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- #include "libsnark_headers.hpp"
- using namespace libsnark;
- // There are two types of values:
- // _constants_ are values known at circuit generation time; they
- // are global constants known to everyone
- // _variables_ are values that change in each use of the circuit;
- // they have two subtypes:
- //
- // _public variables_ are values known to both the prover
- // and verifier but change in each use of the circuit
- // _private variables_ are values known only to the prover
- // and change in each use of the circuit
- // Double a constant EC point (inx,iny) to yield (outx,outy). The input
- // point must not be the point at infinity.
- template<typename FieldT>
- static void ec_double_point(FieldT &outx, FieldT &outy,
- const FieldT &inx, const FieldT &iny)
- {
- FieldT xsq = inx.squared();
- FieldT lambda = (xsq * 3 - 3) * (iny * 2).inverse();
- outx = lambda.squared() - inx * 2;
- outy = lambda * (inx - outx) - iny;
- }
- // Add constant EC points (inx, iny) and (addx, addy) to yield (outx, outy).
- // inx and addx must not be equal.
- template<typename FieldT>
- static void ec_add_points(FieldT &outx, FieldT &outy,
- const FieldT &inx, const FieldT &iny,
- const FieldT &addx, const FieldT &addy)
- {
- FieldT lambda = (addy - iny) * (addx - inx).inverse();
- outx = lambda.squared() - (addx + inx);
- outy = lambda * (inx - outx) - iny;
- }
- // Double the variable EC point (inx,iny) to yield (outx,outy). The
- // input point must not be the point at infinity.
- template<typename FieldT>
- class ec_double_gadget : public gadget<FieldT> {
- private:
- pb_variable<FieldT> lambda, inxsq;
- public:
- const pb_variable<FieldT> outx, outy, inx, iny;
- ec_double_gadget(protoboard<FieldT> &pb,
- const pb_variable<FieldT> &outx,
- const pb_variable<FieldT> &outy,
- const pb_linear_combination<FieldT> &inx,
- const pb_linear_combination<FieldT> &iny) :
- gadget<FieldT>(pb, "ec_double_gadget"), outx(outx), outy(outy),
- inx(inx), iny(iny)
- {
- // Allocate variables to protoboard
- // The strings (like "x") are only for debugging purposes
-
- lambda.allocate(this->pb, "lambda");
- inxsq.allocate(this->pb, "inxsq");
- }
- void generate_r1cs_constraints()
- {
- // inxsq = inx * inx
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(inx, inx, inxsq));
- // 2 * iny * lambda = 3 * inxsq - 3 (a = -3 on our curve)
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(2 * iny, lambda, 3 * inxsq - 3));
- // outx = lambda^2 - 2 * inx
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(lambda, lambda, outx + 2 * inx));
- // outy = lambda * (inx - outx) - iny
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(lambda, inx - outx, outy + iny));
- }
- void generate_r1cs_witness()
- {
- this->pb.val(inxsq) = this->pb.lc_val(inx) * this->pb.lc_val(inx);
- this->pb.val(lambda) = (this->pb.val(inxsq) * 3 - 3) * (this->pb.lc_val(iny) * 2).inverse();
- this->pb.val(outx) = this->pb.val(lambda).squared() - this->pb.lc_val(inx) * 2;
- this->pb.val(outy) = this->pb.val(lambda) * (this->pb.lc_val(inx) - this->pb.val(outx)) - this->pb.lc_val(iny);
- }
- };
- // Add the variable EC point (addx,addy) to the variable EC point
- // (inx,iny) to yield (outx,outy). The input point must not be the
- // point at infinity.
