msm_g2(bases, bigints)
+		}
+		fn bls12_377_mul_projective_g1(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_377_mul_projective_g1(base, scalar)
+		}
+		fn bls12_377_mul_projective_g2(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_377_mul_projective_g2(base, scalar)
+		}
+	}
+
+	type Bls12_377 = Bls12_377Host<Host>;
+	type G1Projective = G1ProjectiveHost<Host>;
+	type G2Projective = G2ProjectiveHost<Host>;
+
+	test_group!(g1; G1Projective; sw);
+	test_group!(g2; G2Projective; sw);
+	test_group!(pairing_output; ark_ec::pairing::PairingOutput<Bls12_377>; msm);
+	test_pairing!(pairing; super::Bls12_377);
+}
@@ -0,0 +1,219 @@
+// This file is part of Substrate.
+
+// Copyright (C) 2017-2022 Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Support functions for bls12_381 to improve the performance of
+//! multi_miller_loop, final_exponentiation, msm's and projective
+//! multiplications by host function calls
+
+use crate::utils::{
+	final_exponentiation_generic, msm_sw_generic, mul_projective_generic, multi_miller_loop_generic,
+};
+use ark_bls12_381::{g1, g2, Bls12_381};
+use sp_std::vec::Vec;
+
+/// Compute a multi miller loop through arkworks
+pub fn multi_miller_loop(a: Vec<u8>, b: Vec<u8>) -> Result<Vec<u8>, ()> {
+	multi_miller_loop_generic::<Bls12_381>(a, b)
+}
+
+/// Compute a final exponentiation through arkworks
+pub fn final_exponentiation(target: Vec<u8>) -> Result<Vec<u8>, ()> {
+	final_exponentiation_generic::<Bls12_381>(target)
+}
+
+/// Compute a multi scalar multiplication for short_weierstrass through
+/// arkworks on G1.
+pub fn msm_g1(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+	msm_sw_generic::<g1::Config>(bases, scalars)
+}
+
+/// Compute a multi scalar multiplication for short_weierstrass through
+/// arkworks on G2.
+pub fn msm_g2(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+	msm_sw_generic::<g2::Config>(bases, scalars)
+}
+
+/// Compute a projective scalar multiplication for short_weierstrass
+/// through arkworks on G1.
+pub fn mul_projective_g1(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+	mul_projective_generic::<g1::Config>(base, scalar)
+}
+
+/// Compute a projective scalar multiplication for short_weierstrass
+/// through arkworks on G2.
+pub fn mul_projective_g2(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+	mul_projective_generic::<g2::Config>(base, scalar)
+}
+
+#[cfg(test)]
+mod tests {
+	use super::*;
+	use ark_algebra_test_templates::*;
+	use ark_ec::{AffineRepr, CurveGroup, Group};
+	use ark_ff::{fields::Field, One, Zero};
+	use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Compress, Validate};
+	use ark_std::{rand::Rng, test_rng, vec, UniformRand};
+	use sp_ark_bls12_381::{
+		fq::Fq, fq2::Fq2, fr::Fr, Bls12_381 as Bls12_381Host, G1Affine as G1AffineHost,
+		G1Projective as G1ProjectiveHost, G2Affine as G2AffineHost,
+		G2Projective as G2ProjectiveHost, HostFunctions,
+	};
+	use sp_ark_models::pairing::PairingOutput;
+
+	#[derive(PartialEq, Eq)]
+	struct Host;
+
+	impl HostFunctions for Host {
+		fn bls12_381_multi_miller_loop(a: Vec<u8>, b: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_381_multi_miller_loop(a, b)
+		}
+		fn bls12_381_final_exponentiation(f12: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_381_final_exponentiation(f12)
+		}
+		fn bls12_381_msm_g1(bases: Vec<u8>, bigints: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_381_msm_g1(bases, bigints)
+		}
+		fn bls12_381_msm_g2(bases: Vec<u8>, bigints: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_381_msm_g2(bases, bigints)
+		}
+		fn bls12_381_mul_projective_g1(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_381_mul_projective_g1(base, scalar)
+		}
+		fn bls12_381_mul_projective_g2(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bls12_381_mul_projective_g2(base, scalar)
+		}
