On finite pseudorandom binary lattices

Abstract

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.2010 Mathematics Subject Classification: Primary 11K45.

Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields

“…Many pseudorandom binary lattices have been obtained and studied by using the subsets in finite fields (see [1][2][3][4][5][6][7][8][9][10][11]). Suppose that = q p n is an odd prime power and q is a finite field with q elements.…”

On the k‐Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields

“…The measures of pseudorandomness of the binary σ was studied in [16] for more general setting. Some related problems were considered in [10,11,12]. In the sequel, we first prove a lower bound on the linear complexity of of σ in Eq.…”