diff --git a/aiogram/utils/auth_widget.py b/aiogram/utils/auth_widget.py
index 4793f28c..7d596d5b 100644
--- a/aiogram/utils/auth_widget.py
+++ b/aiogram/utils/auth_widget.py
@@ -21,7 +21,7 @@ def check_signature(token: str, hash: str, **kwargs: Any) -> bool:
         check_string.encode("utf-8"),
         digestmod=hashlib.sha256,
     ).hexdigest()
-    return hmac_string == hash
+    return hmac.compare_digest(hmac_string, hash)
 
 
 def check_integrity(token: str, data: dict[str, Any]) -> bool:
diff --git a/aiogram/utils/backoff.py b/aiogram/utils/backoff.py
index 5fc1c2d2..afa9daed 100644
--- a/aiogram/utils/backoff.py
+++ b/aiogram/utils/backoff.py
@@ -65,7 +65,10 @@ class Backoff:
         await asyncio.sleep(next(self))
 
     def _calculate_next(self, value: float) -> float:
-        return normalvariate(min(value * self.factor, self.max_delay), self.jitter)
+        return max(
+            self.min_delay,
+            normalvariate(min(value * self.factor, self.max_delay), self.jitter),
+        )
 
     def __next__(self) -> float:
         self._current_delay = self._next_delay
diff --git a/aiogram/utils/media_group.py b/aiogram/utils/media_group.py
index 8a7eb53a..411a168d 100644
--- a/aiogram/utils/media_group.py
+++ b/aiogram/utils/media_group.py
@@ -351,6 +351,10 @@ class MediaGroupBuilder:
 
         :return: List of media objects.
         """
+        if not self._media:
+            msg = "Media group must contain at least one media element"
+            raise ValueError(msg)
+
         update_first_media: dict[str, Any] = {"caption": self.caption}
         if self.caption_entities is not None:
             update_first_media["caption_entities"] = self.caption_entities