diff --git a/crates/utils/src/math.cairo b/crates/utils/src/math.cairo
index 6e77fdbc9..cf13026f3 100644
--- a/crates/utils/src/math.cairo
+++ b/crates/utils/src/math.cairo
@@ -2,6 +2,7 @@ use core::integer::{u512};
 use core::num::traits::{Zero, One, BitSize, OverflowingAdd, OverflowingMul};
 use core::panic_with_felt252;
 use core::traits::{BitAnd};
+use utils::constants::POW_2;
 
 // === Exponentiation ===
 
@@ -236,6 +237,8 @@ impl BitshiftImpl<
     +PartialOrd<T>,
     +BitSize<T>,
     +TryInto<usize, T>,
+    +TryInto<T, usize>,
+    +TryInto<u128, T>,
 > of Bitshift<T> {
     fn shl(self: T, shift: T) -> T {
         // if we shift by more than nb_bits of T, the result is 0
@@ -243,6 +246,12 @@ impl BitshiftImpl<
         if shift > BitSize::<T>::bits().try_into().unwrap() - One::one() {
             panic_with_felt252('mul Overflow');
         }
+        // if the shift is within the bit size of u256 (<= 255 bits),
+        // use the POW_2 lookup table to get 2^shift for efficient multiplication
+        if shift <= BitSize::<u256>::bits().try_into().unwrap() - One::<T>::one() {
+            return self * (*POW_2.span().at(shift.try_into().unwrap())).try_into().unwrap();
+        }
+        // for shifts greater than 255 bits, perform the shift manually
         let two = One::one() + One::one();
         self * two.pow(shift)
     }
@@ -252,6 +261,10 @@ impl BitshiftImpl<
         if shift > BitSize::<T>::bits().try_into().unwrap() - One::one() {
             panic_with_felt252('mul Overflow');
         }
+        // use the POW_2 lookup table when the bit size
+        if shift <= BitSize::<u256>::bits().try_into().unwrap() - One::<T>::one() {
+            return self / (*POW_2.span().at(shift.try_into().unwrap())).try_into().unwrap();
+        }
         let two = One::one() + One::one();
         self / two.pow(shift)
     }
@@ -301,16 +314,24 @@ pub impl WrappingBitshiftImpl<
     +WrappingExponentiation<T>,
     +BitSize<T>,
     +TryInto<usize, T>,
+    +TryInto<T, usize>,
+    +TryInto<u128, T>
 > of WrappingBitshift<T> {
     fn wrapping_shl(self: T, shift: T) -> T {
+        if shift <= BitSize::<u256>::bits().try_into().unwrap() - One::<T>::one() {
+            let (result, _) = self.overflowing_mul((*POW_2.span().at(shift.try_into().unwrap())).try_into().unwrap());
+            return result;
+        }
         let two = One::<T>::one() + One::<T>::one();
         let (result, _) = self.overflowing_mul(two.wrapping_pow(shift));
         result
     }
 
     fn wrapping_shr(self: T, shift: T) -> T {
+        if shift <= BitSize::<u256>::bits().try_into().unwrap() - One::<T>::one() {
+            return self / (*POW_2.span().at(shift.try_into().unwrap())).try_into().unwrap();
+        }
         let two = One::<T>::one() + One::<T>::one();
-
         if shift > BitSize::<T>::bits().try_into().unwrap() - One::one() {
             return Zero::zero();
         }