Title | ||
---|---|---|
Dual universality of hash functions and its applications to classical and quantum cryptography |
Abstract | ||
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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 and a code family,
and thereby defining \epsilon-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 \epsilon-almost dual
universal_2 functions can be used for privacy amplification. We show that a
similar result applies to the quantum wire-tap channel as well. We also apply
these results on quantum models for investigating the classical wire-tap
channel and randomness extraction, and obtain various new results, including
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. Under this setting of quantum simulation, we demonstrate that
our \epsilon-almost dual universal_2 functions are more relevant for security
than the conventional \epsilon-almost universal_2 hash functions, by showing
that the former functions correspond to a linear code family having an
appropriate phase-error correcting property. These examples suggest the
importance of quantum approaches in classical settings of information theory,
as well as the dual universality of hash functions. |
Year | Venue | Keywords |
---|---|---|
2011 | Clinical Orthopaedics and Related Research | information theory,communication model,error correction,quantum wire,quantum cryptography,quantum physics,hash function,quantum channel,linear code,bit error rate |
Field | DocType | Volume |
Quantum technology,Discrete mathematics,Classical capacity,Quantum algorithm,Hash function,Quantum cryptography,Quantum information,Quantum channel,Mathematics,Quantum network | Journal | abs/1101.0 |
Citations | PageRank | References |
0 | 0.34 | 18 |
Authors | ||
2 |
Name | Order | Citations | PageRank |
---|---|---|---|
Toyohiro Tsurumaru | 1 | 21 | 3.67 |
masahito hayashi | 2 | 415 | 52.78 |