Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Cheat-sensitive commitment of a classical bit coded in a block of m × n round-trip qubits

Kaoru Shimizu, Hiroyuki Fukasaka, Kiyoshi Tamaki, Nobuyuki Imoto

Published Aug 4, 2011• 18 citations
Publisher

Abstract

This paper proposes a quantum protocol for a cheat-sensitive commitment of a classical bit. Alice, the receiver of the bit, can examine dishonest Bob, who changes or postpones his choice. Bob, the sender of the bit, can examine dishonest Alice, who violates concealment. For each round-trip case, Alice sends one of two spin states |$S$\ifmmode\pm\else\textpm\fi{}⟩ by choosing basis $S$ at random from two conjugate bases $X$ and $Y$. Bob chooses basis $C$ \ensuremath{\in} {$X$,$Y$} to perform a measurement and returns a resultant state |$C$\ifmmode\pm\else\textpm\fi{}⟩. Alice then performs a measurement with the other basis $R$ (\ensuremath{\ne}$S$) and obtains an outcome |$R$\ifmmode\pm\else\textpm\fi{}⟩. In the opening phase, she can discover dishonest Bob, who unveils a wrong basis with a faked spin state, or Bob can discover dishonest Alice, who infers basis $C$ but destroys |$C$\ifmmode\pm\else\textpm\fi{}⟩ by setting $R$ to be identical to $S$ in the commitment phase. If a classical bit is coded in a block of $m$ \ifmmode\times\else\texttimes\fi{} $n$ qubit particles, impartial examinations and probabilistic security criteria can be achieved.

DOI
10.1103/physreva.84.022308

Related papers

Comment on “Cheat-sensitive commitment of a classical bit coded in a block of m×n round-trip qubits”

Guang Ping He

We found a cheating strategy for the quantum cheat-sensitive bit commitment protocol proposed in Phys. Rev. A 84, 022308 (2011). It enables the receiver of the commitment to cheat with a probability not less than $1/2$, no matter what values are chosen for the security parameters in the protocol. More interestingly, the probability for successful cheating will rise as the number $n$ of the particles used in the protocol increases and will be arbitrarily close to $100%$ in the limit $n\ensuremath{\rightarrow}\ensuremath{\infty}$.

Physical Review A•May 5, 2014•2 citations

Using quantum oblivious transfer to cheat sensitive quantum bit commitment

Andreas Jakoby, Maciej Liśkiewicz, Aleksander Mądry

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. [STOC, 2000] and Hardy and Kent [Phys. Rev. Lett. 92 (2004)] 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 epsilon advantage to a malicious Alice then Bob can detect the cheating with a probability Omega(epsilon^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.

arXiv:quant-ph/0605150•May 17, 2006•1 citation

Possibility, impossibility, and cheat sensitivity of quantum-bit string commitment

Harry Buhrman, Matthias Christandl, Patrick M. Hayden +2 more

Unconditionally secure nonrelativistic bit commitment is known to be impossible in both the classical and the quantum worlds. But when committing to a string of $n$ bits at once, how far can we stretch the quantum limits? In this paper, we introduce a framework for quantum schemes where Alice commits a string of $n$ bits to Bob in such a way that she can only cheat on $a$ bits and Bob can learn at most $b$ bits of information before the reveal phase. Our results are twofold: we show by an explicit construction that in the traditional approach, where the reveal and guess probabilities form the security criteria, no good schemes can exist: $a+b$ is at least $n$. If, however, we use a more liberal criterion of security, the accessible information, we construct schemes where $a=4\text{ }{\text{log}}_{2}\text{ }n+O(1)$ and $b=4$, which is impossible classically. We furthermore present a cheat-sensitive quantum bit string commitment protocol for which we give an explicit tradeoff between Bob's ability to gain information about the committed string, and the probability of him being detected cheating.

arXiv:quant-ph/0504078•Physical Review A•Aug 11, 2008•63 citations

Security of two-state and four-state practical quantum bit-commitment protocols

Ricardo Loura, D. Arsenović, Nikola Paunković +2 more

We study cheating strategies against a practical four-state quantum bit-commitment protocol [A. Danan and L. Vaidman, Quant. Info. Proc. 11, 769 (2012)] and its two-state variant [R. Loura et al., Phys. Rev. A 89, 052336 (2014)] when the underlying quantum channels are noisy and the cheating party is constrained to using single-qubit measurements only. We show that simply inferring the transmitted photons' states by using the Breidbart basis, optimal for ambiguous (minimum-error) state discrimination, does not directly produce an optimal cheating strategy for this bit-commitment protocol. We introduce a strategy, based on certain postmeasurement processes and show it to have better chances at cheating than the direct approach. We also study to what extent sending forged geographical coordinates helps a dishonest party in breaking the binding security requirement. Finally, we investigate the impact of imperfect single-photon sources in the protocols. Our study shows that, in terms of the resources used, the four-state protocol is advantageous over the two-state version. The analysis performed can be straightforwardly generalized to any finite-qubit measurement, with the same qualitative results.

arXiv:1609.08562•Physical Review A•Dec 27, 2016•8 citations

Quantum bit commitment with cheat sensitive binding and approximate sealing

Yan-Bing Li, Sheng-Wei Xu, Wei Huang +1 more

This paper proposes a cheat-sensitive quantum bit commitment scheme based on single photons, in which Alice commits a bit to Bob. Here, Bob's probability of success at cheating as obtains the committed bit before the opening phase becomes close to (just like performing a guess) as the number of single photons used is increased. And if Alice alters her committed bit after the commitment phase, her cheating will be detected with a probability that becomes close to 1 as the number of single photons used is increased. The scheme is easy to realize with present day technology.

arXiv:1407.6939•Journal of Physics A Mathematical and Theoretical•Mar 12, 2015•6 citations

