Fix field division by handling division by zero

[jotabulacios]

Fix field division by handling division by zero

Description

This PR fixes a potential division by zero error in the div function for FieldElement which could cause a panic. Instead of performing direct division, the implementation now returns a Result<FieldElement<L>, FieldError>, ensuring error handling when division by zero occurs.

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 75.59809% with 51 lines in your changes missing coverage. Please review.

Project coverage is 71.66%. Comparing base (7e94a19) to head (d4c9e5c).

Files with missing lines	Patch %	Lines
math/src/field/fields/mersenne31/extensions.rs	31.57%	13 Missing ⚠️
.../src/field/fields/fft_friendly/quartic_babybear.rs	0.00%	9 Missing ⚠️
...rt_weierstrass/curves/bls12_377/field_extension.rs	11.11%	8 Missing ⚠️
...short_weierstrass/curves/bn_254/field_extension.rs	11.11%	8 Missing ⚠️
.../field/fields/fft_friendly/quartic_babybear_u32.rs	0.00%	6 Missing ⚠️
math/src/field/test_fields/u32_test_field.rs	0.00%	3 Missing ⚠️
math/src/field/test_fields/u64_test_field.rs	0.00%	3 Missing ⚠️
math/src/elliptic_curve/short_weierstrass/point.rs	90.90%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #969      +/-   ##
==========================================
+ Coverage   71.65%   71.66%   +0.01%     
==========================================
  Files         156      156              
  Lines       34235    34316      +81     
==========================================
+ Hits        24531    24593      +62     
- Misses       9704     9723      +19     

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[Oppen]

Forgot to flush the review, sorry.

[Oppen]

We should probably use regular unwrap here.
It may be useful to compute the inverse of z only once (not necessary to do now) and multiply later as well.

[Oppen]

I think something like this might be cleaner (assuming inv gives us the inverse and returns a Result<_>:

Suggested change

	if z == FieldElement::zero() {
	let point = Self::new([x, y, z])
	.map_err(|_| DeserializationError::FieldFromBytesError)?;
	if point.is_neutral_element() {
	Ok(point)
	} else {
	Err(DeserializationError::FieldFromBytesError)
	}
	} else if E::defining_equation(unsafe { &(&x / &z).unwrap_unchecked() }, unsafe {
	&(&y / &z).unwrap_unchecked()
	}) == FieldElement::zero()
	{
	Self::new([x, y, z]).map_err(|_| DeserializationError::FieldFromBytesError)
	} else {
	Err(DeserializationError::FieldFromBytesError)
	}
	let Some(z_inv) = z.inv() else {
	let point = Self::new([x, y, z])
	.map_err(|_| DeserializationError::FieldFromBytesError)?;
	return if point.is_neutral_element() {
	Ok(point)
	} else {
	Err(DeserializationError::FieldFromBytesError)
	};
	};
	if E::defining_equation(&(&x * &z_inv), &(&y * &z_inv)) == FieldElement::zero()
	{
	Self::new([x, y, z]).map_err(|_| DeserializationError::FieldFromBytesError)
	} else {
	Err(DeserializationError::FieldFromBytesError)
	}

This version has no unwraps and yet exploits that past the inverse calculation we know z != 0.

[jotabulacios]

Solved in 6f0e40d

[Oppen]

I believe the intent here was to remove the unwrap:

Suggested change

	.map_err(|_| ProverError::DivisionByZero)
	.unwrap();
	.map_err(|_| ProverError::DivisionByZero)?;