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Quantum Coin: Difference between revisions
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(Created page with "Quantum Money is a unique object generated by a Trusted Third Party (TTP). Then, it is circulated among untrusted clients (Transferability property). Each client should be abl...") |
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* '''General Features''': | * '''General Features''': | ||
** No need to quantum communication for quantum coin verification. | |||
** The classical communication channel used for verification can be unencrypted. | |||
** The database of the bank is static, and therefore many de-centralized “verification branches” can exist that do not have to communicate with one another. | |||
** The number of verifications that a quantum coin can go through is limited. | |||
*'''Security Claims''': | |||
**The coins are exponentially hard to counterfeit. | |||
**Secure against an adversary who uses adaptive “attempted verifications” in order to collect information about a coin. | |||
\ | == Protocol == | ||
\begin{itemize} | |||
\item The | \begin{algorithm} | ||
\caption{Quantum coin generation} | |||
\end{ | \noindent\textbf{Input} A secret record consists of $k$ entries $x_1, . . . , x_k, x_i\in\{{0,1}\}^4$\\ | ||
\textbf{Output} A “fresh” quantum coin\\ | |||
The Trusted Third Party (TTP) chooses $x_1, . . . , x_k\in\{{0, 1}\}^4$ at random, keeps them in secret and produces quantum states $\ket{\alpha(x_1)}, . . . , \ket{\alpha(x_k)}$. | |||
A “fresh” quantum coin corresponding to this record consists of: | |||
\begin{itemize} | |||
\item $k$ quantum registers consisting of 2 qubits each, where the $i$’th register contains $\ket{\alpha(x_i)}$; | |||
\item a $k$-bit classical register $P$, that is initially set to $0^k$; | |||
\item a unique identification number. | |||
\end{itemize} | |||
\end{algorithm} | |||
\begin{algorithm} | |||
\caption{Quantum coin verification} | |||
\noindent\textbf{Input} the identification number of the quantum coin\\ | |||
\textbf{Output} Accept or Reject\\ | |||
\renewcommand{\labelenumi}{\alph{enumi})} | |||
\begin{enumerate} | |||
\item The holder sends the identification number of the quantum coin to the TTP. | |||
\item The TTP chooses uniformly at random a set $L_{bn}\subset[k]$ of size $t$, and sends it to the coin holder. | |||
\item The holder consults with P and chooses uniformly at random a set $L_{hl} \subset L_{bn}$ consisting of $2t/3$ yet unmarked positions. He sends $L_{hl}$ to the bank and marks in $P$ all the elements of $L_{hl}$ as used. | |||
\item The TTP chooses at random $2t/3$ values $m_i \in\{{0, 1}\}$, one for each $i \in L_{hl}$ , and sends them to the coin holder. | |||
\item The holder measures the quantum registers corresponding to the elements of $L_{hl}$ in order to produce $2t/3$ pairs $(a_i, b_i)$, such that $(x_i,m_i, a_i, b_i)\in HMP_4$ for all $i \in L_{hl}$ . He sends the list of $(a_i, b_i)$s to the TTP. | |||
\item The TTP checks whether $(x_i,m_i, a_i, b_i)\in HMP_4$ for all $i \in L_{hl}$ , in which case it confirms validity of the quantum coin. Otherwise, the coin is declared to be a counterfeit. | |||
\end{enumerate} | |||
\end{algorithm} | |||