42,714 research outputs found
Quantum broadcast communication
Broadcast encryption allows the sender to securely distribute his/her secret
to a dynamically changing group of users over a broadcast channel. In this
paper, we just consider a simple broadcast communication task in quantum
scenario, which the central party broadcasts his secret to multi-receiver via
quantum channel. We present three quantum broadcast communication schemes. The
first scheme utilizes entanglement swapping and Greenberger-Horne-Zeilinger
state to realize a task that the central party broadcasts his secret to a group
of receivers who share a group key with him. In the second scheme, based on
dense coding, the central party broadcasts the secret to multi-receiver who
share each of their authentication key with him. The third scheme is a quantum
broadcast communication scheme with quantum encryption, which the central party
can broadcast the secret to any subset of the legal receivers
Asynchronous quantum key distribution on a relay network
We show how quantum key distribution on a multi-user, multi-path, network can be used to establish a key between any two end-users in an asynchronous fashion using the technique of bit-transport. By a suitable adaptation of our previous secret-sharing scheme we show that an attacker has to compromise all of the intermediate relays on the network in order to obtain the key. Thus, two end-users can establish a secret key provided they trust at least one of the network relays
Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes
It is a standard result in the theory of quantum error-correcting codes that
no code of length n can fix more than n/4 arbitrary errors, regardless of the
dimension of the coding and encoded Hilbert spaces. However, this bound only
applies to codes which recover the message exactly. Naively, one might expect
that correcting errors to very high fidelity would only allow small violations
of this bound. This intuition is incorrect: in this paper we describe quantum
error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors
with fidelity exponentially close to 1, at the price of increasing the size of
the registers (i.e., the coding alphabet). This demonstrates a sharp
distinction between exact and approximate quantum error correction. The codes
have the property that any components reveal no information about the
message, and so they can also be viewed as error-tolerant secret sharing
schemes.
The construction has several interesting implications for cryptography and
quantum information theory. First, it suggests that secret sharing is a better
classical analogue to quantum error correction than is classical error
correction. Second, it highlights an error in a purported proof that verifiable
quantum secret sharing (VQSS) is impossible when the number of cheaters t is
n/4. More generally, the construction illustrates a difference between exact
and approximate requirements in quantum cryptography and (yet again) the
delicacy of security proofs and impossibility results in the quantum model.Comment: 14 pages, no figure
Secret sharing and duality
Secret sharing is an important building block in cryptography. All explicitly
defined secret sharing schemes with known exact complexity bounds are
multi-linear, thus are closely related to linear codes. The dual of such a
linear scheme, in the sense of duality of linear codes, gives another scheme
for the dual access structure. These schemes have the same complexity, namely
the largest share size relative to the secret size is the same. It is a
long-standing open problem whether this fact is true in general: the complexity
of any access structure is the same as the complexity of its dual. We give an
almost answer to this question. An almost perfect scheme allows negligible
errors, both in the recovery and in the independence. There exists an almost
perfect ideal scheme on 174 participants whose complexity is strictly smaller
than that of its dual
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