We have the functions $E(K, T, X)$ and $D(K, T, X)$ where for both it is the case that $\{0, 1\}^{\ell_{K}} \times \{0, 1\}^{\ell_{T}} \times \{0, 1\}^{\ell_{X}} \rightarrow \{0, 1\}^{\ell_{X}}$. The value of $\ell_{X}$ is twice that of $\ell_{K}$. The values of $\ell_{K}$ and $\ell_{T}$ are equal. I know that in the case of the single-key Even-Mansour scheme, up to $2^{0.5 \times \ell_{X}}$ blocks can safely be encrypted, but what is the case in the scheme I just outlined? Is it the upper bound $2^{\ell_{K}}$?
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