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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Linear Approximations of Addition Modulo 2n-1
verfasst von : Chunfang Zhou, Xiutao Feng, Chuankun Wu
Erschienen in: Fast Software Encryption
Verlag: Springer Berlin Heidelberg
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Addition modulo 2
31
− 1 is a basic arithmetic operation in the stream cipher ZUC. For evaluating ZUC’s resistance against 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 of
k
inputs modulo 2
n
− 1 for
n
≥ 2. As a result, an explicit expression of the correlations of linear approximations of the addition modulo 2
n
− 1 is given when
k
= 2, and an iterative expression when
k
> 2. 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. It is shown 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
.