- template<typename FieldT>
- class ec_add_gadget : public gadget<FieldT> {
- private:
- pb_variable<FieldT> lambda;
- public:
- const pb_variable<FieldT> outx, outy;
- const pb_linear_combination<FieldT> inx, iny, addx, addy;
- ec_add_gadget(protoboard<FieldT> &pb,
- const pb_variable<FieldT> &outx,
- const pb_variable<FieldT> &outy,
- const pb_linear_combination<FieldT> &inx,
- const pb_linear_combination<FieldT> &iny,
- const pb_linear_combination<FieldT> &addx,
- const pb_linear_combination<FieldT> &addy) :
- gadget<FieldT>(pb, "ec_add_gadget"),
- outx(outx), outy(outy), inx(inx), iny(iny), addx(addx), addy(addy)
- {
- // Allocate variables to protoboard
- // The strings (like "x") are only for debugging purposes
-
- lambda.allocate(this->pb, "lambda");
- }
- void generate_r1cs_constraints()
- {
- // (addx - inx) * lambda = addy - iny
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(addx - inx, lambda, addy - iny));
- // outx = lambda^2 - (addx + inx)
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(lambda, lambda, outx + addx + inx));
- // outy = lambda * (inx - outx) - iny
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(lambda, inx - outx, outy + iny));
- }
- void generate_r1cs_witness()
- {
- this->pb.val(lambda) = (this->pb.lc_val(addy) - this->pb.lc_val(iny)) * (this->pb.lc_val(addx) - this->pb.lc_val(inx)).inverse();
- this->pb.val(outx) = this->pb.val(lambda).squared() - (this->pb.lc_val(addx) + this->pb.lc_val(inx));
- this->pb.val(outy) = this->pb.val(lambda) * (this->pb.lc_val(inx) - this->pb.val(outx)) - this->pb.lc_val(iny);
- }
- };
- // Add the variable EC point P to the constant EC point (inx,iny) to
- // yield (outx,outy). The input point must not be the point at
- // infinity.
- template<typename FieldT>
- class ec_constant_add_gadget : public gadget<FieldT> {
- private:
- pb_variable<FieldT> lambda;
- public:
- const pb_variable<FieldT> outx, outy;
- const pb_linear_combination<FieldT> inx, iny;
- const FieldT Px, Py;
- ec_constant_add_gadget(protoboard<FieldT> &pb,
- const pb_variable<FieldT> &outx,
- const pb_variable<FieldT> &outy,
- const pb_linear_combination<FieldT> &inx,
- const pb_linear_combination<FieldT> &iny,
- const FieldT &Px, const FieldT &Py) :
- gadget<FieldT>(pb, "ec_constant_add_gadget"),
- outx(outx), outy(outy), inx(inx), iny(iny), Px(Px), Py(Py)
- {
- // Allocate variables to protoboard
- // The strings (like "x") are only for debugging purposes
-
- lambda.allocate(this->pb, "lambda");
- }
- void generate_r1cs_constraints()
- {
- // (Px - inx) * lambda = Py - iny
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(Px - inx, lambda, Py - iny));
- // outx = lambda^2 - (Px + inx)
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(lambda, lambda, outx + Px + inx));
- // outy = lambda * (inx - outx) - iny
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(lambda, inx - outx, outy + iny));
- }
- void generate_r1cs_witness()
- {
- this->pb.val(lambda) = (Py - this->pb.lc_val(iny)) * (Px - this->pb.lc_val(inx)).inverse();
- this->pb.val(outx) = this->pb.val(lambda).squared() - (Px + this->pb.lc_val(inx));
- this->pb.val(outy) = this->pb.val(lambda) * (this->pb.lc_val(inx) - this->pb.val(outx)) - this->pb.lc_val(iny);
- }
- };
- // Add nothing or the constant EC point P to the variable EC point
- // (inx,iny) to yield (outx,outy). The input point must not be the
- // point at infinity. The input bit do_add controls whether the
- // addition is done.
