137,098 research outputs found
A Note on Non-Perfect Secret Sharing
By using a recently introduced framework for non-perfect secret sharing, several known results on perfect secret sharing are generalized to non-perfect secret sharing schemes with constant increment, in which the amount of information provided by adding a single share to a set is either zero or some constant value. Specifically, we discuss ideal secret sharing schemes, constructions of efficient linear secret sharing schemes, and the search for lower bounds on the length of the shares. Similarly to perfect secret sharing, matroids and polymatroids are very useful to analyze these questions
Almost-perfect secret sharing
Splitting a secret s between several participants, we generate (for each
value of s) shares for all participants. The goal: authorized groups of
participants should be able to reconstruct the secret but forbidden ones get no
information about it. In this paper we introduce several notions of non-
perfect secret sharing, where some small information leak is permitted. We
study its relation to the Kolmogorov complexity version of secret sharing
(establishing some connection in both directions) and the effects of changing
the secret size (showing that we can decrease the size of the secret and the
information leak at the same time).Comment: Acknowledgments adde
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 shares, such that any set of at least shares suffice to
decode the secret, and any set of at most 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 parties participate in decoding, universally for all . 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.Comment: submitted to the IEEE Transactions on Information Theory. New
references and a new construction adde
Security in Locally Repairable Storage
In this paper we extend the notion of {\em locally repairable} codes to {\em
secret sharing} schemes. The main problem that we consider is to find optimal
ways to distribute shares of a secret among a set of storage-nodes
(participants) such that the content of each node (share) can be recovered by
using contents of only few other nodes, and at the same time the secret can be
reconstructed by only some allowable subsets of nodes. As a special case, an
eavesdropper observing some set of specific nodes (such as less than certain
number of nodes) does not get any information. In other words, we propose to
study a locally repairable distributed storage system that is secure against a
{\em passive eavesdropper} that can observe some subsets of nodes.
We provide a number of results related to such systems including upper-bounds
and achievability results on the number of bits that can be securely stored
with these constraints.Comment: This paper has been accepted for publication in IEEE Transactions of
Information Theor
Computer-aided proofs for multiparty computation with active security
Secure multi-party computation (MPC) is a general cryptographic technique
that allows distrusting parties to compute a function of their individual
inputs, while only revealing the output of the function. It has found
applications in areas such as auctioning, email filtering, and secure
teleconference. Given its importance, it is crucial that the protocols are
specified and implemented correctly. In the programming language community it
has become good practice to use computer proof assistants to verify correctness
proofs. In the field of cryptography, EasyCrypt is the state of the art proof
assistant. It provides an embedded language for probabilistic programming,
together with a specialized logic, embedded into an ambient general purpose
higher-order logic. It allows us to conveniently express cryptographic
properties. EasyCrypt has been used successfully on many applications,
including public-key encryption, signatures, garbled circuits and differential
privacy. Here we show for the first time that it can also be used to prove
security of MPC against a malicious adversary. We formalize additive and
replicated secret sharing schemes and apply them to Maurer's MPC protocol for
secure addition and multiplication. Our method extends to general polynomial
functions. We follow the insights from EasyCrypt that security proofs can be
often be reduced to proofs about program equivalence, a topic that is well
understood in the verification of programming languages. In particular, we show
that in the passive case the non-interference-based definition is equivalent to
a standard game-based security definition. For the active case we provide a new
NI definition, which we call input independence
Teleportation and Secret Sharing with Pure Entangled States
We present two optimal methods of teleporting an unknown qubit using any pure
entangled state. We also discuss how such methods can also have succesful
application in quantum secret sharing with pure multipartite entangled states.Comment: Latex, 13 pages, submitted to PRA. One sub section already appeared
in the archive: quant-ph /990701
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