Binary sequences and lattices constructed by discrete logarithms

AIMS Mathematics

卷:7

Yuchan Qi¹  Huaning Liu¹ 

[1] Research Center for Number Theory and Its Applications, School of Mathematics, Northwest University, Xi'an 710127, China;

关键词: discrete logarithm;    pseudorandom binary lattice;    pseudorandom measure;    character sums;    exponential sums;   

DOI  :  10.3934/math.2022259

来源: DOAJ

【 摘 要 】

In 1997, Mauduit and Sárközy first introduced the measures of pseudorandomness for binary sequences. Since then, many pseudorandom binary sequences have been constructed and studied. In particular, Gyarmati presented a large family of pseudorandom binary sequences using the discrete logarithms. Ten years later, to satisfy the requirement from many applications in cryptography (e.g., in encrypting "bit-maps'' and watermarking), the definition of binary sequences is extended from one dimension to several dimensions by Hubert, Mauduit and Sárközy. They introduced the measure of pseudorandomness for this kind of several-dimension binary sequence which is called binary lattices. In this paper, large families of pseudorandom binary sequences and binary lattices are constructed by both discrete logarithms and multiplicative inverse modulo p. The upper estimates of their pseudorandom measures are based on estimates of either character sums or mixed exponential sums.

【 授权许可】

Unknown