The privacy amplification is a technique to distill a secret key from a
random variable by a function so that the distilled key and eavesdropper's
random variable are statistically independent. There are three kinds of
security criteria for the key distilled by the privacy amplification: the
normalized divergence criterion, which is also known as the weak security
criterion, the variational distance criterion, and the divergence criterion,
which is also known as the strong security criterion. As a technique to distill
a secret key, it is known that the encoder of a Slepian-Wolf (the source coding
with full side-information at the decoder) code can be used as a function for
the privacy amplification if we employ the weak security criterion. In this
paper, we show that the encoder of a Slepian-Wolf code cannot be used as a
function for the privacy amplification if we employ the criteria other than the
weak one.Comment: 10 pages, no figure, A part of this paper will be presented at 2009
IEEE International Symposium on Information Theory in Seoul, Korea. Version 2
is a published version. The results are not changed from version 1.
Explanations are polished and some references are added. In version 3, only
style and DOI are edite