Title: Composable security in relativistic quantum cryptography,
Abstract: Relativistic protocols have been proposed to overcome some impossibility
results in classical and quantum cryptography. In such a setting, one takes the
location of honest players into account, and uses the fact that information
cannot travel faster than the speed of light to limit the abilities of
dishonest agents. For example, various relativistic bit commitment protocols
have been proposed. Although it has been shown that bit commitment is
sufficient to construct oblivious transfer and thus multiparty computation,
composing specific relativistic protocols in this way is known to be insecure.
A composable framework is required to perform such a modular security analysis
of construction schemes, but no known frameworks can handle models of
computation in Minkowski space.
By instantiating the systems model from the Abstract Cryptography framework
with Causal Boxes, we obtain such a composable framework, in which messages are
assigned a location in Minkowski space (or superpositions thereof). This allows
us to analyse relativistic protocols and to derive novel possibility and
impossibility results. We show that (1) coin flipping can be constructed from
the primitive channel with delay, (2) biased coin flipping, bit commitment and
channel with delay are all impossible without further assumptions, and (3) it
is impossible to improve a channel with delay. Note that the impossibility
results also hold in the computational and bounded storage settings. This
implies in particular non-composability of all proposed relativistic bit
commitment protocols, of bit commitment in the bounded storage model, and of
biased coin flipping.