Editing Quantum Cheque (section)

==Outline==

This protocol allows a quantum cheque to be issued using quantum cheque books to the bank customers. The customers can then carry forward transactions in a perfectly secure manner and these cheques can be en-cashed after being verified by the trusted bank or its branches, that communicate with the main branch securely. The quantum cheque follows all the properties of a classical cheque - verifiable by a trusted bank, cannot be disavowed by the issuer and cannot be counterfeited by an adversary. </br>

The entire bank transaction process can be divided into three stages, Gen, where the cheque book is generated for the account holder, Sign, where the account holder prepares a cheque and issues it to the third party and Verify, where the third party en-cashes the cheque depending upon its validity.

* '''Gen'''
** In this stage, the bank first creates a cheque book and a key for the account holder.
** Then, the bank and the account holder create a shared key using [[Quantum Key Distribution]]. Both parties agree upon an unconditionally secure digital signature scheme. The account holder stores his private key safely with himself and shares the public key with the bank. 
** The bank then prepares <math>n</math> GHZ triplet states (link to page) and stores only the third entangled qubit of every GHZ in the database, while handing over the first two qubits of every GHZ state to the account holder. Along with this, the bank also creates and shares a corresponding unique serial number for this cheque.
** Finally, the account holder has stored his identity, shared key, private key, public key, serial number and first two entangled qubits of every GHZ triplet state whereas the bank has stored each account holder's identity, shared key, public key, serial number and third entangled qubit of every GHZ triplet states in its database.<br></br>
* '''Sign'''
** In this stage, the issuer's key and amount to be signed is taken as input to produce a quantum state which acts like a cheque.
** Each account holder prepares <math>n</math> quantum states to issue a check worth some amount <math>M</math>. This quantum state is prepared by the quantum one-way function (Link to the page) which takes the shared key, identity of the account holder, a random number and the amount of money <math>M</math> to be signed as the input. Every state from these <math>n</math> quantum states is individually encoded with one of the account holder's entangled qubit of the GHZ states using Quantum Secret Sharing: Splitting of quantum information (Link to the page). The account holder then signs the serial number with their digital signature.
** The quantum cheque thus produces by the account holder contains the information - the identity of the account holder, serial number, generated a random number, digital signature, amount of money signed and the other entangled qubit of the GHZ state.<br></br>
* '''Verify'''
** In this method, the quantum cheque is verified by the trusted bank or its branches and the validity is checked.
** When the quantum cheque is produced at any valid branches of the bank by a third party, the information is securely communicated to the main branch. At the branch, an initial verification is carried by considering the identity of the issuer of the cheque, the serial number of the cheque and the digital signature of the issuer. If the cheque is valid, the verification process is continued, otherwise, the cheque is destroyed and the process is discontinued.
** The main branch performs a measurement on its copy of third entangled qubit of every GHZ triplet state which was stored in the database and securely communicates this result to the branch.
** The branch recovers the quantum state that was prepared by the account holder to issue the cheque, using the information received from the main branch. The branch also computes this same quantum states using the stored account holder's information like the shared key, the identity of the account holder, a random number and the amount of money <math>M</math> as input for verification. A swap test(Link to the page) is performed on both these states and if the cheque is only accepted if this test passes, else it is destroyed and aborted.

This scheme is proven to be impossible to counterfeit and impossible to repudiate. The quantum cheque is a quantum state and thus it cannot be copied or stolen by any eavesdropper, ensuring that only one copy of the quantum cheque exists.