Change to zkSNARKs based on groth's generic group construction probably breaks something

[noresistence]

When submitting #53, my code used pequin @ 8813e516cb2827e8a8752f7d025081fa9aefa161. After the fix for #53, I rebuilt the docker container for the current version @ 312e37eba2b29d9f694e6c89ab2c2a6737ab3839. But there, the same basic example that I used in #53 does compile, but proving fails with the following message:

pepper_prover_example: ../thirdparty/libsnark/libsnark/zk_proof_systems/ppzksnark/r1cs_gg_ppzksnark/r1cs_gg_ppzksnark.tcc:406: libsnark::r1cs_gg_ppzksnark_proof<ppT> libsnark::r1cs_gg_ppzksnark_prover(const libsnark::r1cs_gg_ppzksnark_proving_key<ppT>&, libsnark::r1cs_gg_ppzksnark_primary_input<ppT>&, libsnark::r1cs_gg_ppzksnark_auxiliary_input<ppT>&) [with ppT = libff::bn128_pp; libsnark::r1cs_gg_ppzksnark_primary_input<ppT> = std::vector<libff::Fp_model<4l, ((const libff::bigint<4l>&)(& libff::bn128_modulus_r))>, std::allocator<libff::Fp_model<4l, ((const libff::bigint<4l>&)(& libff::bn128_modulus_r))> > >; typename EC_ppT::Fp_type = libff::Fp_model<4l, ((const libff::bigint<4l>&)(& libff::bn128_modulus_r))>; libsnark::r1cs_gg_ppzksnark_auxiliary_input<ppT> = std::vector<libff::Fp_model<4l, ((const libff::bigint<4l>&)(& libff::bn128_modulus_r))>, std::allocator<libff::Fp_model<4l, ((const libff::bigint<4l>&)(& libff::bn128_modulus_r))> > >]: Assertion `!qap_wit.coefficients_for_H[qap_wit.degree()-2].is_zero()' failed.
./docker_execution.sh: line 57:    34 Aborted                 (core dumped) ./bin/pepper_prover_$PROG prove $PROG.pkey $PROG.inputs $PROG.outputs $PROG.proof

[noresistence]

For completeness, this is the example code from #53:

example.h:

#include <stdint.h>

struct In {
    uint8_t input;
};

struct Out {
    uint8_t out;
};

static const uint32_t k[2] = {0x428a2f98,0x71374491};

example.c:

#include <example.h>

void sha256_transform() {
    uint32_t i, t;
    for (i = 0; i < 2; ++i) {
        t = k[i];
    }
}

void sha256_final() {
    sha256_transform();
}

void compute(struct In *input, struct Out *output) {
    uint32_t k;                               /* for-loop index variable */
    sha256_final();
}

[noresistence]

When instead using pequin at 8813e516cb2827e8a8752f7d025081fa9aefa161 and cherry-picking f4af28fdb1ea697bf1db785d0650063016ea3134 on top, the prove will be executed successfully without the error above.

[maxhowald]

The assertion that is failing is here:

https://github.com/scipr-lab/libsnark/blob/bd2a6ca07d4fb72f7b1174d478852234f45ce0b6/libsnark/zk_proof_systems/ppzksnark/r1cs_gg_ppzksnark/r1cs_gg_ppzksnark.tcc#L406

I suspect that when a computation has no constraints with degree 2, the polynomial H degenerates, which causes the assertion to fail.

For example, adding this line to example.c:

output->out = input->input * input->input;

causes the program to run without error, with the output as expected. Commenting out the assertion also makes the original computation work. So this may be a bug in the libsnark library; perhaps the assertion should be removed or conditional on the constraint system containing at least one degree-2 constraint.