refactor:Tidy up scalar module (#255)

# Rationale for this change

MontScalar and Scalar logic is currently disorganized. We should consolidate this logic.

# What changes are included in this PR?

Moved the Scalar trait to its own "scalar" file within base/scalar.

crates/proof-of-sql/src/base/mod.rs

@@ -10,6 +10,7 @@ pub mod math;
 pub(crate) mod polynomial;
 pub(crate) mod proof;
 pub(crate) mod ref_into;
+/// This module contains the `Scalar` trait as well as the main, generic, implementations of it.
 pub mod scalar;
 mod serialize;
 pub(crate) use serialize::{impl_serde_for_ark_serde_checked, impl_serde_for_ark_serde_unchecked};

crates/proof-of-sql/src/base/scalar/mod.rs

@@ -1,90 +1,15 @@
-//! This module contains the definition of the `Scalar` trait, which is used to represent the scalar field used in Proof of SQL.
+/// This module contains the definition of the `Scalar` trait, which is used to represent the scalar field used in Proof of SQL.
+pub mod scalar;
+pub use scalar::Scalar;
 mod error;
 pub use error::ScalarConversionError;
 mod mont_scalar;
 #[cfg(test)]
 mod mont_scalar_test;
-use alloc::string::String;
-use core::{cmp::Ordering, ops::Sub};
 pub use mont_scalar::Curve25519Scalar;
 pub(crate) use mont_scalar::MontScalar;
 /// Module for a test Scalar
 #[cfg(test)]
 pub mod test_scalar;
 #[cfg(test)]
 mod test_scalar_test;
-use num_bigint::BigInt;
-
-/// A trait for the scalar field used in Proof of SQL.
-pub trait Scalar:
-    Clone
-    + core::fmt::Debug
-    + core::fmt::Display
-    + PartialEq
-    + Default
-    + for<'a> From<&'a str>
-    + Sync
-    + Send
-    + num_traits::One
-    + core::iter::Sum
-    + core::iter::Product
-    + Sub<Output = Self>
-    + Copy
-    + core::ops::MulAssign
-    + core::ops::AddAssign
-    + num_traits::Zero
-    + for<'a> core::convert::From<&'a Self> // Required for `Column` to implement `MultilinearExtension`
-    + for<'a> core::convert::From<&'a bool> // Required for `Column` to implement `MultilinearExtension`
-    + for<'a> core::convert::From<&'a i8> // Required for `Column` to implement `MultilinearExtension`
-    + for<'a> core::convert::From<&'a i16> // Required for `Column` to implement `MultilinearExtension`
-    + for<'a> core::convert::From<&'a i32> // Required for `Column` to implement `MultilinearExtension`
-    + for<'a> core::convert::From<&'a i64> // Required for `Column` to implement `MultilinearExtension`
-    + for<'a> core::convert::From<&'a i128> // Required for `Column` to implement `MultilinearExtension`
-    + for<'a> core::convert::From<&'a u8> // Required for `Column` to implement `MultilinearExtension`
-    + core::convert::TryInto <bool>
-    + core::convert::TryInto <i8>
-    + core::convert::TryInto <i16>
-    + core::convert::TryInto <i32>
-    + core::convert::TryInto <i64>
-    + core::convert::TryInto <i128>
-    + core::convert::Into<[u64; 4]>
-    + core::convert::From<[u64; 4]>
-    + core::cmp::Ord
-    + core::ops::Neg<Output = Self>
-    + num_traits::Zero
-    + core::ops::AddAssign
-    + ark_serialize::CanonicalSerialize //This enables us to put `Scalar`s on the transcript
-    + ark_std::UniformRand //This enables us to get `Scalar`s as challenges from the transcript
-    + num_traits::Inv<Output = Option<Self>> // Note: `inv` should return `None` exactly when the element is zero.
-    + core::ops::SubAssign
-    + super::ref_into::RefInto<[u64; 4]>
-    + for<'a> core::convert::From<&'a String>
-    + super::encode::VarInt
-    + core::convert::From<String>
-    + core::convert::From<i128>
-    + core::convert::From<i64>
-    + core::convert::From<i32>
-    + core::convert::From<i16>
-    + core::convert::From<i8>
-    + core::convert::From<bool>
-    + core::convert::Into<BigInt>
-    + TryFrom<BigInt, Error = ScalarConversionError>
-{
-    /// The value (p - 1) / 2. This is "mid-point" of the field - the "six" on the clock.
-    /// It is the largest signed value that can be represented in the field with the natural embedding.
-    const MAX_SIGNED: Self;
-    /// The 0 (additive identity) element of the field.
-    const ZERO: Self;
-    /// The 1 (multiplicative identity) element of the field.
-    const ONE: Self;
-    /// 1 + 1
-    const TWO: Self;
-    /// Compare two `Scalar`s as signed numbers.
-    fn signed_cmp(&self, other: &Self) -> Ordering {
-        match *self - *other {
-            x if x.is_zero() => Ordering::Equal,
-            x if x > Self::MAX_SIGNED => Ordering::Less,
-            _ => Ordering::Greater,
-        }
-    }
-}

