Recursive pairing gadgets hard-code MNT4 and MNT6, we need MNT[46]753 too...

[PossiblyHarry]

There are a number of places where the MNT4 and MNT6 parameters are hard-coded into gadgets. While we can use the mnt4 and mnt6 specific gadgets with different curve parameters (as.. they are the same types of curves) I am getting build errors when trying to compile against the MNT[46]753 cycle.

Namely:

• libsnark/gadgetlib1/gadgets/pairing/weierstrass_final_exponentiation.tcc:

  54:     compute_w1.reset(new exponentiation_gadget<FqkT<ppT>, Fp6_variable, Fp6_mul_gadget, Fp6_cyclotomic_sqr_gadget, libff::mnt6_q_limbs>(
   55:         pb, *beta_q, libff::mnt6_final_exponent_last_chunk_w1, *w1, FMT(annotation_prefix, " compute_w1")));
   56  
   57:     compute_w0.reset(new exponentiation_gadget<FqkT<ppT>, Fp6_variable, Fp6_mul_gadget, Fp6_cyclotomic_sqr_gadget, libff::mnt6_q_limbs>(
   58:         pb, (libff::mnt6_final_exponent_last_chunk_is_w0_neg ? *inv_beta : *beta), libff::mnt6_final_exponent_last_chunk_abs_of_w0, *w0, FMT(annotation_prefix, " compute_w0")));
...
 137:     compute_w1.reset(new exponentiation_gadget<FqkT<ppT>, Fp4_variable, Fp4_mul_gadget, Fp4_cyclotomic_sqr_gadget, libff::mnt4_q_limbs>(
  138:         pb, *el_q_3_minus_q, libff::mnt4_final_exponent_last_chunk_w1, *w1, FMT(annotation_prefix, " compute_w1")));
  139:     compute_w0.reset(new exponentiation_gadget<FqkT<ppT>, Fp4_variable, Fp4_mul_gadget, Fp4_cyclotomic_sqr_gadget, libff::mnt4_q_limbs>(
  140:         pb, (libff::mnt4_final_exponent_last_chunk_is_w0_neg ? *el_inv_q_2_minus_1 : *el_q_2_minus_1), libff::mnt4_final_exponent_last_chunk_abs_of_w0, *w0, FMT(annotation_prefix, " compute_w0")));

• libsnark/gadgetlib1/gadgets/pairing/weierstrass_precomputation.hpp:

   69      {
   70          pb_linear_combination<FieldT> c0, c1;
   71:         c0.assign(pb, P.Y * ((libff::mnt4_twist).squared().c0));
   72:         c1.assign(pb, P.Y * ((libff::mnt4_twist).squared().c1));
...
   87          pb_linear_combination<FieldT> c0, c1, c2;
   88:         c0.assign(pb, P.Y * ((libff::mnt6_twist).squared().c0));
   89:         c1.assign(pb, P.Y * ((libff::mnt6_twist).squared().c1));
   90:         c2.assign(pb, P.Y * ((libff::mnt6_twist).squared().c2));

Need to update the gadgets to retrieve the twist parameter from the curve parameters (ppT) rather than hard-coding..

The other locations that are referenced are just for tests... It seems Coda haven't made these changes on their side.

Additionally need to specify types in mnt_pairing_params.hpp for these cycles - have done this already locally, so it's only the remaining places which directly reference libff::mnt[46]_

[PossiblyHarry]

In my branch have made aliases of the following variables in their respective ppT class

• mnt6_final_exponent_last_chunk_abs_of_w0
• mnt6_final_exponent_last_chunk_is_w0_neg
• mnt6_final_exponent_last_chunk_w1
• mnt6_q_limbs
• mnt4_final_exponent_last_chunk_w1
• mnt4_final_exponent_last_chunk_is_w0_neg
• mnt4_final_exponent_last_chunk_abs_of_w0
• mnt4_q_limbs

This means you can use other_curve<ppT>::q_limbs for example.