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Quantum Cheque: Difference between revisions
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This [https://link.springer.com/article/10.1007/s11128-016-1273-4 | This [https://link.springer.com/article/10.1007/s11128-016-1273-4 protocol] is a private-key quantum money scheme which allows trusted banks to issue perfectly secure and verifiable quantum cheque books to account holders and also enables them to undertake monetary transactions with other parties. The quantum cheque is secure against [[non-signalling]] adversaries and cannot be counterfeited. | ||
'''Tags:''' [[Quantum Digital Signature]], Private key | '''Tags:''' [[Quantum Digital Signature]], Private-key quantum money. | ||
== Assumptions == | == Assumptions == | ||
* The protocol assumes the account holder and the bank, to be honest. The bank is a trusted party, however, the branches may or may not be trusted. | * The protocol assumes the account holder and the bank, to be honest. The bank is a trusted party, however, the branches may or may not be trusted. | ||
* This protocol assumes perfect state preparations, transmissions, and measurements. | * This protocol assumes perfect state preparations, transmissions, and measurements. | ||
* The protocol takes the assumption that the Quantum Digital Signature | * The protocol takes the assumption that the Quantum Digital Signature and the Quantum key distribution schemes are unconditionally secure. | ||
* The digital signature scheme must satisfy the following security conditions of unforgeability and non-repudiation | * The digital signature scheme must satisfy the following security conditions of unforgeability and non-repudiation | ||
==Outline== | ==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, | 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. | 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''' | * '''Gen''' | ||
** In this | ** 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 the [[Quantum Digital Signature]]. 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. | ** 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 | ** 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''' | * '''Sign''' | ||
** In this | ** 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> | ** 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''' | * '''Verify''' | ||