Semi-Quantum Blind Signature Against Collective Noise

Junhui Wang; Yunxia Li; Han Guo; Jiahua Wei

doi:10.3788/LOP202259.1927001

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 19 >Page 1927001 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 19, 1927001 (2022)

Semi-Quantum Blind Signature Against Collective Noise

Junhui Wang, Yunxia Li, Han Guo, and Jiahua Wei^*

Author Affiliations

Institute of Information and Navigation, Air Force Engineering University, Xi'an 710077, Shaanxi, China

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DOI: 10.3788/LOP202259.1927001 Cite this Article Set citation alerts

Junhui Wang, Yunxia Li, Han Guo, Jiahua Wei. Semi-Quantum Blind Signature Against Collective Noise[J]. Laser & Optoelectronics Progress, 2022, 59(19): 1927001 Copy Citation Text

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Abstract

As an important part of quantum cryptography, quantum blind signature has attracted more and more attention in recent years. Semi-quantum protocol provides a feasible method for the practical application of quantum blind signature. In this paper, a semi-quantum blind signature protocol against collective noise is proposed by combining the semi-quantum and logical qubits resisting collective noise. In the protocol, only the signer Charlie has the complete quantum capability, which makes the demand for quantum resources of the protocol drop drastically. Through security analysis, the protocol can resist internal attack, entanglement-measurement attack and intercept-resend attack. The protocol implements reusability of keys and the scheme can be extended to quantum signature networks to realize cross-center quantum signature.

Keywords

collective noise quantum blind signature quantum cryptography semi-quantum

U_{d p} = (\begin{matrix} 1 & 0 \\ 0 & e x p (i ω) \end{matrix}),

（1）

\begin{array}{l} {|ϕ^{+}〉}_{1234}^{d p} = \frac{1}{\sqrt[]{2}} {({|0〉}_{d p} {|0〉}_{d p} + {|1〉}_{d p} {|1〉}_{d p})}_{1234} = \\ \frac{1}{\sqrt[]{2}} {(|0101〉 + |1010〉)}_{1234} = \\ \frac{1}{\sqrt[]{2}} {(|ϕ^{+}〉 |ϕ^{+}〉 + |ϕ^{-}〉 |ϕ^{-}〉)}_{1324}, \end{array}

（2）

\begin{array}{l} U_{r} |0〉 = c o s θ |0〉 + s i n θ |1〉, \\ U_{r} |1〉 = - s i n θ |0〉 + c o s θ |1〉, \end{array}

（3）

\begin{array}{l} {|ϕ^{+}〉}_{1234}^{r} = \frac{1}{\sqrt[]{2}} {({|0〉}_{r} {|0〉}_{r} + {|1〉}_{r} {|1〉}_{r})}_{1234} = \\ \frac{1}{2 \sqrt[]{2}} {(|0000〉 + |0011〉 + |1100〉 + |1111〉 + |0101〉 - |0110〉 - |1001〉 + |1010〉)}_{1234} = \\ \frac{1}{\sqrt[]{2}} {(|ϕ^{+}〉 |ϕ^{+}〉 + |ψ^{-}〉 |ψ^{-}〉)}_{1324} \end{array}

。（4）

\begin{array}{l} {|φ〉}_{123456}^{d p} = \frac{1}{\sqrt[]{2}} {({|0〉}_{d p} {|0〉}_{d p} {|0〉}_{d p} + {|1〉}_{d p} {|1〉}_{d p} {|1〉}_{d p})}_{123456} = \\ \frac{1}{2 \sqrt[]{2}} [{|ϕ^{+}〉}_{13} {|ϕ^{+}〉}_{24} ({|01〉}_{56} + {|10〉}_{56}) + {|ϕ^{+}〉}_{13} {|ϕ^{-}〉}_{24} ({|01〉}_{56} - {|10〉}_{56}) + \\ {|ϕ^{-}〉}_{13} {|ϕ^{+}〉}_{24} ({|01〉}_{56} - {|10〉}_{56}) + {|ϕ^{-}〉}_{13} {|ϕ^{-}〉}_{24} ({|01〉}_{56} + {|10〉}_{56})], \end{array}

