منابع مشابه
Pseudorandom Permutation Families over Abelian Groups
We propose a general framework for differential and linear cryptanalysis of block ciphers when the block is not a bitstring. We prove piling-up lemmas for the generalized differential probability and the linear potential, and we study their lower bounds and average value, in particular in the case of permutations of Fp. Using this framework, we describe a toy cipher, that operates on blocks of ...
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Let k be a field of characteristic p, where p is a prime number, let ppk(G) be the Grothendieck group of p-permutation kG-modules, where G is a finite group, and let C ppk(G) = C ⊗Z ppk(G). In this article, we find all the composition factors of the biset functor C ppk restricted to the category of abelian groups.
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LetG be a finite additive abelian group with exponent n > 1, and let a1, . . . , an−1 be elements of G. We show that there is a permutation σ ∈ Sn−1 such that all the elements saσ(s) (s = 1, . . . , n− 1) are nonzero if and only if ∣∣∣{1 6 s < n : n d as 6= 0 }∣∣∣ > d− 1 for every positive divisor d of n. When G is the cyclic group Z/nZ, this confirms a conjecture of Z.-W. Sun.
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Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2005
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2004.06.031