Prepare and Measure Quantum Digital Signature: Difference between revisions

Prepare and Measure Quantum Digital Signature (edit)

Revision as of 16:58, 21 March 2019

26 bytes removed , 21 March 2019

→‎Pseudo Code 2

Shraddha

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@@ Line 93: / Line 93: @@
 ==Pseudo Code 2==
   '''function''' key_distribution(n,L)
-   '''For''' k = 0 to 2^n
+   '''For''' k = 0 '''to''' <math>2^n</math>
     '''function''' key_generation (L)
-     '''For l=1 to L
+     '''For l=1 '''to''' L
       <math>\beta_k^l=</math>choose<math>_R(\{0,1,+,-\})</math> //random classical bits
       '''qubit''' |\beta_k^l\rangle= create(\beta_k^l) //a quantum state generation with classical input
@@ Line 106: / Line 106: @@
     <math>|\psi_{Vk}\rangle=|\psi_k\rangle</math>
     Seller<math>\xrightarrow[]{(k,|\psi_{Bk}\rangle)}</math>Buyer
-    Seller<math>\xrightarrow[]{(k,<math>|\psi_{Vk}\rangle)}</math>Verifier
+    Seller<math>\xrightarrow[]{(k,|\psi_{Vk}\rangle)}</math>Verifier
    '''end for''' k
   '''end function''' key_distribution</br>
-  '''function''' state_elimination(A,(<math>|\psi_k\rangle</math>,L))
+  '''function''' state_elimination(<math>|\psi_k\rangle</math>,L)
-   '''For''' l = 1,2,...,L
+   '''For''' l = 1 '''to''' L
     <math>b_k^l=</math>Choose<math>_R(\{X,Z\})</math> //randomly chosen measurement basis
     '''if''' <math>b_k^l=</math>Z '''then'''
@@ Line 125: / Line 125: @@
    '''end for''' l
    '''return''' esign<math>_k</math>
-  '''end function''' state_elimination
+  '''end function''' state_elimination</br>
-  //Buyer's elimnated signatures
+  '''for''' k=0 to <math>2^n</math>
- esign<math>_{B0}</math>= Buyer.state_elimination(<math>|\psi_{B0}\rangle</math>,L)
+  esign<math>_{Bk}</math>= Buyer.'''state_elimination'''(<math>|\psi_{Bk}\rangle</math>,L)
- esign<math>_{B1}</math>= Buyer.state_elimination(<math>|\psi_{B1}\rangle</math>,L)
+  '''end for'''
-  //Verifier's elimnated signatures
+  '''for''' k=0 to <math>2^n</math>
-  esign<math>_{V0}</math>= Verifier.state_elimination(Verifier,(<math>|\psi_{V0}\rangle</math>,L))
+  esign<math>_{Vk}</math>= Verifier.'''state_elimination'''(<math>|\psi_{Vk}\rangle</math>,L)
- esign<math>_{V1}</math>= Verifier.state_elimination(Verifier,(<math>|\psi_{V1}\rangle</math>,L))
+ '''end for'''
+  '''function''' symmetrization(k,Sender,esign_Sk,Receiver,esign_Rk)
+   Sender.choose I<math>\subset_R\{1,2,...,L\}, |I|=[L/2]</math>
-  '''function''' Symmetrisation
+  <math>'''\forall''' i\epsilon I</math>, Sender<math>\xrightarrow[]{(k,i,b^k_i,B^k_i)}</math>Receiver
-   Buyer chooses I<math>\subset_R\{1,2,...,L\}, |I|=[L/2]</math>
+  '''For''' h=1,<math>\ceil{L/2}</math>
-###	<math>\forall i\epsilon I</math>, Buyer sends Verifier <math>(k,i,b^k_i,B^k_i)</math>
+   Sender.receive(j,esign_Rk^j)
-###	Verifier chooses J<math>\subset_R\{1,2,...,L\}, |J|=[L/2]</math>
+   Sender.replace(esign_Sk^j,esign_Rk^j)
-###	<math>\forall j\epsilon J</math>, Verifier sends Buyer <math>(k,j,v^k_j,V^k_j)</math>
+  '''end for''' h
-###	<math>\forall j\epsilon J</math> Buyer replaces <math>B^k_l=V^k_l</math>
+ '''end function''' SYM
-###	<math>\forall i\epsilon I</math> Verifier replaces <math>V^k_l=B^k_l</math>
+ '''for''' k=0 '''to''' <math>2^n</math>
+  '''Call''' SYM(k,Buyer,esign_Bk,Verifier,esign_Vk)||SYM(0,Verifier,esign_Vk,Buyer,esign_Bk)
-  '''function'''
+  '''end function''' symmetrisation
+ // '||' implies that the functions are processed in parallel
 ==Discussion==