Many encryption systems require the user to memorize high entropy passwords or passphrases and reproduce them exactly. This is often a difficult task. We propose a more fault-tolerant scheme, where a high entropy key (or password) is derived from a sequence of low entropy passwords. The user is able to recover the correct key if she remembers a certain percentage of the passwords correctly. In contrast to other systems that have been proposed for fault-tolerant passwords, our basic design is provably secure against a computationally unbounded attacker.