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A New Protocol For Strong Coin Tossing

Roger Colbeck

Published Sep 5, 2006• 0 citations
OpenAlex

Abstract

In the literature, strong coin tossing protocols based on bit commitment have been proposed. Here we examine a protocol that instead tries to achieve the task by sharing entanglement securely. The protocol uses only qubits, and has bias 1/4. This is equal to the best known bias for bit commitment based schemes.

Related papers

Unconditionally Secure Quantum Coin Tossing

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In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually $1/2 + ξ$ where the bias $ξ$ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where $n \in O(\lg m)$. The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than $1/m$. The result is discussed in the light of the impossibility result for exact coin tossing.

arXiv:quant-ph/9904078•Apr 22, 1999•17 citations

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Unconditionally Secure Quantum Coin Tossing. (arXiv:quant-ph/9904078v2 UPDATED)

Dominic Mayers, Louis Salvail, Yoshie Chiba-Kohno

In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually $1/2 + \xi$ where the bias $\xi$ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where $n \in O(\lg m)$. The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than $1/m$. The result is discussed in the light of the impossibility result for exact coin tossing.

•Feb 27, 2018•0 citations

On bit-commitment based quantum coin flipping. (arXiv:quant-ph/0206123v1 CROSS LISTED)

Ashwin Nayak, Peter W. Shor

In this paper, we focus on a special framework for quantum coin flipping protocols,_bit-commitment based protocols_, within which almost all known protocols fit. We show a lower bound of 1/16 for the bias in any such protocol. We also analyse a sequence of multi-round protocol that tries to overcome the drawbacks of the previously proposed protocols, in order to lower the bias. We show an intricate cheating strategy for this sequence, which leads to a bias of 1/4. This indicates that a bias of 1/4 might be optimal in such protocols, and also demonstrates that a cleverer proof technique may be required to show this optimality.

•Mar 21, 2018•0 citations

Bit-commitment-based quantum coin flipping

Ashwin Nayak, Peter W. Shor

In this paper we focus on a special framework for quantum coin-flipping protocols, bit-commitment-based protocols, within which almost all known protocols fit. We show a lower bound of 1/16 for the bias in any such protocol. We also analyze a sequence of multiround protocols that tries to overcome the drawbacks of the previously proposed protocols in order to lower the bias. We show an intricate cheating strategy for this sequence, which leads to a bias of 1/4. This indicates that a bias of 1/4 might be optimal in such protocols, and also demonstrates that a more clever proof technique may be required to show this optimality.

arXiv:quant-ph/0206123•Physical Review A•Jan 8, 2003•64 citations

A Novel Quantum Coin Tossing Protocol Based on Quantum Public-Key Cryptosystem

Guanghui Liu, Dong Cao

Quantum coin tossing is a simple cryptographic primitive with many applications in more complicated tasks and plays a crucial role in complex quantum cryptography protocol design. Coin tossing protocols in classical environment are often based on bit commitment protocol. It has been proved that unconditionally secure quantum bit commitment schemes are insecure. Therefore, quantum coin tossing based on quantum bit commitment protocol isn't unconditionally secure. In general, quantum coin tossing is strictly weaker than bit commitment. In this paper, we have proposed a quantum coin tossing protocol based on quantum public-key cryptosystems. According to quantum CSS codes, we constructed a class of quantum quasi-cyclic low-density parity-check codes, and then proposed a novel quantum coin tossing protocol. Security analysis show that the proposed protocols are more secure.

International Conference on Internet Technology and Applications•Aug 1, 2011•0 citations
In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually 1/2+ξ1/2 + ξ1/2+ξ where the bias ξξξ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where n∈O(lg⁡m)n \in O(\lg m)n∈O(lgm). The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than 1/m1/m1/m. The result is discussed in the light of the impossibility result for exact coin tossing.
In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually 1/2+ξ1/2 + \xi1/2+ξ where the bias ξ\xiξ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where n∈O(lg⁡m)n \in O(\lg m)n∈O(lgm). The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than 1/m1/m1/m. The result is discussed in the light of the impossibility result for exact coin tossing.
In this paper, we focus on a special framework for quantum coin flipping protocols,_bit-commitment based protocols_, within which almost all known protocols fit. We show a lower bound of 1/16 for the bias in any such protocol. We also analyse a sequence of multi-round protocol that tries to overcome the drawbacks of the previously proposed protocols, in order to lower the bias. We show an intricate cheating strategy for this sequence, which leads to a bias of 1/4. This indicates that a bias of 1/4 might be optimal in such protocols, and also demonstrates that a cleverer proof technique may be required to show this optimality.
In this paper we focus on a special framework for quantum coin-flipping protocols, bit-commitment-based protocols, within which almost all known protocols fit. We show a lower bound of 1/16 for the bias in any such protocol. We also analyze a sequence of multiround protocols that tries to overcome the drawbacks of the previously proposed protocols in order to lower the bias. We show an intricate cheating strategy for this sequence, which leads to a bias of 1/4. This indicates that a bias of 1/4 might be optimal in such protocols, and also demonstrates that a more clever proof technique may be required to show this optimality.
Quantum coin tossing is a simple cryptographic primitive with many applications in more complicated tasks and plays a crucial role in complex quantum cryptography protocol design. Coin tossing protocols in classical environment are often based on bit commitment protocol. It has been proved that unconditionally secure quantum bit commitment schemes are insecure. Therefore, quantum coin tossing based on quantum bit commitment protocol isn't unconditionally secure. In general, quantum coin tossing is strictly weaker than bit commitment. In this paper, we have proposed a quantum coin tossing protocol based on quantum public-key cryptosystems. According to quantum CSS codes, we constructed a class of quantum quasi-cyclic low-density parity-check codes, and then proposed a novel quantum coin tossing protocol. Security analysis show that the proposed protocols are more secure.