（5）

{|φ〉}_{123456}^{d p} = {|0〉}_{d p} {|0〉}_{d p} {|0〉}_{d p} = \frac{1}{2} ({|ϕ^{+}〉}_{13} {|ϕ^{+}〉}_{24} {|01〉}_{56} - {|ϕ^{+}〉}_{13} {|ϕ^{-}〉}_{24} {|01〉}_{56} + {|ϕ^{-}〉}_{13} {|ϕ^{+}〉}_{24} {|01〉}_{56} - {|ϕ^{-}〉}_{13} {|ϕ^{-}〉}_{24} {|01〉}_{56}),

（6）

{|φ〉}_{123456}^{d p} = {|1〉}_{d p} {|1〉}_{d p} {|1〉}_{d p} = \frac{1}{2} ({|ϕ^{+}〉}_{13} {|ϕ^{+}〉}_{24} {|10〉}_{56} + {|ϕ^{+}〉}_{13} {|ϕ^{-}〉}_{24} {|10〉}_{56} - {|ϕ^{-}〉}_{13} {|ϕ^{+}〉}_{24} {|10〉}_{56} - {|ϕ^{-}〉}_{13} {|ϕ^{-}〉}_{24} {|10〉}_{56})

。（7）

\begin{array}{l} U_{E} {|0〉}_{d p} |E_{i}〉 = U_{E} |01〉 |E_{i}〉 = a_{00} |00〉 |e_{0} e_{0}〉 + a_{01} |01〉 |e_{0} e_{1}〉 + a_{10} |10〉 |e_{1} e_{0}〉 + a_{11} |11〉 |e_{1} e_{1}〉, \\ U_{E} {|1〉}_{d p} |E_{i}〉 = U_{E} |10〉 |E_{i}〉 = b_{00} |00〉 |e_{0}^{'} e_{0}^{'}〉 + b_{01} |01〉 |e_{0}^{'} e_{1}^{'}〉 + b_{10} |10〉 |e_{1}^{'} e_{0}^{'}〉 + b_{11} |11〉 |e_{1}^{'} e_{1}^{'}〉 \end{array}

，（8）

\begin{array}{l} {|a_{00}|}^{2} + {|a_{01}|}^{2} + {|a_{10}|}^{2} + {|a_{11}|}^{2} = 1, \\ {|b_{00}|}^{2} + {|b_{01}|}^{2} + {|b_{10}|}^{2} + {|b_{11}|}^{2} = 1, \\ a_{01} = b_{10}, a_{10} = b_{01} \end{array}

，（9）

\begin{array}{l} P_{d} ({|0〉}_{d p}) = 1 - ({|a_{01}|}^{2} + {|a_{10}|}^{2}), \\ P_{d} ({|1〉}_{d p}) = 1 - ({|b_{01}|}^{2} + {|b_{10}|}^{2}) 。 \end{array}

（10）

\begin{matrix} U_{E} {|0〉}_{d p} |E_{i}〉 = U_{E} |01〉 |E_{i}〉 = \sqrt[]{α} |01〉 |e_{0} e_{1}〉 + \sqrt[]{1 - α} |10〉 |e_{1} e_{0}〉, \\ U_{E} {|1〉}_{d p} |E_{i}〉 = U_{E} |10〉 |E_{i}〉 = \sqrt[]{1 - α} |01〉 |e_{0}^{'} e_{1}^{'}〉 + \sqrt[]{α} |10〉 |e_{1}^{'} e_{0}^{'}〉, \end{matrix}

