Strongly Secure Privacy Amplification Cannot Be Obtained by Encoder of Slepian-Wolf Code

Understand

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.