Quantum key distribution (QKD) offers a very strong property called everlasting security,
which says if authentication is unbroken during the execution of QKD, the generated key …

Text Let Z n be the ring of residue classes modulo n and Z n⁎ be the group of its units. In
1926, Brauer obtained an explicit formula for the number of solutions of the linear …

In this paper, we develop a method of evaluating general exponential sums with rational
amplitude functions for multiple variables which complements works by T. Cochrane and Z …

Congruences are ubiquitous in computer science, engineering, mathematics, and related
areas. Developing techniques for finding (the number of) solutions of congruences is an …

Let p> 5 be a fixed prime and assume that α 1, α 2, α 3 are coprime to p. We study the
asymptotic behavior of small solutions of congruences of the form α 1 x 1 2+ α 2 x 2 2+ α 3 x …

Let Z n [i] be the ring of Gaussian integers modulo a positive integer n. Very recently,
Camarero and Martinez et al. showed that for every prime number p> 5 such that p≡±5 …

Given a polynomial Q (x 1,⋯, xt)= λ 1 x 1 k 1+⋯+ λ txtkt, for every c∈ Z and n≥ 2, we study
the number of solutions NJ (Q; c, n) of the congruence equation Q (x 1,⋯, xt)≡ c mod n in …

We address three questions posed by Bibak\cite {KB20}, and generalize some results of
Bibak, Lehmer and KG Ramanathan on solutions of linear congruences $\sum_ {i= 1}^ k a_i …

Let Z n be the ring of residue classes modulo n, and let Z n⁎ be the group of its units. 90
years ago, Brauer obtained a formula for the number of representations of c∈ Z n as the …

On One Kind of Character Sums and Its Applications Page 1 Research Article On One Kind of
Character Sums and Its Applications Xiao Wang School of Science, Chang’an University, Xi’an …