  Distributed storage plays an essential role in realizing robust and secure
data storage in a network over long periods of time. A distributed storage
system consists of a data owner machine, multiple storage servers and channels
to link them. In such a system, secret sharing scheme is widely adopted, in
which secret data are split into multiple pieces and stored in each server. To
reconstruct them, the data owner should gather plural pieces. Shamir's (k,
n)-threshold scheme, in which the data are split into n pieces (shares) for
storage and at least k pieces of them must be gathered for reconstruction,
furnishes information theoretic security, that is, even if attackers could
collect shares of less than the threshold k, they cannot get any information
about the data, even with unlimited computing power. Behind this scenario,
however, assumed is that data transmission and authentication must be perfectly
secure, which is not trivial in practice. Here we propose a totally information
theoretically secure distributed storage system based on a user-friendly
single-password-authenticated secret sharing scheme and secure transmission
using quantum key distribution, and demonstrate it in the Tokyo metropolitan
area.
