fix: fix low entropy calc when using Mnemonic XOR

This commit add a fix for shannon entropy calculation of a choosen
entroypy bytes before operate the XOR between input and current
mnemonic.

Author: qlrd

src/krux/pages/home_pages/mnemonic_xor.py

@@ -20,6 +20,7 @@
 # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 # THE SOFTWARE.
 
+import math
 from .. import Menu, LETTERS, MENU_CONTINUE, MENU_EXIT
 from ..login import MnemonicLoader
 from ...krux_settings import Settings, t
@@ -28,6 +29,8 @@
 from ...key import Key
 from ...wallet import Wallet
 
+NORMALIZED_THRESHOLD = 30
+
 
 class MnemonicXOR(MnemonicLoader):
     """
@@ -53,13 +56,46 @@ def _xor_bytes(a: bytes, b: bytes) -> bytearray:
 
         return out
 
+    @staticmethod
+    def _shannon_sum(distribution, sample_size):
+        """Calculates Shannon's entropy of a given distribution.
+
+        Example:
+
+        0x00 *
+        0x01 **
+        Ox02 ********
+        ...  ***
+        0xFD **
+        OxFE ***
+        0xFD **
+        OxFF *
+        """
+        # Calculate entropy
+        unit_entropy = 0
+        for count in distribution:
+            probability = count / sample_size
+            unit_entropy -= probability * (probability and math.log2(probability))
+        return unit_entropy
+
     @staticmethod
     def _validate_entropy(entropy: bytes | bytearray) -> None:
-        """Check for low entropy (all zeros or all ones)"""
-        # TODO: apply a shannon low entropy check for XOR
-        all_zeros = bytes(len(entropy))
-        all_ones = b"\xff" * len(entropy)
-        if entropy in (all_zeros, all_ones):
+        """Check for low entropy against its distribution"""
+        n = len(entropy)
+
+        # Differences lie in [-255, +255], then 511 buckets
+        derivatives = (entropy[i] - entropy[i - 1] for i in range(1, n))
+        d_counts = [0] * 511
+        total_derivatives = 0
+        for d in derivatives:
+            d_counts[d + 255] += 1
+            total_derivatives += 1
+
+        d_entropy = MnemonicXOR._shannon_sum(d_counts, total_derivatives)
+        max_d_entropy = math.log2(len(d_counts))
+        normalized = (d_entropy / max_d_entropy) * 100.0
+
+        if normalized < NORMALIZED_THRESHOLD:
             raise ValueError("Low entropy mnemonic")
 
     @staticmethod