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Arbitrated Quantum Digital Signature: Difference between revisions
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* <math>G</math>: PKG's master key which is a one way function where <math>\{0,1\}^n \xrightarrow{}\{0,1\}^n</math> . | * <math>G</math>: PKG's master key which is a one way function where <math>\{0,1\}^n \xrightarrow{}\{0,1\}^n</math> . | ||
* <math>F</math>: Public quantum one way function selected by Seller to generate quantum digest. | * <math>F</math>: Public quantum one way function selected by Seller to generate quantum digest. | ||
* <math>m</math>: Message sent by Seller to the | * <math>m</math>: Message sent by Seller to the Verifier, where <math>m \in \{0,1\}^n</math>. | ||
* <math>s</math>: Random string of uniform distribution selected by the Seller, where <math>s \in \{0,1\}^n</math>. | * <math>s</math>: Random string of uniform distribution selected by the Seller, where <math>s \in \{0,1\}^n</math>. | ||
* <math>t</math>: Random string of uniform distribution selected by the Seller, where <math>t \in \{0,1\}^n</math>. | * <math>t</math>: Random string of uniform distribution selected by the Seller, where <math>t \in \{0,1\}^n</math>. | ||
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*<math>b_l</math>: measurement result of <math>l^{th}</math> qubit in the concerned quantum state | *<math>b_l</math>: measurement result of <math>l^{th}</math> qubit in the concerned quantum state | ||
* <math>|F\rangle</math>: Quantum digital digest received by PKG. | * <math>|F\rangle</math>: Quantum digital digest received by PKG. | ||
* <math>|F\rangle'</math>: Quantum digital digest generated by | * <math>|F\rangle'</math>: Quantum digital digest generated by Verifier. | ||
* <math>u</math>: The most number of | * <math>u</math>: The most number of verifiers in this scheme. | ||
* <math>w</math>: Safety parameter threshold for acceptance. | * <math>w</math>: Safety parameter threshold for acceptance. | ||
* <math>w_0</math>: Security threshold decided in advance. | * <math>w_0</math>: Security threshold decided in advance. | ||
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* In this protocol, it is proven that no adversary can break the secrecy of the seller's signature private key. | * In this protocol, it is proven that no adversary can break the secrecy of the seller's signature private key. | ||
* The quantum digital signature produced in this protocol is impossible to repudiate and cannot be forged in any condition. | * The quantum digital signature produced in this protocol is impossible to repudiate and cannot be forged in any condition. | ||
* In the protocol the public and the private key | * In the protocol the public and the private key belong to the classical bits, only the signature cipher has quantum nature. | ||
* No Certificate Authority is required to manage digital public-key certificate of sellers. | * No Certificate Authority is required to manage digital public-key certificate of sellers. | ||
* If <math>|F\rangle = |F\rangle'</math>, the measuring result <math>|0\rangle</math> occurs with probability 1, otherwise it occurs with probability <math>\frac{1+\delta^2}{2}</math>. Hence, when repeated for <math>w</math> times, the probability of equality is at least 1-<math>(\frac{1+\delta^2}{2})^w</math>. | * If <math>|F\rangle = |F\rangle'</math>, the measuring result <math>|0\rangle</math> occurs with probability 1, otherwise it occurs with probability <math>\frac{1+\delta^2}{2}</math>. Hence, when repeated for <math>w</math> times, the probability of equality is at least 1-<math>(\frac{1+\delta^2}{2})^w</math>. | ||
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==Further Information== | ==Further Information== | ||
Like most other classical digital signature schemes which provide unconditional security, this scheme also requires a trusted arbitrator who distributes | Like most other classical digital signature schemes which provide unconditional security, this scheme also requires a trusted arbitrator who distributes public key to the recipients. This protocol was preceded by a few other protocols which use an arbitrator to establish quantum digital signatures, most of which used entangled states. | ||
#[https://arxiv.org/abs/quant-ph/0109007 Zeng and Keitel (2002)] | #[https://arxiv.org/abs/quant-ph/0109007 Zeng and Keitel (2002)] | ||
#[https://arxiv.org/abs/quant-ph/0511224 Wang et al (2005)] | #[https://arxiv.org/abs/quant-ph/0511224 Wang et al (2005)] | ||