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Alexander Munch-Hansen 2019-12-24 17:26:44 +01:00
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@ -134,7 +134,7 @@ We will cover an identity based encryption scheme which illustrates a basic usag
\item[Encrypt$(\text{params}, \mathtt{ID}, M)$] Takes the system parameters, \texttt{ID}, and $M \in \mathcal{M}$. Returns some ciphertext $C \in \mathcal{C}$. \item[Encrypt$(\text{params}, \mathtt{ID}, M)$] Takes the system parameters, \texttt{ID}, and $M \in \mathcal{M}$. Returns some ciphertext $C \in \mathcal{C}$.
\item[Decrypt$(\text{params}, C, d)$] Takes the system parameters, some private key $d$ and $C \in \mathcal{C}$. Returns the plaintext $M \in \mathcal{M}$. \item[Decrypt$(\text{params}, C, d)$] Takes the system parameters, some private key $d$ and $C \in \mathcal{C}$. Returns the plaintext $M \in \mathcal{M}$.
\item[Correctness] Naturally, these algorithms must satisfy that: \item[Correctness] Naturally, these algorithms must satisfy that:
$$ \forall M \in M\ :\ \text{Decrypt}(\text{params}, C, d) = M\quad \text{where}\quad C = \text{Encrypt}(\text{params}, ID, M)$$ $$ \forall M \in M\ :\ \text{Decrypt}(\text{params}, C, d) = M\quad \text{where}\quad C = \text{Encrypt}(\text{params}, ID, M)$$ I.e. for all messages $M \in \mathcal{M}$, if this is encrypted for some id \ID, then it decrypts to the same message $M$, if the correct decryption key $d$ for the \ID is used.
\end{description} \end{description}