  Let $\gamma$ be a generator of a cyclic group $G$ of order $n$. The least
index of a self-mapping $f$ of $G$ is the index of the largest subgroup $U$ of
$G$ such that $f(x)x^{-r}$ is constant on each coset of $U$ for some positive
integer~$r$. We determine the index of the univariate Diffie-Hellman mapping
$d(\gamma^a)=\gamma^{a^2}$, $a=0,1,\ldots,n-1$, and show that any mapping of
small index coincides with~$d$ only on a small subset of $G$. Moreover, we
prove similar results for the bivariate Diffie-Hellman mapping
$D(\gamma^a,\gamma^b)=\gamma^{ab}$, $a,b=0,1,\ldots,n-1$. In the special case
that $G$ is a subgroup of the multiplicative group of a finite field we present
improvements.
