Created a deep-linking example.

(Source: my answer at http://stackoverflow.com/questions/31042219/how-to-have-authentication-in-a-telegram-bot)

examples/deep_linking.py

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+# This example shows how to implement deep linking (https://core.telegram.org/bots#deep-linking)
+# with the pyTelegramBotAPI.
+# Note: This is not a working, production-ready sample.
+#
+# In this example we are connecting a user account on a website with a Telegram bot.
+# Implementing this will enable you to push notifications (and other content) to your users' Telegram account.
+# In this explanation the word 'database' can refer to any form of key-value storage.
+# The deep linking explained:
+#
+# 1.	Let the user log in on an actual website with actual username-password authentication.
+#
+# 2. 	Generate a unique hashcode (we will call it unique_code)
+#
+# 3. 	Save unique_code->username to the database.
+#
+# 4. 	Show the user the URL https://telegram.me/YOURBOTNAME?start=unique_code
+#
+# 5. 	Now as soon as the user opens this URL in Telegram and presses 'Start',
+#       your bot will receive a text message containing '/start unique_code',
+#       where unique_code is of course replaced by the actual hashcode.
+#
+# 6. 	Let the bot retrieve the username by querying the database for unique_code.
+#
+# 7. 	Save chat_id->username to the database.
+#
+# 8. 	Now when your bot receives another message, it can query message.chat.id in the database
+#       to check if the message is from this specific user. (And handle accordingly) or
+#       you can push messages to the user using his chat id.
+#
+# Steps 1 to 4 will have to be implemented in a web server, using a language such as PHP, Python, C# or Java. These
+# steps are not shown here. Only steps 5 to 7 are illustrated, some in pseudo-code, with this example.
+
+import telebot
+import time
+
+bot = telebot.TeleBot('TOKEN')
+
+def extract_unique_code(text):
+    # Extracts the unique_code from the sent /start command.
+    return text.split()[1] if len(text.split()) > 1 else None
+
+def in_storage(unique_code):
+    # (pseudo-code) Should check if a unique code exists in storage
+    return True
+
+def get_username_from_storage(unique_code):
+    # (pseudo-code) Does a query to the storage, retrieving the associated username
+    # Should be replaced by a real database-lookup.
+    return "ABC" if in_storage(unique_code) else None
+
+def save_chat_id(chat_id, username):
+    # (pseudo-code) Save the chat_id->username to storage
+    # Should be replaced by a real database query.
+    pass
+
+@bot.message_handler(commands=['start'])
+def send_welcome(message):
+    unique_code = extract_unique_code(message.text)
+    if unique_code: # if the '/start' command contains a unique_code
+        username = get_username_from_storage(unique_code)
+        if username: # if the username exists in our database
+            save_chat_id(message.chat.id, username)
+            reply = "Hello {0}, how are you?".format(username)
+        else:
+            reply = "I have no clue who you are..."
+    else:
+        reply = "Please visit me via a provided URL from the website."
+    bot.reply_to(message, reply)
+
+bot.polling()
+
+while True:
+    time.sleep(0)