• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.789-797
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• 2009

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. When n is large (e.g., n = 64) such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them we will study T-functions which are probably invertible transformation and are very useful in stream ciphers. In this paper we will show that $f(x)=x+(g(x)^2{\vee}C)$ mod $2^n$ is a permutation with a single cycle of length $2^n$ if both the least significant bit and the third significant bit in the constant C are 1, where g(x) is a T-function.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.331-343
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• 2015

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. When n is large such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them we study T-functions which are probably invertible transformations and are very useful in stream ciphers. In this paper we study the number of single cycle T-functions satisfying some conditions and characterize single cycle T-functions on $(\mathbb{Z}_2)^n$ generated by some elements in $(\mathbb{Z}_2)^{n-1}$.

• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.161-166
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• 2007

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_i=Y_i$, for i = 1,2,...,n. In this article, we showed the following: Let L, be a subspace lattice on a Hilbert space H and let X and Y be operators in B(H). Then the following are equivalent: (1) $$sup\{\frac{{\parallel}E^{\bot}Yf{\parallel}}{{\overline}{\parallel}E^{\bot}Xf{\parallel}}\;:\;f{\epsilon}H,\;E{\epsilon}L}\}\;<\;{\infty},\;sup\{\frac{{\parallel}Xf{\parallel}}{{\overline}{\parallel}Yf{\parallel}}\;:\;f{\epsilon}H\}\;<\;{\infty}$$ and $\bar{range\;X}=H=\bar{range\;Y}$. (2) There exists an invertible operator A in AlgL such that AX=Y.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.927-934
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• 2011

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. When n is large (e.g., n = 64) such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them we study T-functions which are probably invertible and are very useful in stream ciphers. In this paper we study some conditions on a T-function h(x) such that f(x) = x + h(x) has a single cycle on ${\mathbb{Z}}_{2^n}$.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.589-598
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• 2004

We consider bilateral operator weighted shift T on $L^2$(K) with weight sequence ${[A_{n}]_{n=-{\infty}}}^{\infty}$ of positive invertible diagonal operators on K. We give a characterization for T to be hypercyclic, and show that the conditions are far simplified in case T is invertible.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.649-657
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• 2018

Let R be a commutative ring. In this paper, the w-projective Basis Lemma for w-projective modules is given. Then it is shown that for a domain, nonzero w-projective ideals and nonzero w-invertible ideals coincide. As an application, it is proved that R is a Krull domain if and only if every submodule of finitely generated projective modules is w-projective.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.547-556
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• 2010

In this paper, we present the reprentation of all operators B which are Drazin invertible and sharing the spectral projections at 0 with a given Drazin invertible operator A. Meanwhile, some related results for EP operators with closed range are obtained.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.559-569
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• 2004

In this paper we shall discuss the quasi-perfect automata associated with power automata. We shall give the fact that its power automaton is invertible if an automaton A is quasi-perfect. Moreover, some subgroups and normal subgroups of the characteristic semigroup X(M) will have the very interesting parts in their structures.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.185-189
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• 2013

In this note we study a class of invertible weighted bilateral shifts on Hilbert space introduced by Haskell Rosenthal recently. We show that every Rosenthal shift is unitarily equivalent to its inverse, not quasisimilar to its adjoint, and has a nontrivial hyperinvariant subspace.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.407-417
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• 2013

In this article, we characterize t-Pr$\ddot{u}$fer modules in the class of faithful multiplication modules. As a corollary, we also characterize Krull modules. Several properties of a $t$-invertible submodule of a faithful multiplication module are given.