1,000 research outputs found
On finite pseudorandom binary lattices
Pseudorandom binary sequences play a crucial role in cryptography. The classical approach to pseudorandomness of binary sequences is based on computational complexity.
This approach has certain weak points thus in the last two decades years a new, more constructive and quantitative approach has been developed. Since multidimensional analogs of binary sequences (called binary lattices) also have important applications thus it is a natural idea to extend this new approach to the multidimensional case. This extension started with a paper published in 2006, and since that about 25 papers have been written on this subject.
Here our goal is to present a survey of all these papers
On linear complexity of binary lattices
The linear complexity is an important and frequently used
measure of unpredictability and pseudorandomness of binary
sequences. In this paper our goal is to extend this notion
to two dimensions. We will define and study the linear complexity of binary lattices. The linear complexity of a truly random binary lattice will be estimated. Finally, we will analyze the connection between the linear complexity and the correlation measures, and we will utilize the inequalities obtained in this way for estimating the linear complexity of an important special binary lattice. Finally,
we will study the connection between the linear complexity of binary lattices and of the associated binary sequences
Pseudorandom Number Generators and the Square Site Percolation Threshold
A select collection of pseudorandom number generators is applied to a Monte
Carlo study of the two dimensional square site percolation model. A generator
suitable for high precision calculations is identified from an application
specific test of randomness. After extended computation and analysis, an
ostensibly reliable value of pc = 0.59274598(4) is obtained for the percolation
threshold.Comment: 11 pages, 6 figure
On linear complexity of binary lattices, II
The linear complexity is an important and frequently used measure of unpredictably and pseudorandomness of binary sequences. In Part I of this paper we extended this notion to two dimensions: we defined and studied the linear complexity of binary and bit lattices. In this paper
first we will estimate the linear complexity of a truly random bit -lattice. Next we will extend the notion of -error linear complexity to bit lattices. Finally, we will present another alternative definition of linear complexity of bit lattices
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