diff --git a/telethon/network/mtproto_plain_sender.py b/telethon/network/mtproto_plain_sender.py
index 7fae3c20..bbb3e297 100644
--- a/telethon/network/mtproto_plain_sender.py
+++ b/telethon/network/mtproto_plain_sender.py
@@ -1,4 +1,3 @@
-import random
 import time
 
 from ..extensions import BinaryReader, BinaryWriter
@@ -42,17 +41,12 @@ class MtProtoPlainSender:
             return response
 
     def _get_new_msg_id(self):
-        """Generates a new message ID based on the current time (in ms) since epoch"""
-        # See https://core.telegram.org/mtproto/description#message-identifier-msg-id
-        ms_time = int(time.time() * 1000)
-        new_msg_id = (((ms_time // 1000) << 32)
-                      |  # "must approximately equal unix time*2^32"
-                      ((ms_time % 1000) << 22)
-                      |  # "approximate moment in time the message was created"
-                      random.randint(0, 524288)
-                      << 2)  # "message identifiers are divisible by 4"
-
-        # Ensure that we always return a message ID which is higher than the previous one
+        """Generates a new message ID based on the current time since epoch"""
+        # See core.telegram.org/mtproto/description#message-identifier-msg-id
+        now = time.time()
+        nanoseconds = int((now - int(now)) * 1e+9)
+        # "message identifiers are divisible by 4"
+        new_msg_id = (int(now) << 32) | (nanoseconds << 2)
         if self._last_msg_id >= new_msg_id:
             new_msg_id = self._last_msg_id + 4
 
diff --git a/telethon/tl/session.py b/telethon/tl/session.py
index ee5f1091..3dfc2ba6 100644
--- a/telethon/tl/session.py
+++ b/telethon/tl/session.py
@@ -2,7 +2,6 @@ import json
 import os
 import pickle
 import platform
-import random
 import time
 from threading import Lock
 from base64 import b64encode, b64decode
@@ -65,15 +64,10 @@ class Session:
                 return self.sequence * 2
 
     def get_new_msg_id(self):
-        """Generates a new message ID based on the current time (in ms) since epoch"""
-        # Refer to mtproto_plain_sender.py for the original method, this is a simple copy
-        ms_time = int(time.time() * 1000)
-        new_msg_id = (((ms_time // 1000 + self.time_offset) << 32)
-                      |  # "must approximately equal unix time*2^32"
-                      ((ms_time % 1000) << 22)
-                      |  # "approximate moment in time the message was created"
-                      random.randint(0, 524288)
-                      << 2)  # "message identifiers are divisible by 4"
+        now = time.time()
+        nanoseconds = int((now - int(now)) * 1e+9)
+        # "message identifiers are divisible by 4"
+        new_msg_id = (int(now) << 32) | (nanoseconds << 2)
 
         if self.last_message_id >= new_msg_id:
             new_msg_id = self.last_message_id + 4
@@ -133,7 +127,7 @@ class JsonSession:
         self._sequence = 0
         self.salt = 0  # Unsigned long
         self.time_offset = 0
-        self.last_message_id = 0  # Long
+        self._last_msg_id = 0  # Long
 
     def save(self):
         """Saves the current session object as session_user_id.session"""
@@ -229,19 +223,16 @@ class JsonSession:
     def get_new_msg_id(self):
         """Generates a new unique message ID based on the current
            time (in ms) since epoch"""
-        # Refer to mtproto_plain_sender.py for the original method,
-        ms_time = int(time.time() * 1000)
-        new_msg_id = (((ms_time // 1000 + self.time_offset) << 32)
-                      |  # "must approximately equal unix time*2^32"
-                      ((ms_time % 1000) << 22)
-                      |  # "approximate moment in time the message was created"
-                      random.randint(0, 524288)
-                      << 2)  # "message identifiers are divisible by 4"
+        # Refer to mtproto_plain_sender.py for the original method
+        now = time.time()
+        nanoseconds = int((now - int(now)) * 1e+9)
+        # "message identifiers are divisible by 4"
+        new_msg_id = (int(now) << 32) | (nanoseconds << 2)
 
-        if self.last_message_id >= new_msg_id:
-            new_msg_id = self.last_message_id + 4
+        if self._last_msg_id >= new_msg_id:
+            new_msg_id = self._last_msg_id + 4
 
-        self.last_message_id = new_msg_id
+        self._last_msg_id = new_msg_id
         return new_msg_id
 
     def update_time_offset(self, correct_msg_id):