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 $\mathbb{E}2^{H_n}$ and $\mathbb{D}2^{H_n}$ 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 additiondifferential cryptanalysisentropy of distribution
Contact author(s)
vysotskaya victory @ gmail com
History
2019-10-28: received
Short URL
https://ia.cr/2019/1253
License
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2019/1253}},
      url = {https://eprint.iacr.org/2019/1253}
}
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