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Measurement Device Independent Quantum Digital Signature (MDI-QDS) (edit)
Revision as of 07:57, 3 June 2019
, 3 June 2019→Pseudocode
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<u>'''Stage 1'''</u> Distribution | <u>'''Stage 1'''</u> Distribution | ||
*'''Input''' Key Length, Threshold values (s_a, s_v) | *'''Input''' Key Length (L), Threshold values (s_a, s_v) | ||
*'''Output''' Seller: <math> | *'''Output''' Seller: <math>S_B^0,S_B^1,S_V^0,S_V^1</math> Buyer: <math>B^0,B^1</math>; Verifier: <math>V^0,V^1</math> | ||
**'''Key Distribution:''' | **'''Key Distribution:''' | ||
#For k = 0,1 | #For k = 0,1 | ||
##<math>S_B^k=B^k=</math>MDI-KGP(Seller, Buyer, Arbitrator) | ##<math>S_B^k=B^k=</math>MDI-KGP(Seller, Buyer, Arbitrator,k) | ||
##<math>S_V^k=V^k=</math>MDI-KGP(Seller, Verifier, Arbitrator) | ##<math>S_V^k=V^k=</math>MDI-KGP(Seller, Verifier, Arbitrator,k) | ||
**'''Symmetrisation''' | **'''Symmetrisation''' | ||
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###Verifier counts the number of mismatches (<math>B^m_l!=S^m_l</math>), b=b+1 | ###Verifier counts the number of mismatches (<math>B^m_l!=S^m_l</math>), b=b+1 | ||
# If <math>(b < s_vL/2)\&\&(v < s_vL/2)</math>, Verifier accepts m else he aborts | # If <math>(b < s_vL/2)\&\&(v < s_vL/2)</math>, Verifier accepts m else he aborts | ||
*'''MDI-KGP'''(Seller, Receiver, Arbitrator) | *'''MDI-KGP'''(Seller, Receiver R, Arbitrator,i) | ||
**For k=0,L | |||
#Seller chooses <math>s_{\text{basis}}\epsilon \{X,Z\}</math> and generates <math>|a\rangle</math> | #Seller chooses <math>s_{\text{basis}}\epsilon \{X,Z\}</math> and generates <math>|a\rangle</math> | ||
#Receiver chooses <math>r_{\text{basis}}\epsilon \{X,Z\}</math> and generates <math>|b\rangle</math> | #Receiver chooses <math>r_{\text{basis}}\epsilon \{X,Z\}</math> and generates <math>|b\rangle</math> | ||
#Seller.send(Arbitrator,<math>|a\rangle</math>) | #Seller.send(Arbitrator,<math>|a\rangle</math>) | ||
#Receiver.send(Arbitrator,<math>|b\rangle</math>) | #Receiver.send(Arbitrator,<math>|b\rangle</math>) | ||
#Arbitrator.'''BSM'''(<math>|a\rangle</math>,<math>|b\rangle</math>) | #|\Psi\rangle=Arbitrator.'''BSM'''(<math>|a\rangle</math>,<math>|b\rangle</math>) | ||
#If (<math>|Psi\!={}</math>)\&\&(<math>s_{\text{basis}}=r_{\text{basis}}</math>) | |||
###A^i_R(k)=a | |||
###If (<math>s_{\text{basis}}=r_{\text{basis}}=Z</math>) | |||
####If (|Psi\rangle=\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle))||(|Psi\rangle=\frac{1}{\sqrt{2}}(|00\rangle-|11\rangle)) '''then''' R^i(k)=b | |||
####If (|Psi\rangle=\frac{1}{\sqrt{2}}(|01\rangle+|10\rangle))||(|Psi\rangle=\frac{1}{\sqrt{2}}(|01\rangle-|10\rangle)) '''then''' <math>R^i(k)=\tilde b</math> | |||
###If (<math>s_{\text{basis}}=r_{\text{basis}}=X</math>) | |||
####If (|Psi\rangle=\frac{1}{\sqrt{2}}(|++\rangle+|--\rangle))||(|Psi\rangle=\frac{1}{\sqrt{2}}(|+-\rangle+|-+\rangle)) '''then''' R^i(k)=b | |||
####If (|Psi\rangle=\frac{1}{\sqrt{2}}(|++\rangle-|--\rangle))||(|Psi\rangle=\frac{1}{\sqrt{2}}(|01\rangle-|+-\rangle)) '''then''' <math>R^i(k)=\tilde b</math> | |||
** | |||
==Further Information== | ==Further Information== | ||