- template<typename FieldT>
- class ec_conditional_constant_add_gadget : public gadget<FieldT> {
- private:
- pb_variable<FieldT> sumx, sumy;
- std::vector<ec_constant_add_gadget<FieldT> > adder;
- public:
- const pb_variable<FieldT> outx, outy;
- const pb_linear_combination<FieldT> inx, iny;
- const pb_variable<FieldT> do_add;
- const FieldT Px, Py;
- ec_conditional_constant_add_gadget(protoboard<FieldT> &pb,
- const pb_variable<FieldT> &outx,
- const pb_variable<FieldT> &outy,
- const pb_linear_combination<FieldT> &inx,
- const pb_linear_combination<FieldT> &iny,
- const pb_variable<FieldT> &do_add,
- const FieldT &Px, const FieldT &Py) :
- gadget<FieldT>(pb, "ec_conditional_constant_add_gadget"),
- outx(outx), outy(outy), inx(inx), iny(iny), do_add(do_add),
- Px(Px), Py(Py)
- {
- // Allocate variables to protoboard
- // The strings (like "x") are only for debugging purposes
-
- sumx.allocate(this->pb, "sumx");
- sumy.allocate(this->pb, "sumy");
- adder.emplace_back(this->pb, sumx, sumy, inx, iny, Px, Py);
- }
- void generate_r1cs_constraints()
- {
- // Strategy: we always do the addition, but if do_add = 0, we throw
- // it away later.
- adder[0].generate_r1cs_constraints();
- // Now we want to conditionally move the sum. We want that
- // outx = do_add ? sumx : inx
- // outy = do_add ? sumy : iny
- // so we compute
- // outx = inx + (sumx - inx) * do_add
- // outy = iny + (sumy - iny) * do_add
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(sumx - inx, do_add, outx - inx));
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(sumy - iny, do_add, outy - iny));
- }
- void generate_r1cs_witness()
- {
- adder[0].generate_r1cs_witness();
- bool move = this->pb.val(do_add) != FieldT(0);
- this->pb.val(outx) = move ? this->pb.val(sumx) : this->pb.lc_val(inx);
- this->pb.val(outy) = move ? this->pb.val(sumy) : this->pb.lc_val(iny);
- }
- };
- // Add nothing, or one of the constant EC points P1, P2, or P3 to the EC
- // point (inx,iny) to yield (outx,outy). The input point must not be
- // the point at infinity. The two input bits add1 and add2 control what
- // is added. Typically, P3 will equal P1+P2, in which case this gadget
- // does two conditional constant adds simultaneously in just 6 constraints.
- template<typename FieldT>
- class ec_add_P123_gadget : public gadget<FieldT> {
- private:
- pb_variable<FieldT> lambda, sumx, sumy, move;
- public:
- const pb_variable<FieldT> outx, outy;
- const pb_linear_combination<FieldT> inx, iny;
- const pb_variable<FieldT> add1, add2;
- const FieldT P1x, P1y, P2x, P2y, P3x, P3y;
- ec_add_P123_gadget(protoboard<FieldT> &pb,
- const pb_variable<FieldT> &outx,
- const pb_variable<FieldT> &outy,
- const pb_linear_combination<FieldT> &inx,
- const pb_linear_combination<FieldT> &iny,
- const pb_variable<FieldT> &add1,
- const pb_variable<FieldT> &add2,
- const FieldT &P1x, const FieldT &P1y,
- const FieldT &P2x, const FieldT &P2y,
- const FieldT &P3x, const FieldT &P3y) :
- gadget<FieldT>(pb, "ec_add_P123_gadget"),
- outx(outx), outy(outy), inx(inx), iny(iny), add1(add1), add2(add2),
- P1x(P1x), P1y(P1y), P2x(P2x), P2y(P2y), P3x(P3x), P3y(P3y)
- {
- // Allocate variables to protoboard
- // The strings (like "x") are only for debugging purposes
-
- lambda.allocate(this->pb, "lambda");
- sumx.allocate(this->pb, "sumx");
- sumy.allocate(this->pb, "sumy");
- move.allocate(this->pb, "move");