+	}
+
+	type Bls12_381 = Bls12_381Host<Host>;
+	type G1Projective = G1ProjectiveHost<Host>;
+	type G2Projective = G2ProjectiveHost<Host>;
+	type G1Affine = G1AffineHost<Host>;
+	type G2Affine = G2AffineHost<Host>;
+
+	test_group!(g1; G1Projective; sw);
+	test_group!(g2; G2Projective; sw);
+	test_group!(pairing_output; PairingOutput<Bls12_381>; msm);
+	test_pairing!(ark_pairing; super::Bls12_381);
+
+	#[test]
+	fn test_g1_endomorphism_beta() {
+		assert!(sp_ark_bls12_381::g1::BETA.pow([3u64]).is_one());
+	}
+
+	#[test]
+	fn test_g1_subgroup_membership_via_endomorphism() {
+		let mut rng = test_rng();
+		let generator = G1Projective::rand(&mut rng).into_affine();
+		assert!(generator.is_in_correct_subgroup_assuming_on_curve());
+	}
+
+	#[test]
+	fn test_g1_subgroup_non_membership_via_endomorphism() {
+		let mut rng = test_rng();
+		loop {
+			let x = Fq::rand(&mut rng);
+			let greatest = rng.gen();
+
+			if let Some(p) = G1Affine::get_point_from_x_unchecked(x, greatest) {
+				if !<G1Projective as ark_std::Zero>::is_zero(&p.mul_bigint(Fr::characteristic())) {
+					assert!(!p.is_in_correct_subgroup_assuming_on_curve());
+					return
+				}
+			}
+		}
+	}
+
+	#[test]
+	fn test_g2_subgroup_membership_via_endomorphism() {
+		let mut rng = test_rng();
+		let generator = G2Projective::rand(&mut rng).into_affine();
+		assert!(generator.is_in_correct_subgroup_assuming_on_curve());
+	}
+
+	#[test]
+	fn test_g2_subgroup_non_membership_via_endomorphism() {
+		let mut rng = test_rng();
+		loop {
+			let x = Fq2::rand(&mut rng);
+			let greatest = rng.gen();
+
+			if let Some(p) = G2Affine::get_point_from_x_unchecked(x, greatest) {
+				if !<G2Projective as Zero>::is_zero(&p.mul_bigint(Fr::characteristic())) {
+					assert!(!p.is_in_correct_subgroup_assuming_on_curve());
+					return
+				}
+			}
+		}
+	}
+
+	// Test vectors and macro adapted from https://github.com/zkcrypto/bls12_381/blob/e224ad4ea1babfc582ccd751c2bf128611d10936/src/test-data/mod.rs
+	macro_rules! test_vectors {
+		($projective:ident, $affine:ident, $compress:expr, $expected:ident) => {
+			let mut e = $projective::zero();
+
+			let mut v = vec![];
+			{
+				let mut expected = $expected;
+				for _ in 0..1000 {
+					let e_affine = $affine::from(e);
+					let mut serialized = vec![0u8; e.serialized_size($compress)];
+					e_affine.serialize_with_mode(serialized.as_mut_slice(), $compress).unwrap();
+					v.extend_from_slice(&serialized[..]);
+
+					let mut decoded = serialized;
+					let len_of_encoding = decoded.len();
+					(&mut decoded[..]).copy_from_slice(&expected[0..len_of_encoding]);
+					expected = &expected[len_of_encoding..];
+					let decoded =
+						$affine::deserialize_with_mode(&decoded[..], $compress, Validate::Yes)
+							.unwrap();
+					assert_eq!(e_affine, decoded);
+
+					e += &$projective::generator();
+				}
+			}
+
+			assert_eq!(&v[..], $expected);
+		};
+	}
+
+	#[test]
+	fn g1_compressed_valid_test_vectors() {
+		let bytes: &'static [u8] = include_bytes!("test-data/g1_compressed_valid_test_vectors.dat");
+		test_vectors!(G1Projective, G1Affine, Compress::Yes, bytes);
+	}
+
+	#[test]
+	fn g1_uncompressed_valid_test_vectors() {
+		let bytes: &'static [u8] =
+			include_bytes!("test-data/g1_uncompressed_valid_test_vectors.dat");
+		test_vectors!(G1Projective, G1Affine, Compress::No, bytes);
+	}
+
+	#[test]
+	fn g2_compressed_valid_test_vectors() {
+		let bytes: &'static [u8] = include_bytes!("test-data/g2_compressed_valid_test_vectors.dat");
+		test_vectors!(G2Projective, G2Affine, Compress::Yes, bytes);
+	}
+
+	#[test]
+	fn g2_uncompressed_valid_test_vectors() {
+		let bytes: &'static [u8] =
+			include_bytes!("test-data/g2_uncompressed_valid_test_vectors.dat");
+		test_vectors!(G2Projective, G2Affine, Compress::No, bytes);
+	}
+}
@@ -0,0 +1,103 @@
+// This file is part of Substrate.
