Johan Wallén

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In this paper we present new and more accurate estimates of the biases of the linear approximation of the FSM of the stream cipher SNOW 2.0. Based on improved bias estimates we also find a new linear distinguisher with bias 2−86.9 that is significantly stronger than the previously found ones by Watanabe et al. (2003) and makes it possible to distinguish the(More)
We study the differential probability adp of exclusive-or when differences are expressed using addition modulo 2 . This function is important when analysing symmetric primitives that mix exclusive-or and addition—especially when addition is used to add in the round keys. (Such primitives include idea, Mars, rc6 and Twofish.) We show that adp can be viewed(More)
Addition modulo 2 − 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 − 1. In this paper we discuss linear approximations of the addition modulo 2 − 1 for integer n ≥ 2. As results, an exact formula on the(More)
We analyse the asymptotic behaviour in the mean of a non-commutative rational series, which originates from differential cryptanalysis, using elementary tools from analysis and linear algebra, and more sophisticated tools from analytic number theory. We show that a probability distribution function describes the asymptotic behaviour of the rational series(More)
We present a detailed analysis of some of the fundamental differential and linear properties of addition modulo 2: the differential probability xdp of addition modulo 2 when differences are expressed using exclusive-or, the dual differential probability adp of exclusive-or when differences are expressed using addition modulo 2 and the correlation lca of(More)
It is challenging to unravel the history of organisms with highly scattered populations. Such species may have fragmented distributions because extant populations are remnants of a previously more continuous range, or because the species has narrow habitat requirements in combination with good dispersal capacity (naturally or vector borne). The northern(More)
Climate change accelerates biodiversity alterations in northern ecosystems. A prevalent example is that tundra regions are invaded by boreal species. This impacts negatively on native species through competition, predation and transmission of zoonoses. Scandinavian red foxes (Vulpes vulpes) have emerged into the tundra and have altered the structure and(More)
Population density and individual dispersal behaviour affect species' distribution dynamics. Population densities vary over time, and some species occasionally increase to very high numbers, for example during outbreaks. In such situations, populations are expected to expand into new areas as a result of density-dependent dispersal which sometimes even(More)