crates/proof-of-sql/src/base/scalar/scalar.rs

@@ -0,0 +1,80 @@
+#![allow(clippy::module_inception)]
+
+use crate::base::{encode::VarInt, ref_into::RefInto, scalar::ScalarConversionError};
+use alloc::string::String;
+use core::{cmp::Ordering, ops::Sub};
+use num_bigint::BigInt;
+
+/// A trait for the scalar field used in Proof of SQL.
+pub trait Scalar:
+    Clone
+    + core::fmt::Debug
+    + core::fmt::Display
+    + PartialEq
+    + Default
+    + for<'a> From<&'a str>
+    + Sync
+    + Send
+    + num_traits::One
+    + core::iter::Sum
+    + core::iter::Product
+    + Sub<Output = Self>
+    + Copy
+    + core::ops::MulAssign
+    + core::ops::AddAssign
+    + num_traits::Zero
+    + for<'a> core::convert::From<&'a Self> // Required for `Column` to implement `MultilinearExtension`
+    + for<'a> core::convert::From<&'a bool> // Required for `Column` to implement `MultilinearExtension`
+    + for<'a> core::convert::From<&'a i8> // Required for `Column` to implement `MultilinearExtension`
+    + for<'a> core::convert::From<&'a i16> // Required for `Column` to implement `MultilinearExtension`
+    + for<'a> core::convert::From<&'a i32> // Required for `Column` to implement `MultilinearExtension`
+    + for<'a> core::convert::From<&'a i64> // Required for `Column` to implement `MultilinearExtension`
+    + for<'a> core::convert::From<&'a i128> // Required for `Column` to implement `MultilinearExtension`
+    + for<'a> core::convert::From<&'a u8> // Required for `Column` to implement `MultilinearExtension`
+    + core::convert::TryInto <bool>
+    + core::convert::TryInto <i8>
+    + core::convert::TryInto <i16>
+    + core::convert::TryInto <i32>
+    + core::convert::TryInto <i64>
+    + core::convert::TryInto <i128>
+    + core::convert::Into<[u64; 4]>
+    + core::convert::From<[u64; 4]>
+    + core::cmp::Ord
+    + core::ops::Neg<Output = Self>
+    + num_traits::Zero
+    + core::ops::AddAssign
+    + ark_serialize::CanonicalSerialize //This enables us to put `Scalar`s on the transcript
+    + ark_std::UniformRand //This enables us to get `Scalar`s as challenges from the transcript
+    + num_traits::Inv<Output = Option<Self>> // Note: `inv` should return `None` exactly when the element is zero.
+    + core::ops::SubAssign
+    + RefInto<[u64; 4]>
+    + for<'a> core::convert::From<&'a String>
+    + VarInt
+    + core::convert::From<String>
+    + core::convert::From<i128>
+    + core::convert::From<i64>
+    + core::convert::From<i32>
+    + core::convert::From<i16>
+    + core::convert::From<i8>
+    + core::convert::From<bool>
+    + core::convert::Into<BigInt>
+    + TryFrom<BigInt, Error = ScalarConversionError>
+{
+    /// The value (p - 1) / 2. This is "mid-point" of the field - the "six" on the clock.
+    /// It is the largest signed value that can be represented in the field with the natural embedding.
+    const MAX_SIGNED: Self;
+    /// The 0 (additive identity) element of the field.
+    const ZERO: Self;
+    /// The 1 (multiplicative identity) element of the field.
+    const ONE: Self;
+    /// 1 + 1
+    const TWO: Self;
+    /// Compare two `Scalar`s as signed numbers.
+    fn signed_cmp(&self, other: &Self) -> Ordering {
+        match *self - *other {
+            x if x.is_zero() => Ordering::Equal,
+            x if x > Self::MAX_SIGNED => Ordering::Less,
+            _ => Ordering::Greater,
+        }
+    }
+}