Prepare and Measure Quantum Digital Signature: Difference between revisions

Prepare and Measure Quantum Digital Signature (edit)

Revision as of 15:36, 21 March 2019

795 bytes added , 21 March 2019

→‎Pseudo Code 2

Shraddha

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@@ Line 92: / Line 92: @@
 #	If <math>S_v < s_vL/2</math>, Verifier accepts m else he aborts
 ==Pseudo Code 2==
+  '''function''' key_distribution(n,L)
-<u>'''Stage 1'''</u> Distribution
-  '''function''' key distribution(n,L)
    '''For''' k = 0 to 2^n
-    '''function''' key generation (L)
+    '''function''' key_generation (L)
      '''For l=1 to L
-      <math>\beta_k^l=</math>Seller.choose<math>_R(\{0,1,+,-\})</math> //random classical bits
+      <math>\beta_k^l=</math>choose<math>_R(\{0,1,+,-\})</math> //random classical bits
-      Seller.generate(|\beta_k^l\rangle) //a quantum state generation
+      '''qubit''' |\beta_k^l\rangle= create(\beta_k^l) //a quantum state generation with classical input
-     '''end for'''
+     '''end for''' l
-     <math>|\psi^k\rangle=\bigotimes^L_{l=1}|\beta^k_l\rangle</math> //quantum string
+     <math>|\psi_k\rangle=\bigotimes^L_{l=1}|\beta^k_l\rangle</math> //quantum public key
-    <math>P_k=|\psi^k\rangle</math> //public key
      <math>s_k=\{\beta_k^0,....\beta_k^L\}</math> //secret key
-     '''return''' (P_k,s_k)
+     '''return''' (<math>|\psi_k\rangle,s_k</math>)
-    '''end function''' key generation
+    '''end function''' key_generation
-    Seller.send(Buyer, (k,P_k)
+   <math>|\psi_{Bk}\rangle=|\psi_k\rangle</math>
-    Seller.send(Verifier (k,P_k)
+   <math>|\psi_{Vk}\rangle=|\psi_k\rangle</math>
-   '''end for'''</br>
+    Seller<math>\xrightarrow[]{(k,|\psi_{Bk}\rangle))}</math>Buyer
-  '''end function''' key distribution
+    Seller<math>\xrightarrow[]{(Verifier,(k,<math>|\psi_{Vk}\rangle</math>))}</math>Verifier
+   '''end for''' k
-**'''State Elimination:'''
+ '''end function''' key_distribution</br>
-#For k = 0,1
+  '''function''' state_elimination(A,(<math>|\psi_k\rangle</math>,L))
-##For l = 1,2,...,L
+  '''For''' l = 1,2,...,L
-###	Buyer chooses <math>b^k_l \epsilon_R {0,1}</math>
+   <math>b_k^l=</math>Choose<math>_R(\{X,Z\})</math> //randomly chosen measurement basis
-###If <math>b^k_l=0</math>, Buyer measures his qubit in X basis <math>\{|+\rangle,|-\rangle\}</math>
+   '''if''' <math>b_k^l=</math>Z '''then'''
-###If <math>b^k_l=0</math>, Buyer measures his qubit in Z basis <math>\{|0\rangle,|1\rangle\}</math>
+    M= Measure<math>_{\{0,1\}}(\beta_k^l)</math>
-###'''return''' <math>m_{b^k_l}</math>
+     '''if''' M=1 '''then''' esign<math>_k^l= 1</math>
-###<math>B^k_l=1-m_{b^k_l}</math>
+     '''if''' M=-1 '''then''' esign<math>_k^l= 0</math>
+     '''end if'''
+   '''if''' b_k^l=X '''then'''
+    M= Measure<math>_{\pm}(\beta_k^l) </math>
+     '''if''' M=1 '''then''' esign<math>_k^l= +</math>
+     '''if''' M=-1 '''then''' esign<math>_k^l= -</math>
+     '''end if'''
+   '''end if'''
+  '''end for''' l
+  '''return''' esign<math>_k</math>
+ '''end function''' state_elimination
+ //Buyer's elimnated signatures
+ esign<math>_{B0}</math>= Buyer.state_elimination(<math>|\psi_{B0}\rangle</math>,L)
+ esign<math>_{B1}</math>= Buyer.state_elimination(<math>|\psi_{B1}\rangle</math>,L)
+ //Verifier's elimnated signatures
+ esign<math>_{V0}</math>= Verifier.state_elimination(Verifier,(<math>|\psi_{V0}\rangle</math>,L))
+ esign<math>_{V1}</math>= Verifier.state_elimination(Verifier,(<math>|\psi_{V1}\rangle</math>,L))
-**Verifier repeats steps 2(a)-2(b) with randomly chosen basis <math>v^k_l</math> to get his eliminated signature elements <math>V^k_l</math>
   '''function''' Symmetrisation