+
+// Copyright (C) 2017-2022 Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Support functions for bw6_761 to improve the performance of
+//! multi_miller_loop, final_exponentiation, msm's and projective
+//! multiplications by host function calls.
+
+use crate::utils::{
+	final_exponentiation_generic, msm_sw_generic, mul_projective_generic, multi_miller_loop_generic,
+};
+use ark_bw6_761::{g1, g2, BW6_761};
+use sp_std::vec::Vec;
+
+/// Compute a multi miller loop through arkworks
+pub fn multi_miller_loop(a: Vec<u8>, b: Vec<u8>) -> Result<Vec<u8>, ()> {
+	multi_miller_loop_generic::<BW6_761>(a, b)
+}
+
+/// Compute a final exponentiation through arkworks
+pub fn final_exponentiation(target: Vec<u8>) -> Result<Vec<u8>, ()> {
+	final_exponentiation_generic::<BW6_761>(target)
+}
+
+/// Compute a multi scalar multiplication for short_weierstrass through
+/// arkworks on G1.
+pub fn msm_g1(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+	msm_sw_generic::<g1::Config>(bases, scalars)
+}
+
+/// Compute a multi scalar multiplication for short_weierstrass through
+/// arkworks on G2.
+pub fn msm_g2(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+	msm_sw_generic::<g2::Config>(bases, scalars)
+}
+
+/// Compute a projective scalar multiplication for short_weierstrass through
+/// arkworks on G1.
+pub fn mul_projective_g1(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+	mul_projective_generic::<g1::Config>(base, scalar)
+}
+
+/// Compute a projective scalar multiplication for short_weierstrass through
+/// arkworks on G2.
+pub fn mul_projective_g2(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+	mul_projective_generic::<g2::Config>(base, scalar)
+}
+
+#[cfg(test)]
+mod tests {
+	use super::*;
+	use ark_algebra_test_templates::*;
+	use sp_ark_bw6_761::{
+		G1Projective as G1ProjectiveHost, G2Projective as G2ProjectiveHost, HostFunctions,
+		BW6_761 as BW6_761Host,
+	};
+
+	#[derive(PartialEq, Eq)]
+	struct Host;
+
+	impl HostFunctions for Host {
+		fn bw6_761_multi_miller_loop(a: Vec<u8>, b: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bw6_761_multi_miller_loop(a, b)
+		}
+		fn bw6_761_final_exponentiation(f12: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bw6_761_final_exponentiation(f12)
+		}
+		fn bw6_761_msm_g1(bases: Vec<u8>, bigints: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bw6_761_msm_g1(bases, bigints)
+		}
+		fn bw6_761_msm_g2(bases: Vec<u8>, bigints: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bw6_761_msm_g2(bases, bigints)
+		}
+		fn bw6_761_mul_projective_g1(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bw6_761_mul_projective_g1(base, scalar)
+		}
+		fn bw6_761_mul_projective_g2(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::bw6_761_mul_projective_g2(base, scalar)
+		}
+	}
+
+	type BW6_761 = BW6_761Host<Host>;
+	type G1Projective = G1ProjectiveHost<Host>;
+	type G2Projective = G2ProjectiveHost<Host>;
+
+	test_group!(g1; G1Projective; sw);
+	test_group!(g2; G2Projective; sw);
+	test_group!(pairing_output; ark_ec::pairing::PairingOutput<BW6_761>; msm);
+	test_pairing!(pairing; super::BW6_761);
+}
@@ -0,0 +1,56 @@
+// This file is part of Substrate.
+
+// Copyright (C) 2017-2022 Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Support functions for ed_on_bls12_377 to improve the performance of
+//! msm and projective multiplication by host function calls
+
+use crate::utils::{msm_te_generic, mul_projective_te_generic};
+use ark_ed_on_bls12_377::EdwardsConfig;
+use sp_std::vec::Vec;
+
+/// Compute a multi scalar mulitplication for twisted_edwards through
+/// arkworks.
+pub fn msm(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+	msm_te_generic::<EdwardsConfig>(bases, scalars)
+}
+
+/// Compute a projective scalar multiplication for twisted_edwards
+/// through arkworks.
