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PAP works basically the same way as the normal login procedure. The client authenticates itself by sending a user name and an (optionally encrypted) password to the server, which the server compares to its secrets database. This technique is vulnerable to eavesdroppers who may try to obtain the password by listening in on the serial line, and to repeated trial and error attacks.
With CHAP, the authenticator (i.e. the server) sends a randomly generated ``challenge'' string to the client, along with its hostname. The client uses the hostname to look up the appropriate secret, combines it with the challenge, and encrypts the string using a one-way hashing function. The result is returned to the server along with the client's hostname. The server now performs the same computation, and acknowledges the client if it arrives at the same result.
Another feature of CHAP is that it doesn't only require the client to authenticate itself at startup time, but sends challenges at regular intervals to make sure the client hasn't been replaced by an intruder, for instance by just switching phone lines.
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