We study the secrecy of a distributed-storage system for passwords. The encoder, Alice, observes a length-n password and describes it using δ s-bit hints, which she stores in different locations. The legitimate receiver, Bob, observes ν of those hints. In one scenario we require that the expected number of guesses it takes Bob to guess the password approach 1 as n tends to infinity, and in the other that the expected size of the shortest list that Bob must form to guarantee that it contain the password approach 1. The eavesdropper, Eve, sees η < ν hints. Assuming that Alice cannot control which hints Bob and Eve observe, we characterize for each scenario the largest normalized (by n) exponent that we can guarantee for the expected number of guesses it takes Eve to guess the password.