diff --git a/jwt/api_jws.py b/jwt/api_jws.py
index a61d22775..401bb91c8 100644
--- a/jwt/api_jws.py
+++ b/jwt/api_jws.py
@@ -113,14 +113,14 @@ def encode(
             key = alg_obj.prepare_key(key)
             signature = alg_obj.sign(signing_input, key)
 
-        except KeyError:
+        except KeyError as e:
             if not has_crypto and algorithm in requires_cryptography:
                 raise NotImplementedError(
                     "Algorithm '%s' could not be found. Do you have cryptography "
                     "installed?" % algorithm
-                )
+                ) from e
             else:
-                raise NotImplementedError("Algorithm not supported")
+                raise NotImplementedError("Algorithm not supported") from e
 
         segments.append(base64url_encode(signature))
 
@@ -236,8 +236,8 @@ def _verify_signature(
             if not alg_obj.verify(signing_input, key, signature):
                 raise InvalidSignatureError("Signature verification failed")
 
-        except KeyError:
-            raise InvalidAlgorithmError("Algorithm not supported")
+        except KeyError as e:
+            raise InvalidAlgorithmError("Algorithm not supported") from e
 
     def _validate_headers(self, headers):
         if "kid" in headers: