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355 mnt4 mnt6 pairing component #357

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355 mnt4 mnt6 pairing component #357

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ebccfac
Working MNT4 pairing components: Miller loop and Final exponentiation…
vo-nil Mar 21, 2024
cd1edb9
cmake submodule sync with master #355
vo-nil Apr 22, 2024
059533f
update naming #355
vo-nil Apr 22, 2024
56221db
Refactored MNT4 code and added MNT6 exponentiation #355
vo-nil Apr 26, 2024
ea0388c
Updates for review, working MNT6 miller loop #355
vo-nil Apr 26, 2024
0de7980
Warnings fixed, removed zero witnesses, components proper stacking #355
vo-nil Apr 29, 2024
73036c2
Comments clarification #355
vo-nil Apr 29, 2024
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76 changes: 76 additions & 0 deletions include/nil/blueprint/components/algebra/fields/plonk/non_native/detail/abstract_fp2.hpp
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//---------------------------------------------------------------------------//
// Copyright (c) 2023 Alexey Yashunsky <a.yashunsky@nil.foundation>
// Copyright (c) 2024 Vasiliy Olekhov <vasiliy.olekhov@nil.foundation>
//
// MIT License
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//---------------------------------------------------------------------------//
// @file Declaration of F_p^2 elements over an abstract entity (to be used with constraints)
// with F_p^2 = F_p[u]/(u^2 - non_residue).
//---------------------------------------------------------------------------//

#ifndef CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_ABSTRACT_FP2_HPP
#define CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_ABSTRACT_FP2_HPP

#include <array>
#include <nil/crypto3/algebra/fields/fp2.hpp>

namespace nil {
namespace blueprint {
namespace components {
namespace detail {
template<typename T, typename UnderlyingFieldType>
class abstract_fp2_element {
public:
using policy_type_fp2 = crypto3::algebra::fields::fp2<UnderlyingFieldType>;
std::array<T,2> data;

T& operator[](std::size_t idx) {
return data[idx];
}
const T& operator[](std::size_t idx) const {
return data[idx];
}


constexpr abstract_fp2_element operator*(const abstract_fp2_element& other) {
return { data[0] * other[0] + policy_type_fp2::extension_policy::non_residue * data[1] * other[1],
data[0] * other[1] + data[1] * other[0]};
}
constexpr abstract_fp2_element operator*(const int x) {
return { data[0]*x, data[1]*x };
}
friend abstract_fp2_element operator*(const int x, const abstract_fp2_element& e) {
return { e[0]*x, e[1]*x };
}
constexpr abstract_fp2_element operator+(const abstract_fp2_element& other) {
return { data[0] + other[0], data[1] + other[1] };
}
constexpr abstract_fp2_element operator-(const abstract_fp2_element& other) {
return { data[0] - other[0], data[1] - other[1] };
}
};

} // namespace detail
} // namespace components
} // namespace blueprint
} // namespace nil

#endif // CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_ABSTRACT_FP2_HPP
79 changes: 79 additions & 0 deletions include/nil/blueprint/components/algebra/fields/plonk/non_native/detail/abstract_fp3.hpp
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//---------------------------------------------------------------------------//
// Copyright (c) 2024 Vasiliy Olekhov <vasiliy.olekhov@nil.foundation>
//
// MIT License
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//---------------------------------------------------------------------------//
// @file Declaration of F_p^3 elements over an abstract entity (to be used with constraints)
// with F_p^3 = F_p[u]/(u^3 + non_residue).
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I think, it should be "minus non-residue", not "plus", i.e. F_p[u]/(u^3 - non_residue) instead of F_p[u]/(u^3 + non_residue)

//---------------------------------------------------------------------------//

#ifndef CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_ABSTRACT_FP3_HPP
#define CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_ABSTRACT_FP3_HPP

#include <array>
#include <nil/crypto3/algebra/fields/fp3.hpp>

namespace nil {
namespace blueprint {
namespace components {
namespace detail {
template<typename T, typename UnderlyingFieldType>
class abstract_fp3_element {
public:
using policy_type_fp3 = crypto3::algebra::fields::fp3<UnderlyingFieldType>;
std::array<T,3> data;

