Prepare and Measure Quantum Digital Signature: Difference between revisions

Prepare and Measure Quantum Digital Signature (edit)

Revision as of 14:49, 21 March 2019

870 bytes removed , 21 March 2019

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Shraddha

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@@ Line 94: / Line 94: @@
 <u>'''Stage 1'''</u> Distribution
-*'''Input''' L
+ '''function''' key distribution(n,L)
-*'''Output''' Seller: <math>\{\beta^0_1,...,\beta^0_L\},\{\beta^1_1,...,\beta^1_L\}</math>; Buyer: <math>B^0,B^1</math>; Verifier: <math>V^0,V^1</math>
+  '''For''' k = 0 to 2^n
-**'''Key Distribution:'''
+   '''function''' key generation (L)
-#For k = 0,1
+    '''For l=1 to L
-##	Seller prepares quantum public key <math>|\psi^k\rangle=\bigotimes^L_{l=1}|\beta^k_l\rangle</math>, where <math>\beta^k_l\in_R \{0,1,+,-\}</math>
+     \beta_k^l=Seller.choose_R(\{0,1,+,-\})
-##	She sends Buyer (k,<math>|\psi^k\rangle</math>)
+     |\psi\rangle=\bigotimes
-##	She sends Verifier (k,<math>|\psi^k\rangle</math>)
+    P_k=
+    s_k=
+    '''return''' (P_k,s_k)
+   '''end function'' key generation
+   Seller.send(Buyer, (k,P_k)
+   Seller.send(Verifier (k,P_k)
+  '''end for'''</br>
+ '''end function''' key distribution
 **'''State Elimination:'''
 #For k = 0,1
@@ Line 112: / Line 120: @@
 **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>
-**'''Symmetrisation'''
+ '''function''' Symmetrisation
-##For k = 0,1
+  Buyer chooses I<math>\subset_R\{1,2,...,L\}, |I|=[L/2]</math>
-###	Buyer chooses I<math>\subset_R\{1,2,...,L\}, |I|=[L/2]</math>
 ###	<math>\forall i\epsilon I</math>, Buyer sends Verifier <math>(k,i,b^k_i,B^k_i)</math>
 ###	Verifier chooses J<math>\subset_R\{1,2,...,L\}, |J|=[L/2]</math>
@@ Line 120: / Line 127: @@
 ###	<math>\forall j\epsilon J</math> Buyer replaces <math>B^k_l=V^k_l</math>
 ###	<math>\forall i\epsilon I</math> Verifier replaces <math>V^k_l=B^k_l</math>
-<u>'''Stage 2'''</u> Messaging
-*'''Input''' Seller: Message m, Private Key for m: <math>\{\beta^m_1,...,\beta^m_L\}</math>
+ '''function'''
-*'''Output''' Buyer: accept or abort, Verifier: accept or abort
-**'''Signing:''' ’mismatch’ is when Buyer finds an eliminated signature element in Seller’s private key
-#	Seller sends Buyer (m,<math>\{\beta^m_1,...,\beta^m_L\}</math>)
-#	For l = 1,2,..,L
-##Buyer counts the number of mismatches (<math>B^m_l=V^m_l</math>) and returns <math>S_b</math>
-#	If <math>S_b < s_aL/2</math>, Buyer accepts m else he aborts
-**'''Transfer'''
-#	Buyer sends Verifier (m,<math>\{\beta^m_1,...,\beta^m_L\}</math>)
-#	For l = 1,2,....,L
-##Verifier counts the number of mismatches (<math>V^m_l=B^m_l</math>) and returns <math>S_v</math>
-#	If <math>S_v < s_vL/2</math>, Verifier accepts m else he aborts
 ==Discussion==