Probabilistic Properties of Modular Addition \\ (Extended abstract)

Victoria Vysotskaya

Paper 2019/1253

Probabilistic Properties of Modular Addition \ (Extended abstract)

Victoria Vysotskaya

Abstract

We studied the applicability of differential cryptanalysis to cryptosystems based on operation of addition modulo $2^{n}$ . We obtained an estimate (accurate up to an additive constant) of expected value of entropy $H_{n}$ in rows of DDT of corresponding mapping. Moreover, the $k$ -th moments of $2^{H_{n}}$ are explored. In particular, asymptotic inequalities that describe the behavior of values $E 2^{H_{n}}$ and $D 2^{H_{n}}$ as $n \to \infty$ were obtained. A simple analytical formula for the size of any given equivalence class was obtained. This formula helped to effectively compute the entropy distribution.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Minor revision. 8th Workshop on Current Trends in Cryptology (CTCrypt 2019) - Svetlogorsk, Russia, 2019 - Pre-proceedings
Keywords: modular addition differential cryptanalysis entropy of distribution
Contact author(s): vysotskaya victory @ gmail com
History: 2019-10-28: received
Short URL: https://ia.cr/2019/1253
License: CC BY

BibTeX

@misc{cryptoeprint:2019/1253,
      author = {Victoria Vysotskaya},
      title = {Probabilistic Properties of Modular Addition \\ (Extended abstract)},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/1253},
      year = {2019},
      url = {https://eprint.iacr.org/2019/1253}
}