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3 Demonstratio Mathematica

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A note on configurence uniformity for single algebras

100%

Chajda I. , Länger H.

2004

tom Vol. 37, nr 1

9--11

It is proved that though for varieties congruence uniformity implies congruence regularity this is not the case with infinite algebras.

Modifications of MV-algebras corresponding to strong ortholattices

100%

Chajda I. , Länger H.

tom Vol. 38, nr 1

1--6

It is well-known that principal filters of MV-algebras are de Morgan algebras with involutory complementation. A modification of the notion of an MV-algebra is presented having the property that all principal filters are ortholattices. It turns out that the commutativity of these modified MV-algebras is equivalent to the distributivity of the corresponding ortholattices.

On ring-like structures related to symmetric cryptosystems

80%

Dorninger D. , Länger H. , Mączyński M.

tom Vol. 38, nr 2

265--276

The aim of this paper is to study cryptographic systems denned as algebras (A,+alfa,+beta,p,s) of type (2,2,0,0) satisfying the axiom (x+alfa p)+beta S = x for all x is an element of A. Some standard and non-standard examples of such systems are given. In particular, we study the systems for which + alfa = + beta= + and p = s where the operation + is the addition operation of a generalized Boolean quasiring (GBQR). We investigate the structure of these algebras revealing their relation to orthomodular lattices and characterize the systems for which s (which is interpreted as coding and decoding key) commutes with all elements of A. By applying direct products to cryptographic algebras one can construct complicated cryptographic systems which may be of importance for practical use. (Then the keys are sequences whose components may be selected at random like in an XOR2 protocol.)