chore: remove noir-lang/ec dependency

noir-projects/noir-protocol-circuits/crates/types/Nargo.toml

@@ -5,5 +5,4 @@ authors = [""]
 compiler_version = ">=0.18.0"
 
 [dependencies]
-ec = { tag = "v0.1.2", git = "https://github.com/noir-lang/ec" }
 sha256 = { tag = "v0.1.2", git = "https://github.com/noir-lang/sha256" }

noir-projects/noir-protocol-circuits/crates/types/src/address/aztec_address.nr

@@ -10,13 +10,13 @@ use crate::{
     hash::poseidon2_hash_with_separator,
     public_keys::{IvpkM, NpkM, OvpkM, PublicKeys, ToPoint, TpkM},
     traits::{Deserialize, Empty, FromField, Packable, Serialize, ToField},
+    utils::field::{pow, sqrt},
 };
 
 // We do below because `use crate::point::Point;` does not work
 use dep::std::embedded_curve_ops::EmbeddedCurvePoint as Point;
 
 use crate::public_keys::AddressPoint;
-use ec::{pow, sqrt};
 use std::{
     embedded_curve_ops::{EmbeddedCurveScalar, fixed_base_scalar_mul as derive_public_key},
     ops::Add,

noir-projects/noir-protocol-circuits/crates/types/src/utils/field.nr

@@ -51,6 +51,51 @@ pub fn min(f1: Field, f2: Field) -> Field {
     }
 }
 
+global C1: u32 = 28;
+global C3: Field = 40770029410420498293352137776570907027550720424234931066070132305055;
+global C5: Field = 19103219067921713944291392827692070036145651957329286315305642004821462161904;
+
+pub(crate) fn pow(x: Field, y: Field) -> Field {
+    let mut r = 1 as Field;
+    let b: [u1; 254] = y.to_le_bits();
+
+    for i in 0..254 {
+        r *= r;
+        r *= (b[254 - 1 - i] as Field) * x + (1 - b[254 - 1 - i] as Field);
+    }
+
+    r
+}
+
+// Tonelli-Shanks algorithm for computing the square root of a Field element.
+// Requires C1 = max{c: 2^c divides (p-1)}, where p is the order of Field
+// as well as C3 = (C2 - 1)/2, where C2 = (p-1)/(2^c1),
+// and C5 = ZETA^C2, where ZETA is a non-square element of Field.
+// These are pre-computed above as globals.
+pub(crate) fn sqrt(x: Field) -> Field {
+    let mut z = pow(x, C3);
+    let mut t = z * z * x;
+    z *= x;
+    let mut b = t;
+    let mut c = C5;
+
+    for i in 0..(C1 - 1) {
+        for _j in 1..(C1 - i - 1) {
+            b *= b;
+        }
+
+        z *= if b == 1 { 1 } else { c };
+
+        c *= c;
+
+        t *= if b == 1 { 1 } else { c };
+
+        b = t;
+    }
+
+    z
+}
+
 #[test]
 unconstrained fn bytes_field_test() {
     // Tests correctness of field_from_bytes_32_trunc against existing methods