feat: Add eddsa_poseidon_to_pub function to stdlib with test + docs (#…

…4473)

# Description

## Problem\*

Gives a source of truth for deriving public keys for EdDSA signatures,
e.g. for testing.

## Summary\*

Adds this function:
```rust
fn eddsa_poseidon_to_pub(secret: Field) -> (Field, Field)
```

## Additional Context



## Documentation\*

Check one:
- [ ] No documentation needed.
- [x] Documentation included in this PR.
- [ ] **[Exceptional Case]** Documentation to be submitted in a separate
PR.

# PR Checklist\*

- [x] I have tested the changes locally.
- [x] I have formatted the changes with [Prettier](https://prettier.io/)
and/or `cargo fmt` on default settings.

---------

Co-authored-by: kevaundray <kevtheappdev@gmail.com>

docs/docs/noir/standard_library/cryptographic_primitives/eddsa.mdx

@@ -16,3 +16,14 @@ fn eddsa_poseidon_verify(public_key_x : Field, public_key_y : Field, signature_s
 ```
 
 <BlackBoxInfo />
+
+## eddsa::eddsa_to_pub
+
+Private to public key conversion.
+
+Returns `(pub_key_x, pub_key_y)`
+
+```rust
+fn eddsa_to_pub(secret : Field) -> (Field, Field)
+```
+

noir_stdlib/src/eddsa.nr

@@ -38,3 +38,10 @@ pub fn eddsa_poseidon_verify(
 
     left.eq(right)
 }
+
+// Returns the public key of the given secret key as (pub_key_x, pub_key_y)
+pub fn eddsa_to_pub(secret: Field) -> (Field, Field) {
+    let bjj = baby_jubjub();
+    let pub_key = bjj.curve.mul(secret, bjj.curve.gen);
+    (pub_key.x, pub_key.y)
+}

test_programs/execution_success/eddsa/src/main.nr

@@ -1,14 +1,20 @@
 use dep::std::compat;
 use dep::std::ec::consts::te::baby_jubjub;
+use dep::std::ec::tecurve::affine::Point as TEPoint;
 use dep::std::hash;
-use dep::std::eddsa::eddsa_poseidon_verify;
+use dep::std::eddsa::{eddsa_to_pub, eddsa_poseidon_verify};
+
 fn main(msg: pub Field, _priv_key_a: Field, _priv_key_b: Field) {
     // Skip this test for non-bn254 backends
     if compat::is_bn254() {
         let bjj = baby_jubjub();
 
         let pub_key_a = bjj.curve.mul(_priv_key_a, bjj.curve.gen);
-        // let pub_key_b = bjj.curve.mul(_priv_key_b, bjj.curve.gen);
+        let pub_key_b = bjj.curve.mul(_priv_key_b, bjj.curve.gen);
+        let (pub_key_a_x, pub_key_a_y) = eddsa_to_pub(_priv_key_a);
+        let (pub_key_b_x, pub_key_b_y) = eddsa_to_pub(_priv_key_b);
+        assert(TEPoint::new(pub_key_a_x, pub_key_a_y) == pub_key_a);
+        assert(TEPoint::new(pub_key_b_x, pub_key_b_y) == pub_key_b);
         // Manually computed as fields can't use modulo. Importantantly the commitment is within
         // the subgroup order. Note that choice of hash is flexible for this step.
         // let r_a = hash::pedersen_commitment([_priv_key_a, msg])[0] % bjj.suborder; // modulus computed manually