Gottesman and Chuang Quantum Digital Signature: Difference between revisions

Gottesman and Chuang Quantum Digital Signature (edit)

Revision as of 12:00, 28 May 2019

237 bytes removed , 28 May 2019

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Shraddha

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 *'''Input''' L
 *'''Output''' Seller: <math>\{k_0^i, k_1^i\}</math>, <math>1\le i\ge M</math>, <math>\{f_{k_0^i}, f_{k_1^i}\}</math>
+**'''Key Generation'''
 #For m = 0,1
 ##For i=0,M
-###Seller generates k_m^i
+###Seller generates <math>k_m^i</math>
 ###Seller performs <math>k_m^i\rightarrow f_{k_m^i}</math>
-Method 1: Trusted Party
-**'''Symmetrisation'''
+**'''Key Distribution: No Trusted Third Party Assumption'''
-##For k = 0,1
+#For m = 0,1
-###	Buyer chooses I<math>\subset_R\{1,2,...,L\}, |I|=[L/2]</math>
+##For i=0,M
-###	<math>\forall i\epsilon I</math>, Buyer sends Verifier <math>(k,i,b^k_i,B^k_i)</math>
+###For j=1,2
-###	Verifier chooses J<math>\subset_R\{1,2,...,L\}, |J|=[L/2]</math>
+####Seller sends f_{k_m^i}^j to buyer and verifier
-###	<math>\forall j\epsilon J</math>, Verifier sends Buyer <math>(k,j,v^k_j,V^k_j)</math>
+####Buyer performs SWAP1(f_{k_m^i}^1, f_{k_m^i}^2)
-###	<math>\forall j\epsilon J</math> Buyer replaces <math>B^k_l=V^k_l</math>
+####If SWAP1= False, Buyer aborts
-###	<math>\forall i\epsilon I</math> Verifier replaces <math>V^k_l=B^k_l</math>
+####If SWAP1= True, Buyer sends f_{k_m^i}^{b}=f_{k_m^i}^2=f_{k_m^i}^1 to verifier
+####Verifier performs similar steps and sends f_{k_m^i}^{v}=f_{k_m^i}^2=f_{k_m^i}^1 to buyer
+####Both perform SWAP(f_{k_m^i}^{b},f_{k_m^i}^{v})
+####If SWAP2= False, protocol aborted
+####If SWAP2= True, distribution successful
 <u>'''Stage 2'''</u> Messaging
-*'''Input''' Seller: Message m, Private Key for m: <math>\{\beta^m_1,...,\beta^m_L\}</math>
+*'''Input''' Seller: Message b, Private Key for k_b
-*'''Output''' Buyer: accept or abort, Verifier: accept or abort
+*'''Output''' Buyer: '''1-ACC''' (Message is valid and transferable), '''0-ACC''' (Message is valid but not transferable), '''REJ''' (Message is invlaid)
-**'''Signing:''' ’mismatch’ is when Buyer finds an eliminated signature element in Seller’s private key
+**'''Signing:'''
-#	Seller sends Buyer (m,<math>\{\beta^m_1,...,\beta^m_L\}</math>)
+# For i=1,M
+#	Seller sends Buyer (b,k_b^i)
 #	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>
+## Buyer performs k_b^i\rightarrow f_{new}
-#	If <math>S_b < s_aL/2</math>, Buyer accepts m else he aborts
+## Buyer performs SWAP(f_{new},f_{k_b^i})
-**'''Transfer'''
+## If SWAP= False s_B=s_B+1
-#	Buyer sends Verifier (m,<math>\{\beta^m_1,...,\beta^m_L\}</math>)
+#If s_B<c_1M, result '''1-ACC'''
-#	For l = 1,2,....,L
+#If c_1M<s_B<c_2M, result '''0-ACC'''
-##Verifier counts the number of mismatches (<math>V^m_l=B^m_l</math>) and returns <math>S_v</math>
+#If s_B>c_2M, result '''REJ'''
-#	If <math>S_v < s_vL/2</math>, Verifier accepts m else he aborts
 ==Further Information==