+pub fn mul_projective(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+	mul_projective_te_generic::<EdwardsConfig>(base, scalar)
+}
+
+#[cfg(test)]
+mod tests {
+	use super::*;
+	use ark_algebra_test_templates::*;
+	use sp_ark_ed_on_bls12_377::{EdwardsProjective as EdwardsProjectiveHost, HostFunctions};
+
+	struct Host {}
+
+	impl HostFunctions for Host {
+		fn ed_on_bls12_377_msm(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::ed_on_bls12_377_msm(bases, scalars)
+		}
+		fn ed_on_bls12_377_mul_projective(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::ed_on_bls12_377_mul_projective(base, scalar)
+		}
+	}
+
+	type EdwardsProjective = EdwardsProjectiveHost<Host>;
+	test_group!(te; EdwardsProjective; te);
+}
@@ -0,0 +1,94 @@
+// This file is part of Substrate.
+
+// Copyright (C) 2017-2022 Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Support functions for ed_on_bls12_381_bandersnatch to improve the
+//! performance of msm' and projective multiplications by host function
+//! calls.
+
+use crate::utils::{
+	msm_sw_generic, msm_te_generic, mul_projective_generic, mul_projective_te_generic,
+};
+use ark_ed_on_bls12_381_bandersnatch::BandersnatchConfig;
+use sp_std::vec::Vec;
+
+/// Compute a multi scalar multiplication for short_weierstrass through
+/// arkworks.
+pub fn sw_msm(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+	msm_sw_generic::<BandersnatchConfig>(bases, scalars)
+}
+
+/// Compute a multi scalar mulitplication for twisted_edwards through
+/// arkworks.
+pub fn te_msm(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+	msm_te_generic::<BandersnatchConfig>(bases, scalars)
+}
+
+/// Compute a projective scalar multiplication for short_weierstrass
+/// through arkworks.
+pub fn sw_mul_projective(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+	mul_projective_generic::<BandersnatchConfig>(base, scalar)
+}
+
+/// Compute a projective scalar multiplication for twisted_edwards
+/// through arkworks.
+pub fn te_mul_projective(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+	mul_projective_te_generic::<BandersnatchConfig>(base, scalar)
+}
+
+#[cfg(test)]
+mod tests {
+	use super::*;
+	use ark_algebra_test_templates::*;
+	use sp_ark_ed_on_bls12_381_bandersnatch::{
+		EdwardsProjective as EdwardsProjectiveHost, HostFunctions, SWProjective as SWProjectiveHost,
+	};
+
+	pub struct Host {}
+
+	impl HostFunctions for Host {
+		fn ed_on_bls12_381_bandersnatch_te_msm(
+			bases: Vec<u8>,
+			scalars: Vec<u8>,
+		) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::ed_on_bls12_381_bandersnatch_te_msm(bases, scalars)
+		}
+		fn ed_on_bls12_381_bandersnatch_sw_msm(
+			bases: Vec<u8>,
+			scalars: Vec<u8>,
+		) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::ed_on_bls12_381_bandersnatch_sw_msm(bases, scalars)
+		}
+		fn ed_on_bls12_381_bandersnatch_te_mul_projective(
+			base: Vec<u8>,
+			scalar: Vec<u8>,
+		) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::ed_on_bls12_381_bandersnatch_te_mul_projective(base, scalar)
+		}
+		fn ed_on_bls12_381_bandersnatch_sw_mul_projective(
+			base: Vec<u8>,
+			scalar: Vec<u8>,
+		) -> Result<Vec<u8>, ()> {
+			crate::elliptic_curves::ed_on_bls12_381_bandersnatch_sw_mul_projective(base, scalar)
+		}
+	}
+
+	type EdwardsProjective = EdwardsProjectiveHost<Host>;
+	type SWProjective = SWProjectiveHost<Host>;
+
+	test_group!(sw; SWProjective; sw);
+	test_group!(te; EdwardsProjective; te);
+}
@@ -0,0 +1,264 @@
+// This file is part of Substrate.
+
+// Copyright (C) Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! The main elliptic curves trait, allowing Substrate to call into host functions
+//! for operations on elliptic curves.
+
+#![warn(missing_docs)]
+#![cfg_attr(not(feature = "std"), no_std)]
+
+pub mod bls12_377;
+pub mod bls12_381;
+pub mod bw6_761;
+pub mod ed_on_bls12_377;
+pub mod ed_on_bls12_381_bandersnatch;
+mod utils;
+
+use sp_runtime_interface::runtime_interface;
+
+/// Interfaces for working with elliptic curves related types from within the runtime.
