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\begin{abstract}
For $n\in \mathbb{Z}, A\subset \mathbb{Z}$, let $\delta_{A}(n)$
denote the number of representations of $n$ in the form $n=a-a'$,
where $a,a'\in A$. A set $A\subset \mathbb{Z}$ is called a unique
difference basis of $\mathbb{Z}$ if $\delta_{A}(n)=1$ for all $n\neq
0$ in $\mathbb{Z}$. In this paper, we prove that there exists a unique
difference basis of $\mathbb{Z}$ whose growth is logarithmic. These
results show that the analogue of the Erd\H{o}s-Tur\'{a}n conjecture
fails to hold in $(\mathbb{Z},-)$.
\end{abstract}

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