Dual universality of hash functions and its applications to quantum cryptography

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In this paper, we introduce the concept of dual universality of hash functions and present its applications to various quantum and classical communication models including cryptography. We begin by establishing the one-to-one correspondence between a linear function family F and a code family C, and thereby defining ε-almost dual universal_2 hash functions, as a generalization of the conventional universal_2 hash functions. Then we give a security proof for the Bennett-Brassard 1984 protocol, where the Shor-Preskill-type argument is used, but nevertheless ε-almost dual universal_2 functions can be used for privacy amplification.
2011-02-24