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Prepare and Measure Quantum Digital Signature: Difference between revisions
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Prepare and Measure Quantum Digital Signature (edit)
Revision as of 11:54, 31 October 2018
, 31 October 2018→Protocol:
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'''Tags:''' [[Multi Party Protocols|Multi Party (three)]], [[Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[Specific Task|Specific Task]], [[Quantum Digital Signature]] | '''Tags:''' [[Multi Party Protocols|Multi Party (three)]], [[Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[Specific Task|Specific Task]], [[Quantum Digital Signature]] | ||
== | == Requirements == | ||
---- | |||
#one to many quantum channels, a complete graph for classical channels | |||
#time, distance, scalability, threshold values numbers, length of the key | |||
*First Network Stage | |||
*Parameters:Length of the keys(L) , Verification threshold per qubit (<math>s_v</math>), Signing threshold (<math>s_a</math>) | |||
*BB84 QKD setup | |||
*Setup Assumptions: classical registers (classical memory), [[authenticated quantum and classical channels]], | |||
Experimental Tags: [[BB84 QKD]], [[BB84 State Preparation]], [[BB84 State Measurement]] | |||
==Example:== | |||
===Outline=== | ===Outline=== | ||
---- | ---- | ||
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Figure | Figure | ||
===Properties=== | ===Properties=== | ||
---- | ---- | ||
*Notations | *Notations | ||
**L: Length of keys used | |||
**<math>s_a</math>: Threshold value for signing | |||
**<math>s_v</math>: threshold value for verification | |||
**<math>|\psi^k\rangle</math>: Quantum Public key for message k | **<math>|\psi^k\rangle</math>: Quantum Public key for message k | ||
**<math>\{\beta^k_1,...,\beta^k_L\}</math>: Classical Private key for classical one-bit message k | **<math>\{\beta^k_1,...,\beta^k_L\}</math>: Classical Private key for classical one-bit message k | ||
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**<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> | ||
*The protocol assumes that all classical quantum channels are authenticated (or dedicated). | |||
*The protocol requires no quantum memory. | |||
*The protocol belongs to the [[First Network Stage: Prepare and Send Quantum Network|First Network Stage: Prepare and Send Quantum Network]] | |||
*The protocol assumes maximum number of participating parties are honest. In the present case at least two parties are honest. | |||
*The protocol 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>. | |||
*The protocol 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 the minimum possible rate at which buyer declares a single signature element which has been eliminated by the verifier. | |||
===Pseudo Code=== | |||
---- | |||
<u>'''Stage 1'''</u> Distribution | <u>'''Stage 1'''</u> Distribution | ||
*'''Input''' L | *'''Input''' L | ||