diff -uNr jira-3.5.0.ORIG/jira/client.py jira-3.5.0/jira/client.py
--- jira-3.5.0.ORIG/jira/client.py	2023-04-01 15:50:58.696922489 +0200
+++ jira-3.5.0/jira/client.py	2023-04-01 15:51:15.678063448 +0200
@@ -3715,13 +3715,13 @@
     def _create_oauth_session(
         self, oauth, timeout: Optional[Union[Union[float, int], Tuple[float, float]]]
     ):
-        from oauthlib.oauth1 import SIGNATURE_RSA
+        from oauthlib.oauth1 import SIGNATURE_HMAC_SHA1
         from requests_oauthlib import OAuth1
 
         oauth_instance = OAuth1(
             oauth["consumer_key"],
             rsa_key=oauth["key_cert"],
-            signature_method=SIGNATURE_RSA,
+            signature_method=SIGNATURE_HMAC_SHA1,
             resource_owner_key=oauth["access_token"],
             resource_owner_secret=oauth["access_token_secret"],
         )
diff -uNr jira-3.5.0.ORIG/jira/jirashell.py jira-3.5.0/jira/jirashell.py
--- jira-3.5.0.ORIG/jira/jirashell.py	2023-04-01 15:50:58.696922489 +0200
+++ jira-3.5.0/jira/jirashell.py	2023-04-01 15:51:15.674396805 +0200
@@ -14,7 +14,7 @@
 
 import keyring
 import requests
-from oauthlib.oauth1 import SIGNATURE_RSA
+from oauthlib.oauth1 import SIGNATURE_HMAC_SHA1
 from requests_oauthlib import OAuth1
 
 from jira import JIRA, __version__
@@ -28,7 +28,7 @@
         verify = server.startswith("https")
 
     # step 1: get request tokens
-    oauth = OAuth1(consumer_key, signature_method=SIGNATURE_RSA, rsa_key=key_cert_data)
+    oauth = OAuth1(consumer_key, signature_method=SIGNATURE_HMAC_SHA1, rsa_key=key_cert_data)
     r = requests.post(
         server + "/plugins/servlet/oauth/request-token", verify=verify, auth=oauth
     )
@@ -70,7 +70,7 @@
     # step 3: get access tokens for validated user
     oauth = OAuth1(
         consumer_key,
-        signature_method=SIGNATURE_RSA,
+        signature_method=SIGNATURE_HMAC_SHA1,
         rsa_key=key_cert_data,
         resource_owner_key=request_token,
         resource_owner_secret=request_token_secret,