Library refactor

By @Bhargavasomu from: https://github.com/ethereum/py_ecc/issues/24#issuecomment-442701351

The following things come to my mind.

• The classes FQ, FQP, FQ2 and FQ12 need not be reinitialized every time as they are not dependent on the type of curve or extension. So probably we could have these created in field_elements.py and we could use them everywhere (bn128, optimized_bn128, bls, optimized_bls).
• We could also have a general class BaseCurve, and then maybe every curve (bn128_curve, optimized_bn128_curve, …) could inherit this and make the changes specific to the inherited class.
• We should probably move the constants into a seperate file (constants.py)
• We should also remove the assert statements which are not part of any function, but are part of the script in general, as shown https://github.com/ethereum/py_ecc/blob/067a40261ad39526f6aa8bd69def7d6982993d13/py_ecc/bn128/bn128_pairing.py#L74-L83
• Also the type hinting should be further generalized wherever possible (in terms of removing redundant types; like Optimized_FQPoint2D could be replaced by FQPoint2D). Similary the type hinting should be carried out for the bs12_381 and optimized_bs12_381 submodules.

Also the only difference I see in all the curves is

• Difference in the constants such as b, b2, b12, G2, G12 …
• Difference in the twist function

@vbuterin are my facts right or am I missing anything. @pipermerriam is the above design ok?

[pipermerriam]

@Bhargavasomu I’ve submitted a request to have a bounty attached to this.

[gitcoinbot]

Issue Status: 1. Open 2. Cancelled

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