+/// All type are (de-)serialized through the wrapper types from the ark-scale trait,
+/// with ark_scale::{ArkScale, ArkScaleProjective};
+#[runtime_interface]
+pub trait EllipticCurves {
+	/// Compute a multi Miller loop for bls12_37
+	/// Receives encoded:
+	/// a: ArkScale<Vec<ark_ec::bls12::G1Prepared::<ark_bls12_377::Config>>>
+	/// b: ArkScale<Vec<ark_ec::bls12::G2Prepared::<ark_bls12_377::Config>>>
+	/// Returns encoded: ArkScale<MillerLoopOutput<Bls12<ark_bls12_377::Config>>>
+	fn bls12_377_multi_miller_loop(a: Vec<u8>, b: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_377::multi_miller_loop(a, b)
+	}
+
+	/// Compute a final exponentiation for bls12_377
+	/// Receives encoded: ArkScale<MillerLoopOutput<Bls12<ark_bls12_377::Config>>>
+	/// Returns encoded: ArkScale<PairingOutput<Bls12<ark_bls12_377::Config>>>
+	fn bls12_377_final_exponentiation(f12: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_377::final_exponentiation(f12)
+	}
+
+	/// Compute a projective multiplication on G1 for bls12_377
+	/// Receives encoded:
+	/// base: ArkScaleProjective<ark_bls12_377::G1Projective>
+	/// scalar: ArkScale<&[u64]>
+	/// Returns encoded: ArkScaleProjective<ark_bls12_377::G1Projective>
+	fn bls12_377_mul_projective_g1(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_377::mul_projective_g1(base, scalar)
+	}
+
+	/// Compute a projective multiplication on G2 for bls12_377
+	/// through arkworks on G2
+	/// Receives encoded:
+	/// base: ArkScaleProjective<ark_bls12_377::G2Projective>
+	/// scalar: ArkScale<&[u64]>
+	/// Returns encoded: ArkScaleProjective<ark_bls12_377::G2Projective>
+	fn bls12_377_mul_projective_g2(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_377::mul_projective_g2(base, scalar)
+	}
+
+	/// Compute a msm on G1 for bls12_377
+	/// Receives encoded:
+	/// bases: ArkScale<&[ark_bls12_377::G1Affine]>
+	/// scalars: ArkScale<&[ark_bls12_377::Fr]>
+	/// Returns encoded: ArkScaleProjective<ark_bls12_377::G1Projective>
+	fn bls12_377_msm_g1(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_377::msm_g1(bases, scalars)
+	}
+
+	/// Compute a msm on G2 for bls12_377
+	/// Receives encoded:
+	/// bases: ArkScale<&[ark_bls12_377::G2Affine]>
+	/// scalars: ArkScale<&[ark_bls12_377::Fr]>
+	/// Returns encoded: ArkScaleProjective<ark_bls12_377::G2Projective>
+	fn bls12_377_msm_g2(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_377::msm_g2(bases, scalars)
+	}
+
+	/// Compute a multi Miller loop on bls12_381
+	/// Receives encoded:
+	/// a: ArkScale<Vec<ark_ec::bls12::G1Prepared::<ark_bls12_381::Config>>>
+	/// b: ArkScale<Vec<ark_ec::bls12::G2Prepared::<ark_bls12_381::Config>>>
+	/// Returns encoded: ArkScale<MillerLoopOutput<Bls12<ark_bls12_381::Config>>>
+	fn bls12_381_multi_miller_loop(a: Vec<u8>, b: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_381::multi_miller_loop(a, b)
+	}
+
+	/// Compute a final exponentiation on bls12_381
+	/// Receives encoded: ArkScale<MillerLoopOutput<Bls12<ark_bls12_381::Config>>>
+	/// Returns encoded:ArkScale<PairingOutput<Bls12<ark_bls12_381::Config>>>
+	fn bls12_381_final_exponentiation(f12: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_381::final_exponentiation(f12)
+	}
+
+	/// Compute a projective multiplication on G1 for bls12_381
+	/// Receives encoded:
