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The average time complexity of probabilistic algorithms for finding generators in finite cyclic groups

Adamski T., Nowakowski W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2015

Vol. 63, nr 4

989--996

Generators of finite cyclic groups play important role in many cryptographic algorithms like public key ciphers, digital signatures, entity identification and key agreement algorithms. The above kinds of cryptographic algorithms are crucial for all secure communication in computer networks and secure information processing (in particular in mobile services, banking and electronic administration). In the paper, proofs of correctness of two probabilistic algorithms (for finding generators of finite cyclic groups and primitive roots) are given along with assessment of their average time computational complexity.

Some differential equations of elasticity and their lie point symmetry generators

Bocko J., Glodová I., Lengvarský P.

Acta Mechanica et Automatica

2014

Vol. 8, no. 2

99--102

The formal models of physical systems are typically written in terms of differential equations. A transformation of the variables in a differential equation forms a symmetry group if it leaves the differential equation invariant. Symmetries of differential equations are very important for understanding of their properties. It can be said that the theory of Lie group symmetries of differential equations is general systematic method for finding solutions of differential equations. Despite of this fact, the Lie group theory is relatively unknown in engineering community. The paper is devoted to some important questions concerning this theory and for several equations resulting from the theory of elasticity their Lie group infinitesimal generators are given.