Prepare and Measure Quantum Digital Signature: Difference between revisions

Prepare and Measure Quantum Digital Signature (edit)

Revision as of 13:47, 21 March 2019

2,375 bytes added , 21 March 2019

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Shraddha

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 ==Pseudo Code==
+<u>'''Stage 1'''</u> Distribution
+*'''Input''' 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>
+**'''Key Distribution:'''
+#For k = 0,1
+##	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>
+##	She sends Buyer (k,<math>|\psi^k\rangle</math>)
+##	She sends Verifier (k,<math>|\psi^k\rangle</math>)
+**'''State Elimination:'''
+#For k = 0,1
+##For l = 1,2,...,L
+###	Buyer chooses <math>b^k_l \epsilon_R {0,1}</math>
+###If <math>b^k_l=0</math>, Buyer measures his qubit in X basis <math>\{|+\rangle,|-\rangle\}</math>
+###If <math>b^k_l=0</math>, Buyer measures his qubit in Z basis <math>\{|0\rangle,|1\rangle\}</math>
+###'''return''' <math>m_{b^k_l}</math>
+###<math>B^k_l=1-m_{b^k_l}</math>
+**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'''
+##For k = 0,1
+###	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>
+###	<math>\forall j\epsilon J</math>, Verifier sends Buyer <math>(k,j,v^k_j,V^k_j)</math>
+###	<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>
+*'''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
+==Pseudo Code 2==
 <u>'''Stage 1'''</u> Distribution