- }
- void generate_r1cs_constraints()
- {
- // Strategy: if add1 = add2 = 0, we compute some nonsense but throw
- // it away later. Otherwise, the coordinates of the point to add
- // are a _linear_ function of add1 and add2 (since P1, P2, and P3
- // are public constants)
- // In particular, the point to add is ( (P3x - P2x) * add1 + (P3x -
- // P1x) * add2 + (P1x + P2x - P3x), (P3y - P2y) * add1 + (P3y - P1y) *
- // add2 + (P1y + P2y - P3y))
- // (addx - inx) * lambda = addy - iny
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>((P3x - P2x) * add1 + (P3x - P1x) * add2 + (P1x + P2x - P3x) - inx, lambda, (P3y - P2y) * add1 + (P3y - P1y) * add2 + (P1y + P2y - P3y) - iny));
- // sumx = lambda^2 - (addx + inx)
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(lambda, lambda, sumx + (P3x - P2x) * add1 + (P3x - P1x) * add2 + (P1x + P2x - P3x) + inx));
- // sumy = lambda * (inx - sumx) - iny
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(lambda, inx - sumx, sumy + iny));
- // Now we want to conditionally move the sum. We want that
- // outx = (add1 || add2) ? sumx : inx
- // outy = (add1 || add2) ? sumy : iny
- // so we compute move = add1 || add2, and then
- // outx = inx + (sumx - inx) * move
- // outy = iny + (sumy - iny) * move
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(1 - add1, 1 - add2, 1 - move));
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(sumx - inx, move, outx - inx));
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(sumy - iny, move, outy - iny));
- }
- void generate_r1cs_witness()
- {
- FieldT addxval = (P3x - P2x) * this->pb.val(add1) + (P3x - P1x) * this->pb.val(add2) + (P1x + P2x - P3x);
- FieldT addyval = (P3y - P2y) * this->pb.val(add1) + (P3y - P1y) * this->pb.val(add2) + (P1y + P2y - P3y);
- this->pb.val(lambda) = (addyval - this->pb.lc_val(iny)) * (addxval - this->pb.lc_val(inx)).inverse();
- this->pb.val(sumx) = this->pb.val(lambda).squared() - (addxval + this->pb.lc_val(inx));
- this->pb.val(sumy) = this->pb.val(lambda) * (this->pb.lc_val(inx) - this->pb.val(sumx)) - this->pb.lc_val(iny);
- bool a1 = this->pb.val(add1) != FieldT(0);
- bool a2 = this->pb.val(add2) != FieldT(0);
- this->pb.val(move) = a1 || a2;
- this->pb.val(outx) = (a1 || a2) ? this->pb.val(sumx) : this->pb.lc_val(inx);
- this->pb.val(outy) = (a1 || a2) ? this->pb.val(sumy) : this->pb.lc_val(iny);
- }
- };
- // Compute a*P as (outx, outy) for a given constant point P, given a
- // as a bit vector. The _caller_ is responsible for proving that the
- // elements of avec are bits.
- template<typename FieldT>
- class ec_constant_scalarmul_vec_gadget : public gadget<FieldT> {
- private:
- FieldT Cx, Cy, CPx, CPy;
- pb_variable_array<FieldT> accumx, accumy;
- std::vector<ec_add_P123_gadget<FieldT> > conddoubleadders;
- std::vector<ec_conditional_constant_add_gadget<FieldT> > condsingleadders;
- std::vector<ec_constant_add_gadget<FieldT> > singleadders;
- public:
- const pb_variable<FieldT> outx, outy;
- const pb_variable_array<FieldT> avec;
- const FieldT Px, Py;
- // Strategy: We compute (as compile-time constants) (powers of 2)
- // times P, and then conditionally add them into an accumulator.
- // Because our adder cannot handle the point at infinity O, we start
- // the accumulator with a value of C, whose discrete log with respect
- // to P should be unknown, so that we won't encounter O along the way.
