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Linear approximations of addition modulo \(2^n-1\). (English) Zbl 1307.94115
Joux, Antoine (ed.), Fast software encryption. 18th international workshop, FSE 2011, Lyngby, Denmark, February 13–16, 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-21701-2/pbk). Lecture Notes in Computer Science 6733, 359-377 (2011).
Summary: 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 \(n \geq 2\). 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 \(k\).
For the entire collection see [Zbl 1217.68011].

MSC:
94A60 Cryptography
68M07 Mathematical problems of computer architecture
Software:
SNOW
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