A large family of pseudorandom binary lattices

Liu, Huaning

doi:10.1090/s0002-9939-08-09706-2

Cited by 5 publications

(5 citation statements)

References 21 publications

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“…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.…”

Section: N Nmentioning

confidence: 99%

Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields

Chen

2020

Open Mathematics

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In 2006, Hubert, Mauduit and Sárközy extended the notion of binary sequences to n-dimensional binary lattices and introduced the measures of pseudorandomness of binary lattices. In 2011, Gyarmati, Mauduit and Sárközy extended the notions of family complexity, collision and avalanche effect from binary sequences to binary lattices. In this paper, we construct pseudorandom binary lattices by using cyclotomic classes in finite fields and study the pseudorandom measure of order k, family complexity, collision and avalanche effect. Results indicate that such binary lattices are “good,” and their families possess a nice structure in terms of family complexity, collision and avalanche effect.

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Section: N Nmentioning

confidence: 99%

Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields

Chen

2020

Open Mathematics

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“…In [26] Liu presented another construction for a large family of pseudorandom binary lattices by using the multiplicative inverse and the quadratic character of finite fields.…”

Section: Theoremmentioning

confidence: 99%

On finite pseudorandom binary lattices

Gyarmati

Mauduit

Sárközy

2017

Discrete Applied Mathematics

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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.

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“…If these sequences are constructed by an algorithm, then we usually speak of pseudorandom generator, and the algorithm is considered a "good" one if it satisfies the "next bit" test; this approach has certain weak points. Large families consisting of binary sequences which are "good" in terms of the pseudorandom measures defined above have been also constructed; see, e.g., [19], [20], [27], [28], [31], [32], [38]. In these constructions it is guaranteed that the individual sequences belonging to the family possess strong pseudorandom properties.…”

Section: Introductionmentioning

confidence: 99%

The cross-correlation measure for families of binary sequences

Gyarmati¹,

Mauduit²,

Sárközy³

2014

Applied Algebra and Number Theory

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Large families of binary sequences of the same length are considered and a new measure, the cross-correlation measure of order k is introduced to study the connection between the sequences belonging to the family. It is shown that this new measure is related to certain other important properties of families of binary sequences. Then the size of the cross-correlation measure is studied. Finally, the cross-correlation measures of two important families of pseudorandom binary sequences are estimated.

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A large family of pseudorandom binary lattices

Cited by 5 publications

References 21 publications

Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields

Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields

On finite pseudorandom binary lattices

The cross-correlation measure for families of binary sequences

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