  We show that duals of certain low-density parity-check (LDPC) codes, when
used in a standard coset coding scheme, provide strong secrecy over the binary
erasure wiretap channel (BEWC). This result hinges on a stopping set analysis
of ensembles of LDPC codes with block length $n$ and girth $\geq 2k$, for some
$k \geq 2$. We show that if the minimum left degree of the ensemble is
$l_\mathrm{min}$, the expected probability of block error is
$\calO(\frac{1}{n^{\lceil l_\mathrm{min} k /2 \rceil - k}})$ when the erasure
probability $\epsilon < \epsilon_\mathrm{ef}$, where $\epsilon_\mathrm{ef}$
depends on the degree distribution of the ensemble. As long as $l_\mathrm{min}
> 2$ and $k > 2$, the dual of this LDPC code provides strong secrecy over a
BEWC of erasure probability greater than $1 - \epsilon_\mathrm{ef}$.
