Paper 2019/1253 Original: eprint.iacr.org/2019/1253 ↗
Probabilistic Properties of Modular Addition \\ (Extended abstract)
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
- Preprint.
- History
- 2019-10-28: last updated
- 2019-10-28: published
- Short URL
- https://ia.cr/2019/1253
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}