T& operator[](std::size_t idx) {
return data[idx];
}
const T& operator[](std::size_t idx) const {
return data[idx];
}

constexpr abstract_fp3_element operator*(abstract_fp3_element const& other) {
auto s = policy_type_fp3::extension_policy::non_residue;
return {
data[0]*other[0] + s*(data[1]*other[2] + data[2]*other[1]),
data[0]*other[1] + data[1]*other[0] + s*data[2]*other[2],
data[0]*other[2] + data[1]*other[1] + data[2]*other[0]
};
}

constexpr abstract_fp3_element operator*(const int x) {
return { data[0]*x, data[1]*x, data[2]*x };
}
friend abstract_fp3_element operator*(const int x, abstract_fp3_element const& e) {
return { e[0]*x, e[1]*x, e[2]*x };
}
constexpr abstract_fp3_element operator+(abstract_fp3_element const& other) {
return { data[0] + other[0], data[1] + other[1], data[2] + other[2] };
}
constexpr abstract_fp3_element operator-(abstract_fp3_element const& other) {
return { data[0] - other[0], data[1] - other[1], data[2] - other[2] };
}
};

} // namespace detail
} // namespace components
} // namespace blueprint
} // namespace nil

#endif // CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_ABSTRACT_FP3_HPP
87 changes: 87 additions & 0 deletions include/nil/blueprint/components/algebra/fields/plonk/non_native/detail/abstract_fp4.hpp
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//---------------------------------------------------------------------------//
// Copyright (c) 2024 Vasiliy Olekhov <vasiliy.olekhov@nil.foundation>
//
// MIT License
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//---------------------------------------------------------------------------//
// @file Declaration of F_p^4 elements over an abstract entity (to be used with constraints)
// with F_p^4 = Fp^2 over Fp^2:
// Fp^4 = Fp^2[x]/(x^2 - u), u = (0,1)
// Fp^2 = Fp[y]/(y^2 - v), v = 17 (0x11), u^2 = v
//---------------------------------------------------------------------------//

#ifndef CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_ABSTRACT_FP4_HPP
#define CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_ABSTRACT_FP4_HPP

#include <array>
#include <cstddef>

#include <nil/crypto3/algebra/fields/fp4.hpp>

namespace nil {
namespace blueprint {
namespace components {
namespace detail {

template<typename T, typename UnderlyingFieldType>
class abstract_fp4_element{
public:
using policy_type_fp4 = crypto3::algebra::fields::fp4<UnderlyingFieldType>;
std::array<T,4> x;

T& operator[](std::size_t idx) {
return x[idx];
}
const T& operator[](std::size_t idx) const {
return x[idx];
}

constexpr abstract_fp4_element operator*(abstract_fp4_element const& y) {
// Devegili et al - Multiplication and squaring in pairing-friendly fields
// https://eprint.iacr.org/2006/471.pdf
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I'd say the reference is misleading because we don't use any optimisation here. Just the "schoolbook" formulas.

constexpr auto s = policy_type_fp4::extension_policy::non_residue;
auto d00 = x[0b00]*y[0b00] + s*(x[0b01]*y[0b01] + x[0b10]*y[0b11] + x[0b11]*y[0b10]);
auto d01 = x[0b00]*y[0b01] + x[0b10]*y[0b10] + x[0b01]*y[0b00] + s*x[0b11]*y[0b11];
auto d10 = x[0b00]*y[0b10] + x[0b10]*y[0b00] + s*(x[0b01]*y[0b11] + x[0b11]*y[0b01]);
auto d11 = x[0b00]*y[0b11] + x[0b01]*y[0b10] + x[0b10]*y[0b01] + x[0b11]*y[0b00];

return { d00, d01, d10, d11};
}

constexpr abstract_fp4_element operator*(const int a) {
return { x[0]*a, x[1]*a, x[2]*a, x[3]*a };
}
friend abstract_fp4_element operator*(const int a, abstract_fp4_element const& x) {
return { x[0]*a, x[1]*a, x[2]*a, x[3]*a };
}
constexpr abstract_fp4_element operator+(abstract_fp4_element const& y) {
return { x[0] + y[0], x[1] + y[1], x[2] + y[2], x[3] + y[3] };
}
constexpr abstract_fp4_element operator-(abstract_fp4_element const& y) {
return { x[0] - y[0], x[1] - y[1], x[2] - y[2], x[3] - y[3] };
}
};