+	/// base: ArkScaleProjective<ark_bls12_381::G1Projective>
+	/// scalar: ArkScale<&[u64]>
+	/// Returns encoded: ArkScaleProjective<ark_bls12_381::G1Projective>
+	fn bls12_381_mul_projective_g1(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_381::mul_projective_g1(base, scalar)
+	}
+
+	/// Compute a projective multiplication on G2 for bls12_381
+	/// Receives encoded:
+	/// base: ArkScaleProjective<ark_bls12_381::G2Projective>
+	/// scalar: ArkScale<&[u64]>
+	/// Returns encoded: ArkScaleProjective<ark_bls12_381::G2Projective>
+	fn bls12_381_mul_projective_g2(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_381::mul_projective_g2(base, scalar)
+	}
+
+	/// Compute a msm on G1 for bls12_381
+	/// Receives encoded:
+	/// bases: ArkScale<&[ark_bls12_381::G1Affine]>
+	/// scalars: ArkScale<&[ark_bls12_381::Fr]>
+	/// Returns encoded: ArkScaleProjective<ark_bls12_381::G1Projective>
+	fn bls12_381_msm_g1(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_381::msm_g1(bases, scalars)
+	}
+
+	/// Compute a msm on G2 for bls12_381
+	/// Receives encoded:
+	/// bases: ArkScale<&[ark_bls12_381::G2Affine]>
+	/// scalars: ArkScale<&[ark_bls12_381::Fr]>
+	/// Returns encoded: ArkScaleProjective<ark_bls12_381::G2Projective>
+	fn bls12_381_msm_g2(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bls12_381::msm_g2(bases, scalars)
+	}
+
+	/// Compute a multi Miller loop on bw6_761
+	/// Receives encoded:
+	/// a: ArkScale<Vec<ark_ec::bw6::G1Prepared::<ark_bw6_761::Config>>>
+	/// b: ArkScale<Vec<ark_ec::bw6::G2Prepared::<ark_bw6_761::Config>>>
+	/// Returns encoded: ArkScale<MillerLoopOutput<Bls12<ark_bw6_761::Config>>>
+	fn bw6_761_multi_miller_loop(a: Vec<u8>, b: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bw6_761::multi_miller_loop(a, b)
+	}
+
+	/// Compute a final exponentiation on bw6_761
+	/// Receives encoded: ArkScale<MillerLoopOutput<BW6<ark_bw6_761::Config>>>
+	/// Returns encoded: ArkScale<PairingOutput<BW6<ark_bw6_761::Config>>>
+	fn bw6_761_final_exponentiation(f12: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bw6_761::final_exponentiation(f12)
+	}
+
+	/// Compute a projective multiplication on G1 for bw6_761
+	/// Receives encoded:
+	/// base: ArkScaleProjective<ark_bw6_761::G1Projective>
+	/// scalar: ArkScale<&[u64]>
+	/// Returns encoded: ArkScaleProjective<ark_bw6_761::G1Projective>
+	fn bw6_761_mul_projective_g1(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bw6_761::mul_projective_g1(base, scalar)
+	}
+
+	/// Compute a projective multiplication on G2 for bw6_761
+	/// Receives encoded:
+	/// base: ArkScaleProjective<ark_bw6_761::G2Projective>
+	/// scalar: ArkScale<&[u64]>
+	/// Returns encoded: ArkScaleProjective<ark_bw6_761::G2Projective>
+	fn bw6_761_mul_projective_g2(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bw6_761::mul_projective_g2(base, scalar)
+	}
+
+	/// Compute a msm on G1 for bw6_761
+	/// Receives encoded:
+	/// bases: ArkScale<&[ark_bw6_761::G1Affine]>
+	/// scalars: ArkScale<&[ark_bw6_761::Fr]>
+	/// Returns encoded: ArkScaleProjective<ark_bw6_761::G1Projective>
+	fn bw6_761_msm_g1(bases: Vec<u8>, bigints: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bw6_761::msm_g1(bases, bigints)
+	}
+
+	/// Compute a msm on G2 for bw6_761
+	/// Receives encoded:
+	/// bases: ArkScale<&[ark_bw6_761::G2Affine]>
