On the Secrecy Capacity of Distributed Storage with Locality and Availability
Stanislav Kruglik, Pavel S. Rybin, Alexey Frolov · 2019
In this paper, we extend the notion of locally recoverable codes with availability to secret sharing schemes. The main problem that we considered is how to store information using locally recoverable codes with all symbol locality and availability in such way that useful information can be recovered using an only small subset of coordinates while a user who observes less than a certain number of coordinates does not get any information. In other words, we have to protect locally recoverable codes with availability over passive eavesdropper that can observe only limited number of coordinates. Upper bounds on number of bits that can be securely stored in such systems together with explicit constructions of codes with such a property are proposed.