- // (Also, a should not be 0 or the group order.) We actually start
- // the accumulator with either C or C+P depending on avec[0], so we
- // get the first conditional add "for free". Then we use the
- // ec_add_P123_gadget to do the conditional adds two at a time (at a
- // cost of 6 constraints per pair, as opposed to 5 for a single
- // conditional add). If the length of avec is even, then there will
- // be one left over, and we do a single conditional add for that one.
- // Finally, we add the public point -C.
- ec_constant_scalarmul_vec_gadget(protoboard<FieldT> &pb,
- const pb_variable<FieldT> &outx,
- const pb_variable<FieldT> &outy,
- const pb_variable_array<FieldT> &avec,
- const FieldT &Px, const FieldT &Py) :
- gadget<FieldT>(pb, "ec_constant_scalarmul_vec_gadget"),
- // Precomputed coordinates of C
- Cx(2),
- Cy("4950745124018817972378217179409499695353526031437053848725554590521829916331"),
- outx(outx), outy(outy), avec(avec), Px(Px), Py(Py)
- {
- size_t numbits = avec.size();
- accumx.allocate(this->pb, numbits/2+1, "accumx");
- accumy.allocate(this->pb, numbits/2+1, "accumy");
- ec_add_points(CPx, CPy, Cx, Cy, Px, Py);
- FieldT twoiPx, twoiPy, twoi1Px, twoi1Py, twoi3Px, twoi3Py;
- size_t i = 1;
- ec_double_point(twoiPx, twoiPy, Px, Py);
- while(i < numbits) {
- // Invariants: i is odd, and twoiP = 2^i * P
- // Compute twoi1P = 2^{i+1} * P = 2 * twoiP and
- // twoi3P = 2^i * 3 * P = 3 * twoiP
- ec_double_point(twoi1Px, twoi1Py, twoiPx, twoiPy);
- ec_add_points(twoi3Px, twoi3Py, twoi1Px, twoi1Py, twoiPx, twoiPy);
- if (i == numbits-1) {
- // There's only one bit of avec left; use a single conditional
- // add.
- condsingleadders.emplace_back(this->pb,
- accumx[(i+1)/2], accumy[(i+1)/2],
- accumx[(i-1)/2], accumy[(i-1)/2],
- avec[i],
- twoiPx, twoiPy);
- } else {
- conddoubleadders.emplace_back(this->pb,
- accumx[(i+1)/2], accumy[(i+1)/2],
- accumx[(i-1)/2], accumy[(i-1)/2],
- avec[i], avec[i+1],
- twoiPx, twoiPy, twoi1Px, twoi1Py, twoi3Px, twoi3Py);
- }
- ec_double_point(twoiPx, twoiPy, twoi1Px, twoi1Py);
- i += 2;
- }
- // If numbits is even, the output so far is in accum[(numbits)/2].
- // If numbits is odd, it is in accum[(numbits-1)/2]. So in either
- // case, it is in accum[numbits/2].
- singleadders.emplace_back(this->pb,
- outx, outy, accumx[numbits/2], accumy[numbits/2],
- Cx, -Cy);
- }
- void generate_r1cs_constraints()
- {
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(Cx + (CPx-Cx) * avec[0], 1, accumx[0]));
- this->pb.add_r1cs_constraint(r1cs_constraint<FieldT>(Cy + (CPy-Cy) * avec[0], 1, accumy[0]));
- for (auto&& gadget : conddoubleadders) {
- gadget.generate_r1cs_constraints();
- }
- for (auto&& gadget : condsingleadders) {
- gadget.generate_r1cs_constraints();
- }
- for (auto&& gadget : singleadders) {
- gadget.generate_r1cs_constraints();
- }
- }
- void generate_r1cs_witness()
- {
- this->pb.val(accumx[0]) = Cx + (CPx-Cx) * this->pb.val(avec[0]);
- this->pb.val(accumy[0]) = Cy + (CPy-Cy) * this->pb.val(avec[0]);
- for (auto&& gadget : conddoubleadders) {
- gadget.generate_r1cs_witness();
- }
- for (auto&& gadget : condsingleadders) {
- gadget.generate_r1cs_witness();
- }
- for (auto&& gadget : singleadders) {
- gadget.generate_r1cs_witness();
- }
- }
- };
- // Compute a*P as (outx, outy) for a given constant point P, given a
- // as a field element.
