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Gottesman and Chuang Quantum Digital Signature: Difference between revisions
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Gottesman and Chuang Quantum Digital Signature (edit)
Revision as of 08:55, 28 May 2019
, 28 May 2019→Outline
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==Outline== | ==Outline== | ||
Gottesman and Chuang signature scheme is based on quantum [https://en.wikipedia.org/wiki/One-way_function one way functions], which take classical bit string as input and give quantum states as output. Quantum Digital Signature (QDS) protocols can be divided into two stages: the distribution stage, where quantum signals (public keys) are sent to all recipients, and the messaging stage, where classical messages are signed, sent and verified. Here, we take the case of three parties, one sender (referred to as seller) and two receivers (buyer and verifier) sharing a one bit message. | Gottesman and Chuang signature scheme is based on quantum [https://en.wikipedia.org/wiki/One-way_function one way functions], which take classical bit string as input and give quantum states as output. Quantum Digital Signature (QDS) protocols can be divided into two stages: the distribution stage, where quantum signals (public keys) are sent to all recipients, and the messaging stage, where classical messages are signed, sent and verified. Here, we take the case of three parties, one sender (referred to as seller) and two receivers (buyer and verifier) sharing a one bit message. | ||
*'''Distribution:''' For each message bit (say 0 and 1) sender selects some (say M) classical bit strings. These are chosen to be her private keys for that message bit. Using this private key as input, Sender generates output of the quantum one-way function/map, which she calls her public key and as assumed above, distributes them to each recipient, for each message bit. In the end of this step, each recipient has 2M public keys, M for message bit 0 and M for message bit 1. | *'''Distribution:''' For each message bit (say 0 and 1) sender selects some (say M) classical bit strings. These are chosen to be her private keys for that message bit. Using this private key as input, Sender generates output of the quantum one-way function/map, which she calls her public key and as assumed above, distributes them to each recipient, for each message bit. In the end of this step, each recipient has 2M public keys, M for message bit 0 and M for message bit 1. | ||
'''Key Distribution:''' The author suggests a few methods for key distribution. One of them is the assumption of a trusted third party who receives public keys from Sender, checks all the keys using [[SWAP Test]] and then if test is passed by each key sent, the trusted party distributes it to the recipients. A second method eliminates the requirement of a trusted third party and instead requires Sender to send two copies of each public key to each recipient, such that, in the end each recipient has 4M keys (2M public keys for each message bit). The recipients perform Swap test for their supposedly identical copies of public keys. Then, if passed, they send one copy to another recipient, who again performs the SWAP test between the received copy and his copy of public key. | ** '''Quantum One Way Functions:''' | ||
** '''Key Distribution:''' The author suggests a few methods for key distribution. One of them is the assumption of a trusted third party who receives public keys from Sender, checks all the keys using [[SWAP Test]] and then if test is passed by each key sent, the trusted party distributes it to the recipients. A second method eliminates the requirement of a trusted third party and instead requires Sender to send two copies of each public key to each recipient, such that, in the end each recipient has 4M keys (2M public keys for each message bit). The recipients perform Swap test for their supposedly identical copies of public keys. Then, if passed, they send one copy to another recipient, who again performs the SWAP test between the received copy and his copy of public key. | |||
*'''Messaging:''' Sender sends her message bit with the associated private keys. The Receiver performs the map on the private key (quantum one way function takes the sent private key as input) and the compares the output thus generated with the public key received in the previous stage. If the number of unmatched bits are below rejection threshold, the message is declared valid, else invalid. If the number of unmatched bits is below acceptance threshold, it is declared transferable, else not transferable. | *'''Messaging:''' Sender sends her message bit with the associated private keys. The Receiver performs the map on the private key (quantum one way function takes the sent private key as input) and the compares the output thus generated with the public key received in the previous stage. If the number of unmatched bits are below rejection threshold, the message is declared valid, else invalid. If the number of unmatched bits is below acceptance threshold, it is declared transferable, else not transferable. | ||
==Properties== | ==Properties== | ||