Arbitrated Quantum Digital Signature: Difference between revisions

Arbitrated Quantum Digital Signature (edit)

Revision as of 23:12, 9 June 2019

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Shraddha

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 ==Pseudocode==
-'''Stage 1''': Key Generation </br>
+'''Stage 1''': Key Distribution </br>
 '''Input''': Seller and PKG (<math>k_at</math>)</br>
 '''Output''': Seller and PKG (<math>k_{pri}</math>); Everyone (<math>k_{pub}</math>)
-* PKG generates <math>k_{pub}= f(</math>Seller's email-id)
+#PKG generates <math>k_{pub}= f(</math>Seller's email-id)
-* PKG chooses <math>G</math>, <math>k_r</math>
+# PKG randomly chooses <math>G</math>, <math>k_r</math>
-* PKG calculates <math>k_{pri} := G(k_{pub}) \oplus k_{r} </math>
+# PKG calculates <math>k_{pri} := G(k_{pub}) \oplus k_{r} </math>
-* PKG encrypts <math>VC(k_{at},k_{pri})=E_{k_{at}}</math>
+# PKG encrypts <math>VC(k_{at},k_{pri})=E_{k_{at}}</math>
-* Seller decrypts <math>VC(k_{at}, E_{k_{at}})=k_{pri}</math>.
+# Seller decrypts <math>VC(k_{at}, E_{k_{at}})=k_{pri}</math>.
-'''Stage 2''': Signature</br>
+'''Stage 2.1''': Messaging: Signature</br>
-'''Output''': PKG receives the quantum digest <math>|F\rangle</math> and the Verifier receives the Signature <math>(ts, m, B_P,|S\rangle_{k_{pri}, m})</math> from the Signer.
+'''Input''': Seller (<math>k_{pri}</math>, <math>m</math>, <math>k_{pub}</math>)
+'''Output''': PKG (<math>|F\rangle</math>), Buyer (Signature <math>(ts, m, B_P,|S\rangle_{k_{pri}, m})</math>
-* Signer wants to sign the message <math>m</math>.
-* Signer selects <math>s</math> and <math>t</math>.
-* For <math>l = 1, 2, ...n</math>:
-** Signer generates the state <math>|\phi\rangle_{s_l,t_l\oplus m_l, m_l}</math>, which is:
-<div style="text-align: center;"><math> |\phi\rangle_{s_l,t_l\oplus m_l, m_l}  = Y^{m_l}H^{s_l}U_{\frac{\pi}{4}}H^{t_l\oplus m_l}|0\rangle</math></div>
-* For <math>l = 1, 2, ...n</math>:
-** Signer generates the Signature quantum state <math>|S\rangle_{{k_{pri}}_l,m_l}</math>, which is
-<div style="text-align: center;"><math> |S\rangle_{{k_{pri}}_l,m_l} = H^{k_{pub_l}\oplus k_{pri_l}}|\phi\rangle_{s_l,t_l\oplus m_l, m_l}</math></div>
-* For <math>l = 1, 2, ...n</math>:
-** Signer generates the private key  quantum state <math>|P\rangle_l</math>, which is
-<div style="text-align: center;"><math>|P\rangle_l = H^{k_{pri_l}} |\phi\rangle_{s_l, t_l\oplus m_l}</math></div>
-**  The classical <math>P_l</math> is calculated based on <math>|P\rangle_l</math>.
-** The basis set is formed by Signer is:
-<div style="text-align: center;"><math>  B_{P_l} = Basis(|P\rangle_l) \in \{+,\times \} </math></div>
+# Seller randomly chooses <math>s</math> and <math>t</math>.
+# For <math>l = 1, 2, ...n</math>:
+## Seller operates <math>Y^{m_l}H^{s_l}U_{\frac{\pi}{4}}H^{t_l\oplus m_l}|0\rangle=|\phi\rangle_{s_l,t_l\oplus m_l, m_l}</math>
+#For <math>l = 1, 2, ...n</math>:
+## Seller generates <math> |S\rangle_{{k_{pri}}_l,m_l} = H^{k_{pub_l}\oplus k_{pri_l}}|\phi\rangle_{s_l,t_l\oplus m_l, m_l}</math>
+#For <math>l = 1, 2, ...n</math>:
+## Seller generates <math>|P\rangle_l = H^{k_{pri_l}} |\phi\rangle_{s_l, t_l\oplus m_l}</math></div>
+#For <math>l = 1, 2, ...n</math>:
+##Seller chooses B_l \epsilon_R\{+,\times\}
+##Seller measures in basis B_l: <math>B_l(|P\rangle_l)=m_l</math>
+##'''If''' <math>B_l = +</math> '''then'''
+###'''If''' <math>m_l=0</math> '''then''' <math>P_l=00</math> '''else''' <math>P_l=01</math>
+##'''If''' <math>B_l = \times</math> '''then'''
+###'''If''' <math>m_l=0</math> '''then''' <math>P_l=10</math> '''else''' <math>P_l=11</math>
 * For <math>k = 1, 2, ...u w</math>: Different copies of the quantum digital digest state is prepared.
 ** For <math>l = 1, 2, ...n</math>: