Tight exponential analysis of universally composable privacy amplification and its applications

Abstract

Motivated by the desirability of universal composability, we analyze in terms of L_1 distinguishability the task of secret key generation from a joint random variable. Under this secrecy criterion, using the Renyi entropy of order 1+s for s in [0,1, we derive a new upper bound of Eve's distinguishability under the application of the universal2 hash functions. It is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions. The result is applied to the wire-tap channel model and to secret key generation (distillation) by public discussion.

Several errors are fixed. The title is slightly changed. The topic and protocol are similar to those in arXiv:0904.0308. However, the security criterion of this paper is different from arXiv:0904.0308. This paper adopts the universal composability while arXiv:0904.0308 adopts the mutual information criterion

References in corpus (4)

• Information Spectrum Approach to Second-Order Coding Rate in Channel Coding
• Exponential decreasing rate of leaked information in universal random privacy amplification
• Strongly Secure Privacy Amplification Cannot Be Obtained by Encoder of Slepian-Wolf Code
• Construction of Codes for Wiretap Channel and Secret Key Agreement from Correlated Source Outputs by Using Sparse Matrices

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