With the introduction of MySQL 4.1, the client authentication procedure was changed (stronger hashing). What the error message means is that you're running MySQL 4.1 or later and that your PHP environment is using a MySQL client library that is pre 4.1. There are three possible solutions to the problem.
1. Install the mysqli extention in your PHP environment. When installed, PunBB's install.php will detect it and enable "MySQL Improved" in the database type drop-down.
2. Upgrade the mysql extension in your PHP environment so that it works with MySQL 4.1 or later.
3. Start the MySQL server with the parameter --old-passwords and update any passwords.
You can find more info on the matter in the MySQL documentation.
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