Title: Guessing Attacks on Distributed-Storage Systems,
Abstract: The secrecy of a distributed-storage system for passwords is studied. The
encoder, Alice, observes a length-n password and describes it using two hints,
which she stores in different locations. The legitimate receiver, Bob, observes
both hints. In one scenario the requirement is that the expected number of
guesses it takes Bob to guess the password approach one 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 one. The eavesdropper, Eve,
sees only one of the hints. Assuming that Alice cannot control which hints Eve
observes, the largest normalized (by n) exponent that can be guaranteed for the
expected number of guesses it takes Eve to guess the password is characterized
for each scenario. Key to the proof are new results on Arikan's guessing and
Bunte and Lapidoth's task-encoding problem; in particular, the paper
establishes a close relation between the two problems. A rate-distortion
version of the model is also discussed, as is a generalization that allows for
Alice to produce {\delta} (not necessarily two) hints, for Bob to observe {\nu}
(not necessarily two) of the hints, and for Eve to observe {\eta} (not
necessarily one) of the hints. The generalized model is robust against {\delta}
- {\nu} disk failures.