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

Sergij V.  Goncharov

Paper 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.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: transfinite cryptology generalized continuum hypothesis bruteforce
Contact author(s): goncharov @ mmf dnu edu ua
History: 2020-06-16: received
Short URL: https://ia.cr/2020/715
License: CC BY

BibTeX

@misc{cryptoeprint:2020/715,
      author = {Sergij V.  Goncharov},
      title = {On (impracticality of) transfinite symmetric encryption with keys smaller than messages under {GCH}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/715},
      year = {2020},
      url = {https://eprint.iacr.org/2020/715}
}