Cryptography Reference
In-Depth Information
procedure. If the first two subshares are transmitted successfully the receiver
can recover the third share and, since he or she already has the first share, also
the entire entangled beam. If transmission of the second subshare fails, the
sender encodes the remaining subshare into three subsubshares and the pro-
cess continues. This nested series of quantum state sharing protocols provides
in principle a 100% successful method to distribute entangled states, and in-
deed any arbitrary quantum states, through channels prone to catastrophic
failures.
8.6.4 Multipartite Quantum Cryptography
Quantum state sharing could be useful for generalized quantum key dis-
tribution. In the usual quantum cryptography protocols, such as BB84 [31],
Alice and Bob share a quantum key, which can be used to create a secure
one-time pad via public channels. A quantum key can be established by Al-
ice sending qubits to Bob, as suggested by Bennett and Brassard, or equiv-
alently by sharing entangled pairs, or ebits, along the lines suggested by
Ekert. To see how quantum state sharing plays a role in quantum key dis-
tribution, let us consider the latter approach of having Alice and Bob share
ebits.
Suppose that Alice and Bob are not planning to use the key themselves
and instead disseminate their shares to other players. Alice's colleagues have
n
A
shares, and Bob's colleagues hold
n
B
shares. At some future time, some of
Alice's colleagues and some of Bob's colleagues can collaborate separately to
extract Alice's state and Bob's state, respectively, and then communicate to
establish the quantum key for secure quantum cryptography.
Acknowledgments
The authors would like to acknowledge Dr. Tomas Tyc for his early con-
tribution to the realization of the quantum state sharing scheme and Dr.
Roman Schnabel for taking part in building the EPR source. We also acknowl-
edge the Australian Research Council (ARC), the Defence Signals Directorate
(DSD), the Defence Science and Technology Organisation (DSTO) and Al-
berta's informatics Circle Of Research Excellence (iCORE) for funding this
project.
References
1. A. Shamir, How to share a secret,
Commun. ACM,
22, 612-613, 1979.
2. M. Hillery, V. Buzek, and A. Berthiaume, Quantum secret sharing,
Phys. Rev.
A
, 59, 1829-1834, 1999.
3. C.L. Liu, Introduction to Combinatorial Mathematics, McGraw-Hill, New
York, 1968.
4. G.R. Blakley, Safeguarding cryptographic keys,
Proc. AFIPS
1979, National
Computer Conference, 313-317, AFIPS, 1979.
