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Known Pairs

For simplicity, we assume the encryption algorithm may be known.

Definition 5

A pair, $\langle p, c \rangle$, is a known plaintext-ciphertext pair with respect to a principal, I , and key, k if and only if $I \mbox{\it{ knows }} \allowbreak \langle p, c \rangle ~\wedge~ \langle p, c, k \rangle.$  

We will use the term known pair to refer to a known plaintext-ciphertext pair. A principal may know that two pairs are encrypted under the same key even though the key is not known to the principal. For a particular block encryption function, it may be the case that $\langle p, c \rangle$ for any p and c . However, in our analysis, it is of interest to know this fact in the context of receiving particular c and associating it with sets of under the same k . Knowledge of a pair does not imply knowledge of the corresponding key. That is knowing $c= e_{\tiny k}(p)$ or $p= e^{-1}_{\tiny k}{(c)}$ does not imply knowing k .