## Cryptology ePrint Archive: Report 2020/715

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

Sergij V. Goncharov

Abstract: 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.

Category / Keywords: foundations / transfinite cryptology, generalized continuum hypothesis, bruteforce