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pay-to-sudoku
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Enforce that the solution is a subset of the puzzle

This commit is contained in:
Sean Bowe 2015-12-04 22:33:29 -07:00
parent 84d1e5b519
commit b4566fa446
2 changed files with 53 additions and 0 deletions
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3
src/gadget.hpp
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@ -15,6 +15,9 @@ public:
std::vector<pb_variable_array<FieldT>> puzzle_values;
std::vector<pb_variable_array<FieldT>> solution_values;
pb_variable_array<FieldT> puzzle_enforce;
pb_linear_combination_array<FieldT> puzzle_enforce_as;
l_gadget(protoboard<FieldT> &pb, unsigned int n);
void generate_r1cs_constraints();

50
src/gadget.tcc
View File

@ -11,6 +11,9 @@ l_gadget<FieldT>::l_gadget(protoboard<FieldT> &pb, unsigned int n) :
this->pb.set_input_sizes(input_size_in_field_elements);
}
puzzle_enforce.allocate(pb, n*n, "puzzle solution subset enforcement");
puzzle_enforce_as.reserve(n*n);
puzzle_values.resize(n*n);
solution_values.resize(n*n);
@ -27,6 +30,35 @@ l_gadget<FieldT>::l_gadget(protoboard<FieldT> &pb, unsigned int n) :
template<typename FieldT>
void l_gadget<FieldT>::generate_r1cs_constraints()
{
std::vector<linear_combination<FieldT>> puzzle_numbers;
std::vector<linear_combination<FieldT>> solution_numbers;
for (unsigned int i = 0; i < (dimension*dimension); i++) {
for (unsigned int j = 0; j < 8; j++) {
// ensure bitness
generate_boolean_r1cs_constraint<FieldT>(this->pb, solution_values[i][j], "solution_bitness");
}
puzzle_numbers.push_back(pb_packing_sum<FieldT>(pb_variable_array<FieldT>(puzzle_values[i].rbegin(), puzzle_values[i].rend())));
solution_numbers.push_back(pb_packing_sum<FieldT>(pb_variable_array<FieldT>(solution_values[i].rbegin(), solution_values[i].rend())));
// enforce solution is subset of puzzle
// puzzle_numbers[i] must be 0 or 1
generate_boolean_r1cs_constraint<FieldT>(this->pb, puzzle_enforce[i], "enforcement bitness");
// puzzle_numbers[i] must be 1 if the puzzle value is nonzero
this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(puzzle_numbers[i], 1 - puzzle_enforce[i], 0), FMT(this->annotation_prefix, " balance"));
// we must be able to construct an inv such that
// solution_numbers[i] * puzzle_enforce[i] = inv
// puzzle_numbers[i] * puzzle_enforce[i] = inv
// to enforce that the solutions are equal if puzzle_enforce[i] is 1
// or that they can be unequal if puzzle_enforce[i] is 0
this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(solution_numbers[i], puzzle_enforce[i], puzzle_enforce_as[i]), FMT(this->annotation_prefix, " balance"));
this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(puzzle_numbers[i], puzzle_enforce[i], puzzle_enforce_as[i]), FMT(this->annotation_prefix, " balance"));
}
unpack_inputs->generate_r1cs_constraints(true);
}
@ -42,6 +74,24 @@ void l_gadget<FieldT>::generate_r1cs_witness(std::vector<bit_vector> &input_puzz
assert(input_solution_values[i].size() == 8);
puzzle_values[i].fill_with_bits(this->pb, input_puzzle_values[i]);
solution_values[i].fill_with_bits(this->pb, input_solution_values[i]);
// if any of the bits of the input puzzle value is nonzero,
// we must enforce it
bool enforce = false;
for (unsigned int j = 0; j < 8; j++) {
if (input_puzzle_values[i][j]) {
enforce = true;
break;
}
}
this->pb.val(puzzle_enforce[i]) = enforce ? FieldT::one() : FieldT::zero();
pb_linear_combination<FieldT> enforce_as;
enforce_as.assign(this->pb, pb_packing_sum<FieldT>(pb_variable_array<FieldT>(solution_values[i].rbegin(), solution_values[i].rend())) * this->pb.val(puzzle_enforce[i]));
enforce_as.evaluate(this->pb);
puzzle_enforce_as.emplace_back(enforce_as);
}
unpack_inputs->generate_r1cs_witness_from_bits();