+	/// scalars: ArkScale<&[ark_bw6_761::Fr]>
+	/// Returns encoded: ArkScaleProjective<ark_bw6_761::G2Projective>
+	fn bw6_761_msm_g2(bases: Vec<u8>, bigints: Vec<u8>) -> Result<Vec<u8>, ()> {
+		bw6_761::msm_g2(bases, bigints)
+	}
+
+	/// Compute projective multiplication on ed_on_bls12_377
+	/// Receives encoded:
+	/// base: ArkScaleProjective<ark_ed_on_bls12_377::EdwardsProjective>
+	/// scalar: ArkScale<&[u64]>
+	/// Returns encoded: ArkScaleProjective<ark_ed_on_bls12_377::EdwardsProjective>
+	fn ed_on_bls12_377_mul_projective(base: Vec<u8>, scalar: Vec<u8>) -> Result<Vec<u8>, ()> {
+		ed_on_bls12_377::mul_projective(base, scalar)
+	}
+
+	/// Compute msm on ed_on_bls12_377
+	/// Receives encoded:
+	/// bases: ArkScale<&[ark_ed_on_bls12_377::EdwardsAffine]>
+	/// scalars:
+	/// ArkScale<&[ark_ed_on_bls12_377::Fr]>
+	/// Returns encoded:
+	/// ArkScaleProjective<ark_ed_on_bls12_377::EdwardsProjective>
+	fn ed_on_bls12_377_msm(bases: Vec<u8>, scalars: Vec<u8>) -> Result<Vec<u8>, ()> {
+		ed_on_bls12_377::msm(bases, scalars)
+	}
+
+	/// Compute short weierstrass projective multiplication on ed_on_bls12_381_bandersnatch
+	/// Receives encoded:
+	/// base: ArkScaleProjective<ark_ed_on_bls12_381_bandersnatch::SWProjective>
+	/// scalar: ArkScale<&[u64]>
+	/// Returns encoded: ArkScaleProjective<ark_ed_on_bls12_381_bandersnatch::SWProjective>
+	fn ed_on_bls12_381_bandersnatch_sw_mul_projective(
+		base: Vec<u8>,
+		scalar: Vec<u8>,
+	) -> Result<Vec<u8>, ()> {
+		ed_on_bls12_381_bandersnatch::sw_mul_projective(base, scalar)
+	}
+
+	/// Compute twisted edwards projective multiplication on ed_on_bls12_381_bandersnatch
+	/// Receives encoded:
+	/// base: ArkScaleProjective<ark_ed_on_bls12_381_bandersnatch::EdwardsProjective>
+	/// scalar: ArkScale<&[u64]>
+	/// Returns encoded: ArkScaleProjective<ark_ed_on_bls12_381_bandersnatch::EdwardsProjective>
+	fn ed_on_bls12_381_bandersnatch_te_mul_projective(
+		base: Vec<u8>,
+		scalar: Vec<u8>,
+	) -> Result<Vec<u8>, ()> {
+		ed_on_bls12_381_bandersnatch::te_mul_projective(base, scalar)
+	}
+
+	/// Compute short weierstrass msm on ed_on_bls12_381_bandersnatch
+	/// Receives encoded:
+	/// bases: ArkScale<&[ark_ed_on_bls12_381_bandersnatch::SWAffine]>
+	/// scalars: ArkScale<&[ark_ed_on_bls12_381_bandersnatch::Fr]>
+	/// Returns encoded:
+	/// ArkScaleProjective<ark_ed_on_bls12_381_bandersnatch::SWProjective>
+	fn ed_on_bls12_381_bandersnatch_sw_msm(
+		bases: Vec<u8>,
+		scalars: Vec<u8>,
+	) -> Result<Vec<u8>, ()> {
+		ed_on_bls12_381_bandersnatch::sw_msm(bases, scalars)
+	}
+
+	/// Compute twisted edwards msm on ed_on_bls12_381_bandersnatch
+	/// Receives encoded:
+	/// base: ArkScaleProjective<ark_ed_on_bls12_381_bandersnatch::EdwardsProjective>
+	/// scalars: ArkScale<&[ark_ed_on_bls12_381_bandersnatch::Fr]>
+	/// Returns encoded:
+	/// ArkScaleProjective<ark_ed_on_bls12_381_bandersnatch::EdwardsProjective>
+	fn ed_on_bls12_381_bandersnatch_te_msm(
+		bases: Vec<u8>,
+		scalars: Vec<u8>,
+	) -> Result<Vec<u8>, ()> {
+		ed_on_bls12_381_bandersnatch::te_msm(bases, scalars)
+	}
+}
@@ -0,0 +1,130 @@
+// This file is part of Substrate.
+
+// Copyright (C) Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! The generic executions of the operations on arkworks elliptic curves
+//! which get instantiatied by the corresponding curves.
