scholarly journals Linear(hull) Cryptanalysis of Round-reduced Versions of KATAN

2016 ◽  
Author(s):  
Danping Shi ◽  
Lei Hu ◽  
Siwei Sun ◽  
Ling Song
Keyword(s):  
Linear Hull

scholarly journals Linear Cryptanalysis: Key Schedules and Tweakable Block Ciphers

2017 ◽  
pp. 474-505 ◽  
Author(s):  
Thorsten Kranz ◽  
Gregor Leander ◽  
Friedrich Wiemer
Keyword(s):  
Block Ciphers ◽  
Linear Cryptanalysis ◽  
Linear Hull ◽  
Key Schedule ◽  
Schedule Design ◽  
Key Scheduling

This paper serves as a systematization of knowledge of linear cryptanalysis and provides novel insights in the areas of key schedule design and tweakable block ciphers. We examine in a step by step manner the linear hull theorem in a general and consistent setting. Based on this, we study the influence of the choice of the key scheduling on linear cryptanalysis, a – notoriously difficult – but important subject. Moreover, we investigate how tweakable block ciphers can be analyzed with respect to linear cryptanalysis, a topic that surprisingly has not been scrutinized until now.

Subspaces with property (b) in locally convex spaces of quasi-barrelled type

1980 ◽  
Vol 88 (2) ◽  
pp. 331-337 ◽  
Author(s):  
Bella Tsirulnikov
Keyword(s):  
Convex Space ◽  
Locally Convex Space ◽  
Dense Subspace ◽  
Locally Convex Spaces ◽  
Linear Hull ◽  
Bounded Set ◽  
Property B ◽  
Locally Convex ◽  
Strong Dual ◽  
Convex Spaces

A subspace G of a locally convex space E has property (b) if for every bounded set B of E the codimension of G in the linear hull of G ∪ B is finite, (5). Extending the results of (5) and (14), we prove that, if the strong dual of E is complete, then subspaces with property (b) inherit the following properties of E: σ-evaluability, evaluability, the property of being Mazur, semibornological and bornological. We also prove that a dense subspace with property (b) of a Mazur space is sequentially dense, and of a semibornological space – dense in the sense of Mackey (locally dense, following M. Valdivia).

scholarly journals Identities on Maximal Subgroups of GLn(D)

2005 ◽  
Vol 12 (03) ◽  
pp. 461-470 ◽  
Author(s):  
D. Kiani ◽  
M. Mahdavi-Hezavehi
Keyword(s):  
Maximal Subgroup ◽  
Division Algebra ◽  
Division Ring ◽  
Group Identity ◽  
Subnormal Subgroup ◽  
Maximal Subgroups ◽  
Polynomial Identities ◽  
Linear Hull ◽  
Finite Dimensional ◽  
Group Identities

Let D be a division ring with centre F. Assume that M is a maximal subgroup of GLn(D) (n≥1) such that Z(M) is algebraic over F. Group identities on M and polynomial identities on the F-linear hull F[M] are investigated. It is shown that if F[M] is a PI-algebra, then [D:F]<∞. When D is non-commutative and F is infinite, it is also proved that if M satisfies a group identity and F[M] is algebraic over F, then we have either M=K* where K is a field and [D:F]<∞, or M is absolutely irreducible. For a finite dimensional division algebra D, assume that N is a subnormal subgroup of GLn(D) and M is a maximal subgroup of N. If M satisfies a group identity, it is shown that M is abelian-by-finite.

Simple motion systems and Banach spaces associated to uniformly bounded representations

1999 ◽  
Vol 127 (1) ◽  
pp. 133-147
Author(s):  
MATTHIAS MAYER ◽  
CHRISTIAN SALLER
Keyword(s):  
Convex Hull ◽  
Locally Compact Group ◽  
Irreducible Representations ◽  
Minkowski Functional ◽  
Linear Hull ◽  
Locally Compact ◽  
Simple Motion ◽  
Motion System ◽  
Bounded Representation ◽  
Uniformly Bounded

Given a uniformly bounded representation of a locally compact group, we consider the closed circled convex hull K of the orbit of a vector. We call K a simple motion system (SMS) and endow its linear hull with the Minkowski functional of K. The representation theory on these ‘SMS-spaces’ is discussed, in particular for C0-representations, for irreducible representations of connected groups and for integrable representations. As an application we give a criterion for the decomposibility of representations.

Generalization of Matsui’s Algorithm 1 to linear hull for key-alternating block ciphers

2012 ◽  
Vol 66 (1-3) ◽  
pp. 175-193 ◽  
Author(s):  
Andrea Röck ◽  
Kaisa Nyberg
Keyword(s):  
Block Ciphers ◽  
Linear Hull

scholarly journals Improved linear (hull) cryptanalysis of round-reduced versions of SIMON

2016 ◽  
Vol 60 (3) ◽  
Author(s):  
Danping Shi ◽  
Lei Hu ◽  
Siwei Sun ◽  
Ling Song ◽  
Kexin Qiao ◽  
...  
Keyword(s):  
Linear Hull
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