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Quantum Cheque: Difference between revisions
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* Account holder signs the serial number <math>s</math> using <math>\Pi</math>, as <math>\sigma \xleftarrow{} Sign_{sk}(s)</math>. | * Account holder signs the serial number <math>s</math> using <math>\Pi</math>, as <math>\sigma \xleftarrow{} Sign_{sk}(s)</math>. | ||
* Account holder produces <math>\chi</math>. | * Account holder produces <math>\chi</math>. | ||
'''Stage 3''': Verify </br> | |||
'''Output''': Cheque gets accepted or the process is aborted and the cheque is destroyed. | |||
* Third party produces the <math>\chi</math> at a valid branch of the bank. | |||
* Branch communicates with main branch of the bank and checks validity of <math>(id, s)</math> and runs <math>{Vrfy}_{pk}(\sigma, s)</math>. | |||
** If invalid: | |||
*** Bank aborts the process and destroys the cheque. | |||
** else: | |||
*** Bank continues the verification process. | |||
* Main branch of the bank performs the measurement in Hadamard basis on its copy of <math>|\phi^{(i)}\rangle_{B}</math> and obtains outcome <math>|+\rangle</math> or <math>|-\rangle</math>. | |||
* Main branch communicates this result with the local branch. | |||
* For <math>i = 1, 2, ...n</math>: | |||
** Based on outcome, branch performs the corresponding Pauli matrix operation on <math>|\phi^{(i)}\rangle_{A_2}</math> to recover <math>|\Psi^{(i)}\rangle</math> : <math>|+\rangle \xrightarrow{} I, |-\rangle \xrightarrow{} \sigma_z</math> | |||
* For <math>i = 1, 2, ...n</math>: | |||
** Bank computes <math>|\Psi^{,(i)}\rangle </math>, 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> | |||
* For <math>i = 1, 2, ...n</math>: | |||
** Bank performs swap test on <math>|\Psi^{(i)}\rangle</math> and <math>|\Psi^{,(i)}\rangle</math>. | |||
*** If <math>\langle\Psi^{(i)}|\Psi^{,(i)}\rangle \geq \kappa</math>: | |||
**** Bank aborts the process and destroys the cheque. | |||
*** else: | |||
**** Bank continues the verification process. | |||
* Bank accepts the cheque. | |||
==Further information== | |||
<div style='text-align: right;'>''*contributed by Rhea Parekh''</div> | |||