- template<typename FieldT>
- class ec_constant_scalarmul_gadget : public gadget<FieldT> {
- private:
- pb_variable_array<FieldT> avec;
- std::vector<packing_gadget<FieldT> > packers;
- std::vector<ec_constant_scalarmul_vec_gadget<FieldT> > vecgadget;
- public:
- const pb_variable<FieldT> outx, outy, a;
- const FieldT Px, Py;
- ec_constant_scalarmul_gadget(protoboard<FieldT> &pb,
- const pb_variable<FieldT> &outx,
- const pb_variable<FieldT> &outy,
- const pb_variable<FieldT> &a,
- const FieldT &Px, const FieldT &Py) :
- gadget<FieldT>(pb, "ec_constant_scalarmul_gadget"),
- outx(outx), outy(outy), a(a), Px(Px), Py(Py)
- {
- // Allocate variables to protoboard
- // The strings (like "x") are only for debugging purposes
-
- size_t numbits = FieldT::num_bits;
- avec.allocate(this->pb, numbits, "avec");
- packers.emplace_back(this->pb, avec, a);
- vecgadget.emplace_back(this->pb, outx, outy, avec, Px, Py);
- }
- void generate_r1cs_constraints()
- {
- packers[0].generate_r1cs_constraints(true);
- vecgadget[0].generate_r1cs_constraints();
- }
- void generate_r1cs_witness()
- {
- packers[0].generate_r1cs_witness_from_packed();
- vecgadget[0].generate_r1cs_witness();
- }
- };
- // Compute a*G + b*H as (outx, outy), given a and b as field elements.
- template<typename FieldT>
- class ec_pedersen_gadget : public gadget<FieldT> {
- private:
- pb_variable<FieldT> aoutx, aouty, boutx, bouty;
- std::vector<ec_constant_scalarmul_gadget<FieldT> > mulgadgets;
- std::vector<ec_add_gadget<FieldT> > addgadget;
- const FieldT Gx, Gy, Hx, Hy;
- public:
- const pb_variable<FieldT> outx, outy, a, b;
- ec_pedersen_gadget(protoboard<FieldT> &pb,
- const pb_variable<FieldT> &outx,
- const pb_variable<FieldT> &outy,
- const pb_variable<FieldT> &a,
- const pb_variable<FieldT> &b) :
- gadget<FieldT>(pb, "ec_pedersen_gadget"),
- outx(outx), outy(outy), a(a), b(b),
- // Precomputed coordinates of G and H
- Gx(0),
- Gy("11977228949870389393715360594190192321220966033310912010610740966317727761886"),
- Hx(1),
- Hy("21803877843449984883423225223478944275188924769286999517937427649571474907279")
- {
- // Allocate variables to protoboard
- // The strings (like "x") are only for debugging purposes
-
- aoutx.allocate(this->pb, "aoutx");
- aouty.allocate(this->pb, "aouty");
- boutx.allocate(this->pb, "boutx");
- bouty.allocate(this->pb, "bouty");
- mulgadgets.emplace_back(this->pb, aoutx, aouty, a, Gx, Gy);
- mulgadgets.emplace_back(this->pb, boutx, bouty, b, Hx, Hy);
- addgadget.emplace_back(this->pb, outx, outy, aoutx, aouty, boutx, bouty);
- }
- void generate_r1cs_constraints()
- {
- mulgadgets[0].generate_r1cs_constraints();
- mulgadgets[1].generate_r1cs_constraints();
- addgadget[0].generate_r1cs_constraints();
- }
- void generate_r1cs_witness()
- {
- mulgadgets[0].generate_r1cs_witness();
- mulgadgets[1].generate_r1cs_witness();
- addgadget[0].generate_r1cs_witness();
- }
- };
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