We study the entropy of the set traced by an n-step simple symmetric random walk on ℤd. We show that for d≥3, the entropy is of order n. For d=2, the entropy is of order n/log2n. These values are essentially governed by the size of the boundary of the trace.
In the paper the entropy of – fuzzy numbers is studied. It is shown that for a given norm function, the computation of the entropy of – fuzzy numbers reduces to using a simple formula which depends only on the spreads and shape functions of incoming numbers. In detail the entropy of –sums and –products of – fuzzy numbers is investigated. It is shown that the resulting entropy can be computed only by means of the entropy of incoming fuzzy numbers or by means of their parameters without the...
We describe a conceptual approach which provides a unified view of various entropy-like functionals on the class of semimetric spaces, endowed with a bounded measure. The entropy considered in the author’s previous articles is modified so as to assume finite values for a fairly wide class of spaces which fail to be totally bounded.
In 1994, the well-known Diffie-Hellman key exchange protocol was for the first time implemented in a non-group based setting. Here, the underlying key space was the set of reduced principal ideals of a real quadratic number field. This set does not possess a group structure, but instead exhibits a so-called infrastructure. More recently, the scheme was extended to real quadratic congruence function fields, whose set of reduced principal ideals has a similar infrastructure. As always, the security...
Pseudorandom binary sequences are required in stream ciphers and other applications of modern communication systems. In the first case it is essential that the sequences be unpredictable. The linear complexity of a sequence is the amount of it required to define the remainder. This work addresses the problem of the analysis and computation of the linear complexity of certain pseudorandom binary sequences. Finally we conclude some characteristics of the nonlinear function that produces the sequences...