loose_multiplexing.hpp

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//---------------------------------------------------------------------------//
// Copyright (c) 2018-2021 Mikhail Komarov <nemo@nil.foundation>
// Copyright (c) 2020-2021 Nikita Kaskov <nbering@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
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//
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//---------------------------------------------------------------------------//
 
#ifndef CRYPTO3_ZK_BLUEPRINT_LOOSE_MULTIPLEXING_COMPONENT_HPP
#define CRYPTO3_ZK_BLUEPRINT_LOOSE_MULTIPLEXING_COMPONENT_HPP
 
#include <cassert>
#include <memory>
 
#include <nil/crypto3/zk/components/component.hpp>
#include <nil/crypto3/zk/components/packing.hpp>
#include <nil/crypto3/zk/components/inner_product.hpp>
 
#include <nil/crypto3/multiprecision/number.hpp>
#include <nil/crypto3/zk/snark/relations/constraint_satisfaction_problems/r1cs.hpp>
 
namespace nil {
    namespace crypto3 {
        namespace zk {
            namespace components {
 
                /*
                  loose_multiplexing implements loose multiplexer:
                  index not in bounds -> success_flag = 0
                  index in bounds && success_flag = 1 -> result is correct
                  however if index is in bounds we can also set success_flag to 0 (and then result will be forced to
                  be 0)
                */
                template<typename FieldType>
                class loose_multiplexing : public component<FieldType> {
                public:
                    blueprint_variable_vector<FieldType> alpha;
 
                private:
                    std::shared_ptr<inner_product<FieldType>> compute_result;
 
                public:
                    const blueprint_linear_combination_vector<FieldType> arr;
                    const blueprint_variable<FieldType> index;
                    const blueprint_variable<FieldType> result;
                    const blueprint_variable<FieldType> success_flag;
 
                    loose_multiplexing(blueprint<FieldType> &bp,
                                       const blueprint_linear_combination_vector<FieldType> &arr,
                                       const blueprint_variable<FieldType> &index,
                                       const blueprint_variable<FieldType> &result,
                                       const blueprint_variable<FieldType> &success_flag) :
                        component<FieldType>(bp),
                        arr(arr), index(index), result(result), success_flag(success_flag) {
                        alpha.allocate(bp, arr.size());
                        compute_result.reset(new inner_product<FieldType>(bp, alpha, arr, result));
                    };
 
                    void generate_r1cs_constraints() {
                        /* \alpha_i (index - i) = 0 */
                        for (std::size_t i = 0; i < arr.size(); ++i) {
                            this->bp.add_r1cs_constraint(snark::r1cs_constraint<FieldType>(alpha[i], index - i, 0));
                        }
 
                        /* 1 * (\sum \alpha_i) = success_flag */
                        blueprint_linear_combination<FieldType> a, b, c;
                        a.add_term(blueprint_variable<FieldType>(0));
                        for (std::size_t i = 0; i < arr.size(); ++i) {
                            b.add_term(alpha[i]);
                        }
                        c.add_term(success_flag);
                        this->bp.add_r1cs_constraint(snark::r1cs_constraint<FieldType>(a, b, c));
 
                        /* now success_flag is constrained to either 0 (if index is out of
                           range) or \alpha_i. constrain it and \alpha_i to zero */
                        generate_boolean_r1cs_constraint<FieldType>(this->bp, success_flag);
 
                        /* compute result */
                        compute_result->generate_r1cs_constraints();
                    }
 
                    void generate_r1cs_witness() {
 
                        /* assumes that idx can be fit in ulong; true for our purposes for now */
                        const typename FieldType::value_type valint = this->bp.val(index);
 
                        unsigned long idx = static_cast<unsigned long>(typename FieldType::integral_type(valint.data));
 
                        if (idx >= arr.size() || typename FieldType::integral_type(valint.data) >= arr.size()) {
                            for (std::size_t i = 0; i < arr.size(); ++i) {
                                this->bp.val(alpha[i]) = FieldType::value_type::zero();
                            }
 
                            this->bp.val(success_flag) = FieldType::value_type::zero();
                        } else {
                            for (std::size_t i = 0; i < arr.size(); ++i) {
                                this->bp.val(alpha[i]) =
                                    (i == idx ? FieldType::value_type::one() : FieldType::value_type::zero());
                            }
 
                            this->bp.val(success_flag) = FieldType::value_type::one();
                        }
 
                        compute_result->generate_r1cs_witness();
                    }
                };
 
            }    // namespace components
        }        // namespace zk
    }            // namespace crypto3
}    // namespace nil
#endif    // CRYPTO3_ZK_BLUEPRINT_LOOSE_MULTIPLEXING_COMPONENT_HPP