When I was working with XAMPP in Ubuntu and asked write PHP script to connect to remote MySQL server which is using PASSWORD hash function to save the password for user, and I found following error.

Warning: mysql_connect() [function.mysql-connect]: Premature end of data (mysqlnd_wireprotocol.c:554) in path/to/the/file/where/connection/script/is/written/

Warning: mysql_connect() [function.mysql-connect]: OK packet 1 bytes shorter than expected in path/to/the/file/where/connection/script/is/written/

Warning: mysql_connect() [function.mysql-connect]: mysqlnd cannot connect to MySQL 4.1+ using the old insecure authentication. Please use an administration tool to reset your password with the command SET PASSWORD = PASSWORD('your_existing_password'). This will store a new, and more secure, hash value in mysql.user. If this user is used in other scripts executed by PHP 5.2 or earlier you might need to remove the old-passwords flag from your my.cnf file in path/to/the/file/where/connection/script/is/written/

As you will see, the core issue here is that MySQL can have passwords with hashes stored in the old 16-character format, which is not supported by PHP 5.3′s new mysqlnd library.

Since I couldn’t find a good solution with a quick Google, here is how I solved this without having to downgrade PHP or MySQL (as some of the solutions suggested):

 
1. Change MySQL to NOT to use old_passwords
It seems that even MySQL 5.x versions still default to the old password hashes. You need to change this in “my.cnf” (e.g. /etc/my.cnf): remove or comment out the line that says
old_passwords = 1
Restart MySQL. If you don’t, MySQL will keep using the old password format, which will mean that you cannot upgrade the passwords using the builtin PASSWORD() hashing function. You can test this by running:
  
mysql> SELECT Length(PASSWORD('xyz')); +-------------------------+ | Length(PASSWORD('xyz')) | +-------------------------+ | 16 | +-------------------------+ 1 row in set (0.00 sec)
The old password hashes are 16 characters, the new ones are 41 characters.
2. Change the format of all the passwords in the database to the new format
Connect to the database, and run the following query:
mysql> SELECT user, Length(`Password`) FROM `mysql`.`user`;

This will show you which passwords are in the old format, ex:
+----------+--------------------+ | user | Length(`Password`) | +----------+--------------------+ | root | 41 | | root | 16 | | user2 | 16 | | user2 | 16 | +----------+--------------------+
Notice here that each user can have multiple rows (one for each different host specification).
To update the password for each user, run the following:
UPDATE mysql.user SET Password = PASSWORD('password') WHERE user = 'username';
Finally, flush privileges:
FLUSH PRIVILEGES;