Arbitrated Quantum Digital Signature: Difference between revisions

Arbitrated Quantum Digital Signature (edit)

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-* <math>|P\rangle</math>: Private key quantum state where <math>|P\rangle \in {(|\+\rangle, |\-\rangle, |1\rangle,|0\rangle\)^n}</math> and it is the quantum state
+* <math>|P\rangle</math>: Private key quantum state where <math>|P\rangle \in \{|+\rangle, |-\rangle, |1\rangle, |0\rangle\}^n</math> and it is the quantum state:
 <math>|P\rangle := H^{k_{pri}}|\phi\rangle_{s, t\oplus m}</math>
+* <math>P</math>: Classical 2n-bit for <math>n</math>-qubit <math>|P\rangle</math> where <math>|+\rangle</math> is encoded to 10, <math>|-\rangle</math> to 11, <math>|1\rangle</math> to 00 and <math>|0\rangle</math> is encoded to 01.
+* <math>B_P</math>: This is the set of the basis of each qubit state in <math>|P\rangle</math>.
-* $P$: Classical 2n-bit for $n$-qubit $\ket{P}$ where $\ket{+}$ is encoded to 10, $\ket{-}$ to 11, $\ket{1}$ to 00 and $\ket{0}$ is encoded to 01.
+<math> B_P = Basis(|P\rangle) \in \{+,\times \}</math>
-* $B_P$: This is the set of the basis of each qubit state in $\ket{P}$.
+* <math>|F\rangle</math>: Quantum digital digest received by PKG.
-     \begin{equation}
+* <math>|F'\rangle</math>: Quantum digital digest generated by Verifier.
-         B_P = Basis(\ket{P}) \in \{+,\times \}
+* <math>u</math>: The most number of verifiers in this scheme.
-     \end{equation}
+* <math>w</math>: Safety parameter threshold for acceptance.
-* $\ket{F}$: Quantum digital digest received by PKG.
+* <math>w_0</math>: Security threshold decided in advance.
-* $\ket{F}'$: Quantum digital digest generated by Verifier.
+* <math>w'</math>: Number of times SWAP test is performed.
-* $u$: The most number of verifiers in this scheme.
+* <math>|V\rangle_{m, k_{pub},S}</math>: A quantum state, where
-* $w$: Safety parameter threshold for acceptance.
+<math>|V\rangle_{m, k_{pub},S} := Y^m H^{k_{pub}}|S\rangle_{k_{pri}, m}</math>
-* $w_0$: Security threshold decided in advance.
+This state is also expressed as <math>\beta|\phi\rangle_{k_{pri}\oplus s, t\oplus m}</math> where <math>\beta \in \{1, -1, \iota, -\iota\}</math>
-* $w'$: Number of times SWAP test is performed.
+* <math>|Q\rangle</math>: Result of Verifier's measurement of <math>|V\rangle_{m, k_{pub},S}</math>.
-* $\ket{V}_{m, k_{pub},S}$: A quantum state, where
+* <math>Q</math>: Classical bit string denoted as <math>Q \in \{00, 01, 10, 11\}^n</math>. It is proven that <math>P=Q</math>.
-     \begin{equation}
+* <math>\delta</math>: <math>\langle F|F\rangle'</math>, where <math>\delta \in [0,1)</math>.
-        \ket{V}_{k_{pub},S} := Y^m H^{k_{pub}}\ket{S}_{k_{pri}, m}
-     \end{equation}
-     This state is also expressed as $\beta\ket{\phi}_{k_{pri}\oplus s, t\oplusm}$ where $\beta \in \{1, -1, \iota, -\iota\}$
-* $\ket{Q}$: Result of Verifier's measurement of $\ket{V}_{m, k_{pub},S}$.
-* $Q$: Classical bit string denoted as $Q \in \{00, 01, 10, 11\}^n$. It is proven that $P=Q$.
-* $\delta$: $\braket{F}{F}'$, where $\delta \in [0,1)$.