Dual universality of hash functions and its applications to classical and quantum cryptography

Toyohiro Tsurumaru (Mitsubishi Electric Corporation) and Masahito Hayashi (Graduate School of Information Sciences, Tohoku University / Centre for Quantum Technologies, National University of Singapore)

 

The concept of universal hash functions has a variety of cryptographic applications, for example, for the information theoretically secure signatures, the hash functions for the wire-tap channel and for privacy amplification.
In this paper, we introduce the concept of $\varepsilon$-almost dual universal hash functions and present its applications to various quantum and classical communication models including cryptography.
The first application is to a security proof for quantum key distribution (QKD) and the quantum-wiretap channel.
Next we apply our results on these quantum models for investigating the classical wire-tap channel and randomness extraction, and obtain various new results, such as the existence of a deterministic hash function that is universally secure against different types of wire-tapper.
For proving these results, we present an extremely simple argument by simulating the classical channels by quantum channels, where the strength of Eve's wire-tapping can be measured by the phase bit error rate.
These examples suggest the importance of quantum approaches in classical settings of information theory, as well as the dual universality of hash functions.