Cheating in quantum Rabin oblivious transfer using delayed measurements

James T. Peat, Erika Andersson

Oblivious transfer has been the interest of study as it can be used as a building block for multiparty computation. There are many forms of oblivious transfer; we explore a variant known as Rabin oblivious transfer. Here the sender Alice has one bit, and the receiver Bob obtains this bit with a certain probability. The sender does not know whether the receiver obtained the bit or not. For a previously suggested protocol, we show a possible attack using a delayed measurement. This allows a cheating party to pass tests carried out by the other party, while gaining more information than if they would have been honest. We show how this attack allows perfect cheating, unless the protocol is modified, and suggest changes which lower the cheating probability for the examined cheating strategies.

arXiv:2408.12388•Aug 22, 2024•0 citations
This paper proposes a quantum protocol for a cheat-sensitive commitment of a classical bit. Alice, the receiver of the bit, can examine dishonest Bob, who changes or postpones his choice. Bob, the sender of the bit, can examine dishonest Alice, who violates concealment. For each round-trip case, Alice sends one of two spin states |SSS\ifmmode\pm\else\textpm\fi{}⟩ by choosing basis SSS at random from two conjugate bases XXX and YYY. Bob chooses basis CCC \ensuremath{\in} {XXX,YYY} to perform a measurement and returns a resultant state |CCC\ifmmode\pm\else\textpm\fi{}⟩. Alice then performs a measurement with the other basis RRR (\ensuremath{\ne}SSS) and obtains an outcome |RRR\ifmmode\pm\else\textpm\fi{}⟩. In the opening phase, she can discover dishonest Bob, who unveils a wrong basis with a faked spin state, or Bob can discover dishonest Alice, who infers basis CCC but destroys |CCC\ifmmode\pm\else\textpm\fi{}⟩ by setting RRR to be identical to SSS in the commitment phase. If a classical bit is coded in a block of mmm \ifmmode\times\else\texttimes\fi{} nnn qubit particles, impartial examinations and probabilistic security criteria can be achieved.
We found a cheating strategy for the quantum cheat-sensitive bit commitment protocol proposed in Phys. Rev. A 84, 022308 (2011). It enables the receiver of the commitment to cheat with a probability not less than 1/21/21/2, no matter what values are chosen for the security parameters in the protocol. More interestingly, the probability for successful cheating will rise as the number nnn of the particles used in the protocol increases and will be arbitrarily close to 100100%100 in the limit $n\ensuremath{\rightarrow}\ensuremath{\infty}$.
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. [STOC, 2000] and Hardy and Kent [Phys. Rev. Lett. 92 (2004)] 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 epsilon advantage to a malicious Alice then Bob can detect the cheating with a probability Omega(epsilon^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.
Unconditionally secure nonrelativistic bit commitment is known to be impossible in both the classical and the quantum worlds. But when committing to a string of nnn bits at once, how far can we stretch the quantum limits? In this paper, we introduce a framework for quantum schemes where Alice commits a string of nnn bits to Bob in such a way that she can only cheat on aaa bits and Bob can learn at most bbb bits of information before the reveal phase. Our results are twofold: we show by an explicit construction that in the traditional approach, where the reveal and guess probabilities form the security criteria, no good schemes can exist: a+ba+ba+b is at least nnn. If, however, we use a more liberal criterion of security, the accessible information, we construct schemes where a=4 log2 n+O(1)a=4\text{ }{\text{log}}_{2}\text{ }n+O(1)a=4 log2​ n+O(1) and b=4b=4b=4, which is impossible classically. We furthermore present a cheat-sensitive quantum bit string commitment protocol for which we give an explicit tradeoff between Bob's ability to gain information about the committed string, and the probability of him being detected cheating.
We study cheating strategies against a practical four-state quantum bit-commitment protocol [A. Danan and L. Vaidman, Quant. Info. Proc. 11, 769 (2012)] and its two-state variant [R. Loura et al., Phys. Rev. A 89, 052336 (2014)] when the underlying quantum channels are noisy and the cheating party is constrained to using single-qubit measurements only. We show that simply inferring the transmitted photons' states by using the Breidbart basis, optimal for ambiguous (minimum-error) state discrimination, does not directly produce an optimal cheating strategy for this bit-commitment protocol. We introduce a strategy, based on certain postmeasurement processes and show it to have better chances at cheating than the direct approach. We also study to what extent sending forged geographical coordinates helps a dishonest party in breaking the binding security requirement. Finally, we investigate the impact of imperfect single-photon sources in the protocols. Our study shows that, in terms of the resources used, the four-state protocol is advantageous over the two-state version. The analysis performed can be straightforwardly generalized to any finite-qubit measurement, with the same qualitative results.
This paper proposes a cheat-sensitive quantum bit commitment scheme based on single photons, in which Alice commits a bit to Bob. Here, Bob's probability of success at cheating as obtains the committed bit before the opening phase becomes close to (just like performing a guess) as the number of single photons used is increased. And if Alice alters her committed bit after the commitment phase, her cheating will be detected with a probability that becomes close to 1 as the number of single photons used is increased. The scheme is easy to realize with present day technology.
Oblivious transfer has been the interest of study as it can be used as a building block for multiparty computation. There are many forms of oblivious transfer; we explore a variant known as Rabin oblivious transfer. Here the sender Alice has one bit, and the receiver Bob obtains this bit with a certain probability. The sender does not know whether the receiver obtained the bit or not. For a previously suggested protocol, we show a possible attack using a delayed measurement. This allows a cheating party to pass tests carried out by the other party, while gaining more information than if they would have been honest. We show how this attack allows perfect cheating, unless the protocol is modified, and suggest changes which lower the cheating probability for the examined cheating strategies.