Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Communication Efficient Secret Sharing   A secret sharing scheme is a method to store information securely and
reliably. Particularly, in a threshold secret sharing scheme, a secret is
encoded into $n$ shares, such that any set of at least $t_1$ shares suffice to
decode the secret, and any set of at most $t_2 < t_1$ shares reveal no
information about the secret. Assuming that each party holds a share and a user
wishes to decode the secret by receiving information from a set of parties; the
question we study is how to minimize the amount of communication between the
user and the parties. We show that the necessary amount of communication,
termed "decoding bandwidth", decreases as the number of parties that
participate in decoding increases. We prove a tight lower bound on the decoding
bandwidth, and construct secret sharing schemes achieving the bound.
Particularly, we design a scheme that achieves the optimal decoding bandwidth
when $d$ parties participate in decoding, universally for all $t_1 \le d \le
n$. The scheme is based on Shamir's secret sharing scheme and preserves its
simplicity and efficiency. In addition, we consider secure distributed storage
where the proposed communication efficient secret sharing schemes further
improve disk access complexity during decoding.

3
The categories of this paper are: physics
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga