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Hello,

While trying to run in cocks_pinch_example.py the first example cp.gen_params_from_r(r,k) using large values for r, for example a 256-bit long integer, I run into this issue :

   5361         """
   5362         if isinstance(b, int):
-> 5363             return mpz_kronecker_si(self.value, b)
   5364         if not isinstance(b, Integer):
   5365             b = Integer(b)

OverflowError: Python int too large to convert to C long

Have you run into this issue before ? If yes, how can you handle large integers that fit the standard recommandation of 128-bit level ?

Thanks !

The current implementation in ecfactory to search BN curves did not evaluate the subgroup security, as discussed in https://eprint.iacr.org/2015/247.pdf.

Mainly, pairing might be subject to subgroup attacks. To prevent such attacks, this paper adds additional criteria on selecting good curves, by also requiring the h of the G_2 and G_T to have a large prime factor. This new requirement places a lot of constraints on the choices of parameters.

Note that the parameters of BN254 (which indeed has a historical meaning) in arkworks do not have such properties, since those parameters are sampled before this paper.

Therefore, it is left as a TODO to add BN curve searching algorithms that have subgroup security guarantees.