### Linear Approximations of Addition Modulo $2^n$-1

Xiutao Feng, Chunfang Zhou, and Chuankun Wu

##### Abstract

Addition modulo $2^{31}-1$ is a basic arithmetic operation in the stream cipher ZUC. For evaluating ZUC in resistance to linear cryptanalysis, it is necessary to study properties of linear approximations of the addition modulo $2^{31}-1$. In this paper we discuss linear approximations of the addition modulo $2^n-1$ for integer $n\ge2$. As results, an exact formula on the correlations of linear approximations of the addition modulo $2^n-1$ is given for the case when two inputs are involved, and an iterative formula for the case when more than two inputs are involved. For a class of special linear approximations with all masks being equal to 1, we further discuss the limit of their correlations when $n$ goes to infinity. Let $k$ be the number of inputs of the addition modulo $2^n-1$. It's shows that when $k$ is even, the limit is equal to zero, and when $k$ is odd, the limit is bounded by a constant depending on $k$.

Available format(s)
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
fengxt @ gmail com
fengxt @ is iscas ac cn
History
Short URL
https://ia.cr/2010/521

CC BY

BibTeX

@misc{cryptoeprint:2010/521,
author = {Xiutao Feng and Chunfang Zhou and Chuankun Wu},
title = {Linear Approximations of Addition Modulo $2^n$-1},
howpublished = {Cryptology ePrint Archive, Paper 2010/521},
year = {2010},
note = {\url{https://eprint.iacr.org/2010/521}},
url = {https://eprint.iacr.org/2010/521}
}
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