+use ark_ec::{
+	pairing::{MillerLoopOutput, Pairing, PairingOutput},
+	short_weierstrass,
+	short_weierstrass::SWCurveConfig,
+	twisted_edwards,
+	twisted_edwards::TECurveConfig,
+	CurveConfig, VariableBaseMSM,
+};
+use ark_scale::hazmat::ArkScaleProjective;
+use ark_std::vec::Vec;
+use codec::{Decode, Encode};
+
+const HOST_CALL: ark_scale::Usage = ark_scale::HOST_CALL;
+type ArkScale<T> = ark_scale::ArkScale<T, HOST_CALL>;
+
+pub(crate) fn multi_miller_loop_generic<Curve: Pairing>(
+	g1: Vec<u8>,
+	g2: Vec<u8>,
+) -> Result<Vec<u8>, ()> {
+	let g1 = <ArkScale<Vec<<Curve as Pairing>::G1Affine>> as Decode>::decode(&mut g1.as_slice())
+		.map_err(|_| ())?;
+	let g2 = <ArkScale<Vec<<Curve as Pairing>::G2Affine>> as Decode>::decode(&mut g2.as_slice())
+		.map_err(|_| ())?;
+
+	let result = Curve::multi_miller_loop(g1.0, g2.0).0;
+
+	let result: ArkScale<<Curve as Pairing>::TargetField> = result.into();
+	Ok(result.encode())
+}
+
+pub(crate) fn final_exponentiation_generic<Curve: Pairing>(target: Vec<u8>) -> Result<Vec<u8>, ()> {
+	let target =
+		<ArkScale<<Curve as Pairing>::TargetField> as Decode>::decode(&mut target.as_slice())
+			.map_err(|_| ())?;
+
+	let result = Curve::final_exponentiation(MillerLoopOutput(target.0)).ok_or(())?;
+
+	let result: ArkScale<PairingOutput<Curve>> = result.into();
+	Ok(result.encode())
+}
+
+pub(crate) fn msm_sw_generic<Curve: SWCurveConfig>(
+	bases: Vec<u8>,
+	scalars: Vec<u8>,
+) -> Result<Vec<u8>, ()> {
+	let bases =
+		<ArkScale<Vec<short_weierstrass::Affine<Curve>>> as Decode>::decode(&mut bases.as_slice())
+			.map_err(|_| ())?;
+	let scalars = <ArkScale<Vec<<Curve as CurveConfig>::ScalarField>> as Decode>::decode(
+		&mut scalars.as_slice(),
+	)
+	.map_err(|_| ())?;
+
+	let result =
+		<short_weierstrass::Projective<Curve> as VariableBaseMSM>::msm(&bases.0, &scalars.0)
+			.map_err(|_| ())?;
+
+	let result: ArkScaleProjective<short_weierstrass::Projective<Curve>> = result.into();
+	Ok(result.encode())
+}
+
+pub(crate) fn msm_te_generic<Curve: TECurveConfig>(
+	bases: Vec<u8>,
+	scalars: Vec<u8>,
+) -> Result<Vec<u8>, ()> {
+	let bases =
+		<ArkScale<Vec<twisted_edwards::Affine<Curve>>> as Decode>::decode(&mut bases.as_slice())
+			.map_err(|_| ())?;
+	let scalars = <ArkScale<Vec<<Curve as CurveConfig>::ScalarField>> as Decode>::decode(
+		&mut scalars.as_slice(),
+	)
+	.map_err(|_| ())?;
+
+	let result = <twisted_edwards::Projective<Curve> as VariableBaseMSM>::msm(&bases.0, &scalars.0)
+		.map_err(|_| ())?;
+
+	let result: ArkScaleProjective<twisted_edwards::Projective<Curve>> = result.into();
+	Ok(result.encode())
+}
+
+pub(crate) fn mul_projective_generic<Group: SWCurveConfig>(
+	base: Vec<u8>,
+	scalar: Vec<u8>,
+) -> Result<Vec<u8>, ()> {
+	let base = <ArkScaleProjective<short_weierstrass::Projective<Group>> as Decode>::decode(
+		&mut base.as_slice(),
+	)
+	.map_err(|_| ())?;
+	let scalar = <ArkScale<Vec<u64>> as Decode>::decode(&mut scalar.as_slice()).map_err(|_| ())?;
+
+	let result = <Group as SWCurveConfig>::mul_projective(&base.0, &scalar.0);
+
+	let result: ArkScaleProjective<short_weierstrass::Projective<Group>> = result.into();
+	Ok(result.encode())
+}
+
+pub(crate) fn mul_projective_te_generic<Group: TECurveConfig>(
+	base: Vec<u8>,
+	scalar: Vec<u8>,
+) -> Result<Vec<u8>, ()> {
+	let base = <ArkScaleProjective<twisted_edwards::Projective<Group>> as Decode>::decode(
+		&mut base.as_slice(),
+	)
+	.map_err(|_| ())?;
+	let scalar = <ArkScale<Vec<u64>> as Decode>::decode(&mut scalar.as_slice()).map_err(|_| ())?;
+
+	let result = <Group as TECurveConfig>::mul_projective(&base.0, &scalar.0);
+
+	let result: ArkScaleProjective<twisted_edwards::Projective<Group>> = result.into();
+	Ok(result.encode())
+}