From 133afae13f40418f395e19ba2a18924c05f9f0db Mon Sep 17 00:00:00 2001
From: Sergio Chouhy <41742639+schouhy@users.noreply.github.com>
Date: Fri, 22 Sep 2023 13:42:12 -0300
Subject: [PATCH] Change generator in the Stark252PrimeField to one of maximal
 order $2^{192}$ (#572)

* use a generator of the 2-Sylow subgroup in the Stark252PrimeField

* use square
---
 .../fields/fft_friendly/stark_252_prime_field.rs    | 13 ++++---------
 math/src/field/traits.rs                            |  5 +++--
 2 files changed, 7 insertions(+), 11 deletions(-)

diff --git a/math/src/field/fields/fft_friendly/stark_252_prime_field.rs b/math/src/field/fields/fft_friendly/stark_252_prime_field.rs
index c9baf79b00..abea28907b 100644
--- a/math/src/field/fields/fft_friendly/stark_252_prime_field.rs
+++ b/math/src/field/fields/fft_friendly/stark_252_prime_field.rs
@@ -17,16 +17,11 @@ impl IsModulus<U256> for MontgomeryConfigStark252PrimeField {
 pub type Stark252PrimeField = U256PrimeField<MontgomeryConfigStark252PrimeField>;
 
 impl IsFFTField for Stark252PrimeField {
-    const TWO_ADICITY: u64 = 48;
+    const TWO_ADICITY: u64 = 192;
     // Change this line for a new function like `from_limbs`.
-    const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: U256 = UnsignedInteger {
-        limbs: [
-            219038664817244121,
-            2879838607450979157,
-            15244050560987562958,
-            16338897044258952332,
-        ],
-    };
+    const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: U256 = UnsignedInteger::from_hex_unchecked(
+        "5282db87529cfa3f0464519c8b0fa5ad187148e11a61616070024f42f8ef94",
+    );
 
     fn field_name() -> &'static str {
         "stark256"
diff --git a/math/src/field/traits.rs b/math/src/field/traits.rs
index 7953e8b040..50a2298c87 100644
--- a/math/src/field/traits.rs
+++ b/math/src/field/traits.rs
@@ -42,8 +42,9 @@ pub trait IsFFTField: IsPrimeField {
         if order > F::TWO_ADICITY {
             return Err(FieldError::RootOfUnityError(order));
         }
-        let power = 1u64 << (F::TWO_ADICITY - order);
-        Ok(two_adic_primitive_root_of_unity.pow(power))
+        let log_power = F::TWO_ADICITY - order;
+        let root = (0..log_power).fold(two_adic_primitive_root_of_unity, |acc, _| acc.square());
+        Ok(root)
     }
 }