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Quantum Cheque: Difference between revisions
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(Created page with "Quantum cheque scheme is a private-key protocol which allows trusted banks to issue perfectly secure and verifiable quantum cheque books to account holders and also enables th...") |
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* In the verification process, the bank sets a thresholding security parameter <math>\kappa</math>. The swap test is passed if <math>\{ \langle\psi^{(i)}|\psi^{,(i)}\rangle \geq \kappa\}_{i=1:l}</math> | * In the verification process, the bank sets a thresholding security parameter <math>\kappa</math>. The swap test is passed if <math>\{ \langle\psi^{(i)}|\psi^{,(i)}\rangle \geq \kappa\}_{i=1:l}</math> | ||
* No quantum memory would be required for the account holder to store the quantum check if the transaction is occurring in real time. | * No quantum memory would be required for the account holder to store the quantum check if the transaction is occurring in real time. | ||
==Notation== | |||
* <math>k</math>: Shared key between account holder and bank where <math>k \in \{0,1\}^L</math>. | |||
* <math>\Pi</math>: Digital signature scheme, where <math>\Pi=(Gen, Sign, Vrfy)</math>. | |||
* <math>id</math>: Account holder's identity. | |||
* <math>pk</math>: Account holder's public key. | |||
* <math>sk</math>: Account holder's private key. | |||
* <math>s</math>: Unique serial number where <math>s \in \{0,1\}^{l(n)}</math>. | |||
* <math>{|\phi^{(i)}\rangle_{GHZ}}</math>: <math>n</math> GHZ triplet states where, | |||
<div style="text-align: center;"><math>|\phi^{(i)}\rangle_{GHZ} = \frac{1}{\sqrt{2}}(|0^{(i)}\rangle_{A_1}|0^{(i)}\rangle_{A_2}|0^{(i)}\rangle_{B} + |1^{(i)}\rangle_{A_1}|1^{(i)}\rangle_{A_2}|1^{(i)}\rangle_{B})</math></div> | |||
* <math>{|\phi^{(i)}\rangle_{A_1}}</math>: First entangled qubit from every GHZ triplet state which is given to account holder. | |||
* <math>{|\phi^{(i)}\rangle_{A_2}}</math>: Second entangled qubit from every GHZ triplet state which is given to account holder. | |||
* <math>{|\phi^{(i)}\rangle_{B}}</math>: First entangled qubit from every GHZ triplet state which stays with bank. | |||
* <math>r</math>: Generated random number where <math>r \in \{0,1\}^L</math>. | |||
* <math>M</math>: Amount of money account holder signs on the cheque. | |||
* <math>f</math>: Quantum one way function. | |||
* <math>x\mid\mid</math>y: concatenation of two bit strings <math>x</math> and <math>y</math>. | |||
* <math>{|\psi^{(i)}\rangle}</math>: quantum state prepared by the account where, | |||
<div style="text-align: center;"><math>|\psi^{(i)}\rangle = f(k \mid\mid id\mid\mid r\mid\mid M\mid\mid i)</math></div>. This quantum state is also denoted as <math>\alpha_i|0\rangle + \beta_i|1\rangle</math>. | |||
* <math>|\Phi^\pm\rangle</math>: Bell state <math>\frac{|00\rangle \pm |11\rangle}{\sqrt{2}}</math> | |||
* <math>|\Psi^\pm\rangle</math>: Bell state <math>\frac{|10\rangle \pm |01\rangle}{\sqrt{2}}</math> | |||
* <math>\sigma</math>: In <math>\chi</math>, output of signing with <math>s</math>. | |||
* <math>\chi</math>: Quantum cheque where, | |||
<div style="text-align: center;"><math> | |||
\chi = (id, s, r, \sigma, M, \{{|\phi^{(i)}\rangle_{A_1}}\}_{i=1:n}) | |||
</math></div> | |||
* <math>\kappa</math>: Threshold constant set as a security parameter by the bank in the swap test. | |||
* <math>|\psi^{,(i)}\rangle</math>: Quantum state prepared by the bank for verification. | |||