scholarly journals Primitivity of PRESENT and other lightweight ciphers

2018 ◽  
Vol 17 (06) ◽  
pp. 1850115 ◽  
Author(s):  
Riccardo Aragona ◽  
Marco Calderini ◽  
Antonio Tortora ◽  
Maria Tota
Keyword(s):  
Sufficient Conditions ◽  
Primitive Group ◽  
Alternating Group

We provide two sufficient conditions to guarantee that the round functions of a translation-based cipher generate a primitive group. Furthermore, under the same hypotheses, and assuming that a round of the cipher is strongly proper and consists of [Formula: see text]-bit S-Boxes, with [Formula: see text] or [Formula: see text], we prove that such a group is the alternating group. As an immediate consequence, we deduce that the round functions of some lightweight translation-based ciphers, such as the PRESENT cipher, generate the alternating group.

scholarly journals Group closures of one-to-one transformations

2001 ◽  
Vol 64 (2) ◽  
pp. 177-188 ◽  
Author(s):  
Inessa Levi
Keyword(s):  
Normal Subgroup ◽  
Symmetric Group ◽  
Permutation Group ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Alternating Group ◽  
One To One ◽  
Necessary And Sufficient ◽  
Infinite Set

For a semigroup S of transformations of an infinite set X let Gs be the group of all the permutations of X that preserve S under conjugation. Fix a permutation group H on X and a transformation f of X, and let 〈f: H〉 = 〈{hfh−1: h ∈ H}〉 be the H-closure of f. We find necessary and sufficient conditions on a one-to-one transformation f and a normal subgroup H of the symmetric group on X to satisfy G〈f:H〉 = H. We also show that if S is a semigroup of one-to-one transformations of X and GS contains the alternating group on X then Aut(S) = Inn(S) ≅ GS.

Generation of the alternating group by modular additions

2019 ◽  
Vol 29 (5) ◽  
pp. 303-309
Author(s):  
Fedor M. Malyshev
Keyword(s):  
Permutation Group ◽  
Cartesian Product ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Local Action ◽  
Alternating Group ◽  
Permutation Groups ◽  
Cartesian Products ◽  
Strong Connectedness ◽  
Necessary And Sufficient

Abstract The paper is concerned with systems of generators of permutation groups on Cartesian products of residue rings. Each separate permutation from the system of generators is constructed on the basis of additions, is characterized by the local action, and leaves fixed the major parts of the components of the element being transformed. A criterion of 2-transitivity of the generated permutation group is given in the form of the strong connectedness of the digraph which corresponds to the system of generators and which is defined on the set of numbers of residue rings in the Cartesian product. Necessary and sufficient conditions under which this group contains an alternating group are formulated.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

Budgeting in Socio-economic Development Strategies (Raising a Problem)

2008 ◽  
pp. 134-151
Author(s):  
A. Shastitko ◽  
M. Ovchinnikov
Keyword(s):  
Economic Policy ◽  
Economic Development ◽  
Social Change ◽  
Eastern Europe ◽  
Statistical Data ◽  
Sufficient Conditions ◽  
Transitional Period ◽  
Socio Economic Development ◽  
Necessary And Sufficient ◽  
Economic Development Strategies

The article proposes an approach to the analysis of social change and contributes to the clarification of concepts of economic policy. It deals in particular with the notion of "change of system". The author considers positive and normative aspects of the analysis of capitalist and socialist systems. The necessary and sufficient conditions for the system to be changed are introduced, their fulfillment is discussed drawing upon the historical and statistical data. The article describes both economic and political peculiarities of the transitional period in different countries, especially in Eastern Europe.

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