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No. Yes, by choosing an authenticated encryption scheme with a known $\:I\hspace{.03 in}V\hspace{.04 in}||\hspace{.04 in}C\hspace{.04 in}||\hspace{.04 in}tag\:$ and $k_{\hspace{.02 in}0}$ and $k_1$ such that decrypting $\:I\hspace{.03 in}V\hspace{.04 in}||\hspace{.04 in}C\hspace{.04 in}||\hspace{.04 in}tag\:$ with $k_{\hspace{.02 in}0}$ and $k_1$ yields ...


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The following picture shows EAX: As you can see there is a OMAC calculation (or CMAC as it is usually called) over both N (the nonce) and H (the header / associated data). With regards to security it doesn't matter where you place the nonce and the other data in the header. I'll not go into the security of XOR'ing the calculated OMAC values for nonce, ...



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