Classical cryptographic protocols based on user-chosen keys allow an attacker to mount password-guessing attacks. We introduce a novel combination of asymmetric (public-key) and symmetric (secret-key) cryptography that allow two parties sharing a common password to exchange confidential and authenticated information over an insecure network. These protocols are secure against active attacks, and have the property that the password is protected against off-line "dictionary" attacks. There are a number of other useful applications as well, including secure public telephones.

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