（11）

U_{F} U_{E} {|0〉}_{d p} |E_{i}〉 = \sqrt[]{α} (\sqrt[]{β} |01〉 |ε_{0} ε_{0}〉 + \sqrt[]{1 - β} |10〉 |ε_{0} ε_{1}〉) + \sqrt[]{1 - α} (\sqrt[]{β} |10〉 |ε_{1}^{} ε_{0}^{}〉 + \sqrt[]{1 - β} |01〉 |ε_{1}^{} ε_{1}^{}〉),

（12）

U_{F} U_{E} {|1〉}_{d p} |E_{i}〉 = \sqrt[]{1 - α} (\sqrt[]{β} |01〉 |ε_{0}^{'} ε_{0}^{'}〉 + \sqrt[]{1 - β} |10〉 |ε_{0}^{'} ε_{1}^{'}〉) + \sqrt[]{α} (\sqrt[]{β} |10〉 |ε_{1}^{'} ε_{0}^{'}〉 + \sqrt[]{1 - β} |01〉 |ε_{1}^{'} ε_{1}^{'}〉),

（13）

\begin{array}{l} U_{F} U_{E} |ψ〉 = \frac{1}{\sqrt[]{2}} [((\sqrt[]{α} \sqrt[]{β} {|01〉}_{12} |ε_{0} ε_{0}〉 + \sqrt[]{α} \sqrt[]{1 - β} {|10〉}_{12} |ε_{0} ε_{1}〉) {|01〉}_{34} + \\ (\sqrt[]{1 - α} \sqrt[]{β} {|10〉}_{12} |ε_{1} ε_{0}〉 + \sqrt[]{1 - α} \sqrt[]{1 - β} {|01〉}_{12} |ε_{1} ε_{1}〉) {|01〉}_{34} + \\ (\sqrt[]{α} \sqrt[]{β} {|10〉}_{12} |ε_{1}^{'} ε_{0}^{'}〉 + \sqrt[]{α} \sqrt[]{1 - β} {|01〉}_{12} |ε_{1}^{'} ε_{1}^{'}〉) {|10〉}_{34} + \\ (\sqrt[]{1 - α} \sqrt[]{β} {|01〉}_{12} |ε_{0}^{'} ε_{0}^{'}〉 + \sqrt[]{1 - α} \sqrt[]{1 - β} {|10〉}_{12} |ε_{0}^{'} ε_{1}^{'}〉) {|10〉}_{34}] \end{array}

，（14）

U_{F} U_{E} |ψ〉 = \frac{1}{\sqrt[]{2}} ({|01〉}_{12} |ε_{0} ε_{0}〉 {|01〉}_{34} + {|10〉}_{12} |ε_{1}^{'} ε_{0}^{'}〉 {|10〉}_{34})

，（15）

\begin{array}{l} ρ_{1} = \frac{1}{2} (|01〉 |ε_{0} ε_{0}〉 |01〉 〈01| 〈01| 〈ε_{0} ε_{0}| + |10〉 |ε_{1}^{'} ε_{0}^{'}〉 |10〉 〈10| 〈10| 〈ε_{1}^{'} ε_{0}^{'}| + \\ |01〉 |ε_{0} ε_{0}〉 |01〉 〈10| 〈10| 〈ε_{1}^{'} ε_{0}^{'}| + |10〉 |ε_{1}^{'} ε_{0}^{'}〉 |10〉 〈01| 〈01| 〈ε_{0} ε_{0}|) \end{array}

，（16）

ρ_{1}^{'} = |ε_{0} ε_{0}〉 〈ε_{0} ε_{0}| + |ε_{1}^{'} ε_{0}^{'}〉 〈ε_{1}^{'} ε_{0}^{'}|,

（17）

ρ_{1}^{'} = (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}) 。

（18）

Junhui Wang, Yunxia Li, Han Guo, Jiahua Wei. Semi-Quantum Blind Signature Against Collective Noise[J]. Laser & Optoelectronics Progress, 2022, 59(19): 1927001

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