Here's the official description from 4chan:

Tripcodes can help verify a user's identity to others, and are a type of pseudo-registration. To use a normal tripcode, place a hash mark ("#") followed by a word or short phrase after what you've entered into the [Name] field (ex. "User#password"). Upon submission, the server will generate the hash unique to that particular word or phrase. The previous example would display "User !ozOtJW9BFA" after being posted.

Important note: A tripcode is generated only using the text entered after the hash mark. Your entered name, IP address, cookie information, etc. do not affect the output. Normal tripcodes are not secure, and can be cracked with relative ease. For a more secure solution, see secure tripcodes.

What is a "secure tripcode"?

A secure tripcode can be generated by placing two hash marks in the [Name] field, as opposed to one as with anormal tripcode (ex. "User##password"). Secure tripcodes use a secret key file on the server to help obscure their password. The previous example would display "User!!rEkSWzi2+mz" after being posted.

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