Arbitrated Quantum Digital Signature: Difference between revisions

* <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</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>.

<math> B_P = Basis(|P\rangle) \in \{+,\times \}</math>

* <math>|F\rangle</math>: Quantum digital digest received by PKG.

* <math>|F'\rangle</math>: Quantum digital digest generated by Verifier.

* <math>u</math>: The most number of verifiers in this scheme.

* <math>w</math>: Safety parameter threshold for acceptance.

* <math>w_0</math>: Security threshold decided in advance.

* <math>w'</math>: Number of times SWAP test is performed.

* <math>|V\rangle_{m, k_{pub},S}</math>: A quantum state, where

<math>|V\rangle_{m, k_{pub},S} := Y^m H^{k_{pub}}|S\rangle_{k_{pri}, m}</math>

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>

* <math>|Q\rangle</math>: Result of Verifier's measurement of <math>|V\rangle_{m, k_{pub},S}</math>.

* <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>.

* <math>\delta</math>: <math>\langle F|F\rangle'</math>, where <math>\delta \in [0,1)</math>.