feat(BigNatMultMod): `BitNat` -> `BigUint`

[cyphersnake]

          should we allow all zero limbs here?

_Originally posted by @chaosma in https://github.com/snarkify/Sirius/pull/4#discussion_r1312150576_

@chaosma will check is it needed

[chaosma]

@cyphersnake In set theory or computer science, natural number starts from $0$. In number theory, natural number starts from $1$. In our case, we can either use the nameBigNat or BigInt (whichever you prefer). And we allow all zero limbs.

[drouyang]

bigint is a typical name. biguint is a type in num_bigint.

https://docs.rs/num-bigint/latest/num_bigint/struct.BigUint.html

[cyphersnake]

BigInt - signed, BigUint - unsigned

int\uint is common for CS, in Rust abbreviated versions are used, but all types also correspond to this naming. I'm not sure who authored this abbreviation, but it must have been C

If we don't need numbers with a sign, BigUint is the most correct choice, since BigNat causes misunderstandings (due to differences in interpretation in math and CS), and BigInt implies a sign (like any integer type by default).

[drouyang]

I know the difference of int and uint.

If you look at the name of big integer libraries in other languages, I think bignum or bigint are typical.

[drouyang]

I think bigint or bignum refers to big integer/number arithmetic, not a specific signed or unsigned type.

[drouyang]

Is bignat referring to a directory here or a specific type here?

[cyphersnake]

As a developer, I will always expect significance from BigInt. see Int. I looked at several implementations in Rust, all of them have a division into signed and unsigned logic. In the C++ world, if I remember correctly, there is also this division

Let's stop with BigNum, since it doesn't refer to whether the number is signed or unsigned.