Adding Stark curve + test large 2-adicity fields

[shramee]

Description

closes #1000

Support for fields with large 2 adicity

Currently tests fail to fields with large 2-adicity Field::TWO_ADICITY > 31 (currently limited by u32 used in tests).

1. Use Field element instead of 1_u32 << ADICITY.
2. Limit testing roots of unity to 63 in favour of get_root_of_unity using u64.

Adds Stark curve on 252 bit field.

This library implements the Stark curve, An elliptic curve defined over the
STARK field by equation y² ≡ x³ + α·x + β (mod q)
Where:

• α = 1
• β = 0x6f21413efbe40de150e596d72f7a8c5609ad26c15c915c1f4cdfcb99cee9e89
• q = 3618502788666131213697322783095070105623107215331596699973092056135872020481
• or, q = 2^251 + 17 * 2^192 + 1
  Generator point:
• x = 0x1ef15c18599971b7beced415a40f0c7deacfd9b0d1819e03d723d8bc943cfca
• y = 0x5668060aa49730b7be4801df46ec62de53ecd11abe43a32873000c36e8dc1f

https://docs.starknet.io/architecture/cryptography/#the_stark_curve

---

Before we can merge this PR, please make sure that all the following items have been
checked off. If any of the checklist items are not applicable, please leave them but
write a little note why.

• Targeted PR against correct branch (master)
• Linked to GitHub issue with discussion and accepted design OR have an explanation in the PR that describes this work.
• Update: Existing tests for fields and curve group via the macro.
• Updated relevant documentation in the code
• Added a relevant changelog entry to the Pending section in CHANGELOG.md
• Re-reviewed Files changed in the GitHub PR explorer

[Pratyush]

Thank you for the PR!

I think the suggested comments should improve the tests without the need for hacks.

[Pratyush]

Actually, we can write the loop more efficiently as:

Suggested change

	pub fn k_adicity_big_int(k: BigUint, mut n: BigUint) -> u32 {
	let mut r = 0;
	while &n > &1_u8.into() {
	if &n % &k == 0_u8.into() {
	r += 1;
	n /= &k;
	} else {
	return r;
	}
	}
	r
	}
	pub fn k_adicity_big_int(k: u64, mut n: BigUint) -> u32 {
	if n.is_zero() {
	return 0;
	}
	let mut r = 0;
	while (&n % k).is_zero() {
	r += 1;
	n /= k;
	}
	r
	}

[shramee]

Apologies for the dirty commit.

#1001 (comment) This looks really pretty! I took the liberty to update the base k_adicity function the same way! ;)

[shramee]

Rebased (for the failing tests) and cleaned up the commit history if we want to preserve it on merging because of all the different stuff included in the PR.

new: added ZeroFlag after rebase.

[Pratyush]

LGTM modulo the comment about documentation.