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Revision #1 to TR06-085 | 13th December 2006 00:00

#### Using Quantum Oblivious Transfer for Cheat Sensitive Quantum Bit Commitment Revision of: TR06-085

Revision #1
Authors: Andreas Jakoby, Maciej Liskiewicz, Aleksander Madry
Accepted on: 13th December 2006 00:00
Keywords:

Abstract:

We investigate two-party cryptographic protocols, called cheat
sensitive protocols,
which guarantee that if one party cheats then the other has good
probability of detecting the
mistrustful party. We give quantum protocols for two basic cryptographic
primitives: bit
commitment and one-out-of-two oblivious transfer ($\binom{2}{1}$-OT),
and prove that they
are cheat sensitive. For the quantum bit commitment scheme we show that
if a cheating gives
$\varepsilon$ advantage i.e. information about the committed bit then
the committer can detect
the cheating with a probability $\Omega(\varepsilon^2)$; If the
committer cheats trying to change
his mind during the revealing phase then the probability of detecting
the cheating is greater
than some fixed constant $\lambda>0$. This improves the probabilities of
cheating detections shown
by Hardy and Kent [Phys.Rev.Lett.'04], as well as the scheme by
Aharonov et~al.~[Proc. STOC'00]
who presented a protocol that is sensitive against cheating by one
party, but not both parties
at the same time. Our cheat sensitive quantum $\binom{2}{1}$-OT protocol
guarantees that if
cheating gives any mistrustful party $\varepsilon$ advantage then the
other party can detect
the cheating with a probability $\Omega(\varepsilon^2)$.
The heart of the both cheat-sensitive protocols is a weakened version of
quantum
$\binom{2}{1}$-OT which we call {\em susceptible} quantum
$\binom{2}{1}$-OT. In this version,
similarly as in the standard definition, Alice has initially secret bits
$a_0,a_1$ and Bob
has a secret selection bit $i$ and if both parties are honest they solve
the $\binom{2}{1}$-OT
problem fulfilling the standard security requirements. However, if Alice
is dishonest and she
gains some information about the secret selection bit then the
probability that Bob computes
the correct value is proportionally small. Moreover, if Bob is dishonest
and he learns something
about both bits, then he is not able to gain full information about one
of them.

### Paper:

TR06-085 | 15th May 2006 00:00

#### Using Quantum Oblivious Transfer to Cheat Sensitive Quantum Bit Commitment

TR06-085
Authors: Andreas Jakoby, Maciej Liskiewicz, Aleksander Madry
Publication: 19th July 2006 09:25
Keywords:

Abstract:

It is well known that unconditionally secure bit commitment is impossible
even in the quantum world. In this paper a weak variant of quantum bit
commitment, introduced independently by Aharonov et al. and Hardy and Kent
is investigated. In this variant, the parties require some nonzero probability
of detecting a cheating, i.e. if Bob, who commits a bit $b$ to Alice,
changes his mind during the revealing phase then Alice detects the cheating
with a positive probability (we call this property binding); and if Alice
gains information about the committed bit before the revealing phase then
Bob discovers this with positive probability (sealing). In our paper we give
quantum bit commitment scheme that is simultaneously binding and sealing and
we show that if a cheating gives $\varepsilon$ advantage to a malicious Alice
then Bob can detect the cheating with a probability $\Omega(\varepsilon^2)$.
If Bob cheats then Alice's probability of detecting the cheating is greater
than some fixed constant $\lambda>0$. This improves the probabilities of
cheating detections shown by Hardy and Kent and the scheme by Aharonov et al.
who presented a protocol that is either binding or sealing, but not
simultaneously both.

To construct a cheat sensitive quantum bit commitment scheme we use a protocol
for a weak quantum one-out-of-two oblivious transfer ($\binom{2}{1}$-OT). In this
version, similarly as in the standard definition, Alice has initially secret bits
$a_0,a_1$ and Bob has a secret selection bit $i$ and if both parties are honest
they solve the $\binom{2}{1}$-OT problem fulfilling the standard security
requirements. However, if Alice is dishonest and she gains some information
about the secret selection bit then the probability that Bob computes the correct
value is proportionally small. Moreover, if Bob is dishonest and he learns something
about both bits, then he is not able to gain full information about one of them.

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