On (impracticality of) transfinite symmetric encryption with keys smaller than messages under GCH

In this short trivial note we argue that, assuming Generalized Continuum Hypothesis to be true, it is impractical to use encryption with $Key \in \{ 0, 1 \}^K$ and $Message \in \{ 0, 1 \}^M$ such that $\aleph_0 \leqslant \mathrm{card}\,K < \mathrm{card}\,M$, because complexity of the known-plaintext bruteforce attack equals complexity of a single $En/Decrypt(Key, Message)$ computation then

Dijk, Cryptography in an Unbounded Computational Model

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Dijk, Cryptography in an Unbounded Computational Model

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