Strongly secure privacy amplification cannot be obtained by encoder of Slepian-Wolf code

The privacy amplification is a technique to distill a secret key from a random variable by a hash function so that the distilled key and an eavesdropper´s random variable is statistically independent. There are two kinds of security criteria for the key distilled by the privacy amplification: the weak security criterion and 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 hash 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 hash function for the privacy amplification if we employ the strong security criterion.