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This paper investigates the privacy amplification problem, and compares theexisting two bounds: the exponential bound derived by one of the authors andthe min-entropy bound derived by Renner. It turns out that the exponentialbound is better than the min-entropy bound when a security parameter is rathersmall for a block length, and that the min-entropy bound is better than theexponential bound when a security parameter is rather large for a block length.Furthermore, we present another bound that interpolates the exponential boundand the min-entropy bound by a hybrid use of the Renyi entropy and theinf-spectral entropy.

Non-Asymptotic Analysis of Privacy Amplification via Renyi Entropy and Inf-Spectral Entropy