Division operator for GTElement (e1/e2)

[lokingdav]

Currently creating a witness encryption scheme based on BLS signatures. I am using this library. However, I needed the GTElement class to support inversing through divisions. Instead of reimplementing element classes (since r is private in GT), this PR fixed the issue.

I know BLS signature implementation does not use division, but libraries that depend on this might need it. Moreover, my witness encryption library currently depends on my fork, and I want to use the main Chia-Network/bls-signatures instead.

[coveralls-official]

Pull Request Test Coverage Report for Build 6819261096

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• 9 of 9 (100.0%) changed or added relevant lines in 2 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.03%) to 94.677%

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Totals
Change from base Build 6614779237:	0.03%
Covered Lines:	1654
Relevant Lines:	1747

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💛 - Coveralls

[hoffmang9]

Thanks for your contribution

[hoffmang9]

Can you sign your commit?

[hoffmang9]

Looks like something is still a bit off.

[lokingdav]

Looks like something is still a bit off.

Yeah i noticed and I'm resolving it. Used a different email for this repository

[github-actions]

'This PR has been flagged as stale due to no activity for over 60
days. It will not be automatically closed, but it has been given
a stale-pr label and should be manually reviewed.'

[emlowe]

Apologies for the long delay in looking at this. But I have a question. The included test is odd since division is not normally commutative - so one doesn't expect a test where a/b == b/a

I would expect something like (a*b)/b == a - does this version of division pass that test?

Reading a little more carefully, I see gt1 and gt2 are actually the same element - the test is then a/a == a/a which doesn't seem very useful?

[lokingdav]

Hi @emlowe thanks for this message. In fact, I forgot about this PR.

Your observation is correct, which would be a more precise test. The current test works because gt1 and gt2 are both GT generators and are the same. It will make more sense that gt1 and gt2 are different elements. I'll update the test.

[github-actions]

'This PR has been flagged as stale due to no activity for over 60
days. It will not be automatically closed, but it has been given
a stale-pr label and should be manually reviewed.'

[emlowe]

I'm not sure it's correct to call "multiplication of the inverse" a division operation