} // namespace detail
} // namespace components
} // namespace blueprint
} // namespace nil

#endif // CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_abstract_FP4_HPP
98 changes: 98 additions & 0 deletions include/nil/blueprint/components/algebra/fields/plonk/non_native/detail/abstract_fp6.hpp
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//---------------------------------------------------------------------------//
// Copyright (c) 2024 Vasiliy Olekhov <vasiliy.olekhov@nil.foundation>
//
// MIT License
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//---------------------------------------------------------------------------//
// @file Declaration of F_p^6 elements over an abstract entity (to be used with constraints)
// with F_p^6 = Fp^2 over Fp^3:
// Fp^6 = Fp^2[x]/(x^2 - u), u = (0,1,0)
// Fp^3 = Fp[y]/(y^3 - v), for MNT6: v = 5
//---------------------------------------------------------------------------//

#ifndef CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_ABSTRACT_FP4_HPP
#define CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_ABSTRACT_FP4_HPP

#include <array>
#include <cstddef>

#include <nil/crypto3/algebra/fields/fp6_2over3.hpp>

namespace nil {
namespace blueprint {
namespace components {
namespace detail {

template<typename T, typename UnderlyingFieldType>
class abstract_fp6_element{
public:
using policy_type_fp6 = crypto3::algebra::fields::fp6_2over3<UnderlyingFieldType>;
std::array<T, 6> x;

T& operator[](std::size_t idx) {
return x[idx];
}
const T& operator[](std::size_t idx) const {
return x[idx];
}

constexpr abstract_fp6_element operator*(abstract_fp6_element const& y) {
// Devegili et al - Multiplication and squaring in pairing-friendly fields
// https://eprint.iacr.org/2006/471.pdf, page 15, direct sextic
// Take note on isomorphism between a (Fp 2 over 3) and c (direct sextic)
// Indices map is on page 17
constexpr std::size_t
_0 = 0, _1 = 3, _2 = 1,
_3 = 4, _4 = 2, _5 = 5;

constexpr auto s = policy_type_fp6::extension_policy::non_residue;

T c[6] = {
x[_0]*y[_0] + s*(x[_1]*y[_5] + x[_2]*y[_4] + x[_3]*y[_3] + x[_4]*y[_2] + x[_5]*y[_1]),
x[_0]*y[_1] + x[_1]*y[_0] + s*(x[_2]*y[_5] + x[_3]*y[_4] + x[_4]*y[_3] + x[_5]*y[_2]),
x[_0]*y[_2] + x[_1]*y[_1] + x[_2]*y[_0] + s*(x[_3]*y[_5] + x[_4]*y[_4] + x[_5]*y[_3]),
x[_0]*y[_3] + x[_1]*y[_2] + x[_2]*y[_1] + x[_3]*y[_0] + s*(x[_4]*y[_5] + x[_5]*y[_4]),
x[_0]*y[_4] + x[_1]*y[_3] + x[_2]*y[_2] + x[_3]*y[_1] + x[_4]*y[_0] + s* x[_5]*y[_5],
x[_0]*y[_5] + x[_1]*y[_4] + x[_2]*y[_3] + x[_3]*y[_2] + x[_4]*y[_1] + x[_5]*y[_0]
};

return { c[0], c[2], c[4], c[1], c[3], c[5]};
}

constexpr abstract_fp6_element operator*(const int a) {
return { x[0]*a, x[1]*a, x[2]*a, x[3]*a, x[4]*a, x[5]*a };
}
friend abstract_fp6_element operator*(const int a, abstract_fp6_element const& x) {
return { x[0]*a, x[1]*a, x[2]*a, x[3]*a, x[4]*a, x[5]*a };
}
constexpr abstract_fp6_element operator+(abstract_fp6_element const& y) {
return { x[0] + y[0], x[1] + y[1], x[2] + y[2], x[3] + y[3], x[4] + y[4], x[5] + y[5]};
}
constexpr abstract_fp6_element operator-(abstract_fp6_element const& y) {
return { x[0] - y[0], x[1] - y[1], x[2] - y[2], x[3] - y[3], x[4] - y[4], x[5] - y[5]};
}
};

} // namespace detail
} // namespace components
} // namespace blueprint
} // namespace nil

#endif // CRYPTO3_BLUEPRINT_COMPONENTS_PLONK_abstract_FP4_HPP
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