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Prepare and Measure Quantum Digital Signature: Difference between revisions

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Prepare and Measure Quantum Digital Signature (edit)

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This [[Prepare and Measure Quantum Digital Signature#Discussion|example protocol]] achieves the task of [[Quantum Digital Signature]] which allows for the exchange of single or multiple bit classical messages from sender to multiple recipients such that parties are required to prepare and measure quantum states instantly without having to store them. For simplicity, most protocols take into account the case of one sender and two recipients (Seller, buyer and verifier) exchanging single-bit classical messages.</br> It ensures that the sender (seller) cannot deny at a later stage having signed the message, a recipient (buyer) cannot fake or alter the QDS and another sender (verifier) can use the above two properties to verify if the sent message is signed by the genuine sender, thus, satisfying properties of  [[Quantum Digital Signature#Properties|transferability]],[[Quantum Digital Signature#Properties|non-repudiation]] and [[Quantum Digital Signature#Properties|unforgeability]]. It allows the user to sign electronic documents.</br>
Prepare and Measure QDS achieves the task of [[Quantum Digital Signature]] which allows for the exchange of single or multiple bit classical messages from sender to multiple recipients such that parties are required to prepare and measure quantum states instantly without having to store them. For simplicity, most protocols take into account the case of one sender and two recipients (Seller, buyer and verifier) exchanging single-bit classical messages.</br> It ensures that the sender (seller) cannot deny at a later stage having signed the message, a recipient (buyer) cannot fake or alter the QDS and another sender (verifier) can use the above two properties to verify if the sent message is signed by the genuine sender, thus, satisfying properties of  [[Quantum Digital Signature#Properties|transferability]],[[Quantum Digital Signature#Properties|non-repudiation]] and [[Quantum Digital Signature#Properties|unforgeability]].</br>


'''Tags:''' [[:Category:Multi Party Protocols|Multi Party (three)]], [[:Category:Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[:Category:Specific Task|Specific Task]], [[Quantum Digital Signature]], [[Quantum Digital Signature with Quantum Memory]], [[Measurement Device Independent Quantum Digital Signature (MDI-QDS)]], Unconditional Security
'''Tags:''' [[:Category:Multi Party Protocols|Multi Party (three)]], [[:Category:Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[:Category:Specific Task|Specific Task]], [[Quantum Digital Signature]], [[Quantum Digital Signature with Quantum Memory]], [[Measurement Device Independent Quantum Digital Signature (MDI-QDS)]], Unconditional Security
[[Category:Multi Party Protocols]] [[Category:Quantum Enhanced Classical Functionality]][[Category:Specific Task]][[Category:Prepare and Measure Network Stage]]
[[Category:Multi Party Protocols]] [[Category:Quantum Enhanced Classical Functionality]][[Category:Specific Task]][[Category:Prepare and Measure Network Stage]]


== Requirements ==
==Assumptions ==
*'''Network Stage:''' [[:Category:Prepare and Measure Network Stage|Prepare and Measure]]
The protocol-
*'''Relevant Network Parameters:''' <math>\epsilon_T, \epsilon_M</math> (see [[:Category:Prepare and Measure Network Stage|Prepare and Measure]])
*assumes maximum number of participating parties are honest. In the present case at least two parties are honest.
*'''Benchmark values:''' Transmission distance(d):, Estimated time (t):, QBER(%):
*quantum and classical [[authenticated]] channel


==Use Case==
==Outline==
Online Transactions, Signing Marksheets
 
==Example:==
===Outline===
----
Quantum Digital Signature (QDS) protocols can be separated 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.  
Quantum Digital Signature (QDS) protocols can be separated 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 phase can be divided into the following steps:
Distribution phase can be divided into the following steps:
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*''' Transfer:''' Buyer forwards the same message and private key to the other receiver (called verifier) who compares it with his eliminated signature for this message.
*''' Transfer:''' Buyer forwards the same message and private key to the other receiver (called verifier) who compares it with his eliminated signature for this message.


===Properties===
==Notations used==
----
*The protocol-
**involves three parties (Seller, Buyer, Verifier) exchanging one-bit classical messages.
**'''Requires''' [[BB84 QKD|BB84 QKD]] setup, [[authenticated]] quantum and classical channels
**assumes maximum number of participating parties are honest. In the present case at least two parties are honest.
**provides information-theoretic security
**provides security against repudiation, i.e. the probability that seller succeeds in making buyer and seller disagree on the validity of her sent quantum signature decays exponentially with L, as stated by the formula <math>P(\text{rep})\le e^{-(s_v-s_a)^2L}</math>.
**provides security against forgery, i.e. any recipient (verifier) with high probability rejects any message which was not originally sent by the seller herself. Forging probability is given by the formula, <math>P(\text{forge})\le e^{-(c_{\min}-2s_v)^2L}</math>, where <math>c_{\min}</math> is 3/8 (calculated using uncertainty principle).
 
===Pseudo Code===
----
*'''Notations Used:'''
**L: Length of keys used
**L: Length of keys used
**<math>s_a</math>: Threshold value for signing
**<math>s_a</math>: Threshold value for signing
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**<math>v^k_l</math>: Verifier’s random bit to determine the measurement basis of <math>l^{th}</math> qubit in <math>|\psi^k\rangle</math>
**<math>v^k_l</math>: Verifier’s random bit to determine the measurement basis of <math>l^{th}</math> qubit in <math>|\psi^k\rangle</math>
**<math>m_{b^k_l}</math>: measurement outcome of <math>b^k_l</math>
**<math>m_{b^k_l}</math>: measurement outcome of <math>b^k_l</math>
==Hardware Requirements==
**'''Requires''' [[BB84 QKD|BB84 QKD]] setup, [[authenticated]] quantum and classical channels
==Properties==
*The protocol-
**involves three parties (Seller, Buyer, Verifier) exchanging one-bit classical messages.
**provides information-theoretic security
**provides security against repudiation, i.e. the probability that seller succeeds in making buyer and seller disagree on the validity of her sent quantum signature decays exponentially with L, as stated by the formula <math>P(\text{rep})\le e^{-(s_v-s_a)^2L}</math>.
**provides security against forgery, i.e. any recipient (verifier) with high probability rejects any message which was not originally sent by the seller herself. Forging probability is given by the formula, <math>P(\text{forge})\le e^{-(c_{\min}-2s_v)^2L}</math>, where <math>c_{\min}</math> is 3/8 (calculated using uncertainty principle).
==Pseudo Code==


<u>'''Stage 1'''</u> Distribution
<u>'''Stage 1'''</u> Distribution
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# If <math>S_v < s_vL/2</math>, Verifier accepts m else he aborts
# If <math>S_v < s_vL/2</math>, Verifier accepts m else he aborts


==Relevant Papers==
==Discussion==
'''Theoretical Papers'''
'''Theoretical Papers'''
#[https://arxiv.org/abs/1403.5551  WDKA (2015)] above example
#[https://arxiv.org/abs/1403.5551  WDKA (2015)] above example
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