Cryptology ePrint Archive: Report 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.

Category / Keywords: secret-key cryptography / modular addition, differential cryptanalysis, entropy of distribution

Original Publication (with minor differences): 8th Workshop on Current Trends in Cryptology (CTCrypt 2019) - Svetlogorsk, Russia, 2019 - Pre-proceedings

Date: received 26 Oct 2019

Contact author: vysotskaya victory at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20191028:082713 (All versions of this report)

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