168 research outputs found
Statistical Zero Knowledge and quantum one-way functions
One-way functions are a very important notion in the field of classical
cryptography. Most examples of such functions, including factoring, discrete
log or the RSA function, can be, however, inverted with the help of a quantum
computer. In this paper, we study one-way functions that are hard to invert
even by a quantum adversary and describe a set of problems which are good such
candidates. These problems include Graph Non-Isomorphism, approximate Closest
Lattice Vector and Group Non-Membership. More generally, we show that any hard
instance of Circuit Quantum Sampling gives rise to a quantum one-way function.
By the work of Aharonov and Ta-Shma, this implies that any language in
Statistical Zero Knowledge which is hard-on-average for quantum computers,
leads to a quantum one-way function. Moreover, extending the result of
Impagliazzo and Luby to the quantum setting, we prove that quantum
distributionally one-way functions are equivalent to quantum one-way functions.
Last, we explore the connections between quantum one-way functions and the
complexity class QMA and show that, similarly to the classical case, if any of
the above candidate problems is QMA-complete then the existence of quantum
one-way functions leads to the separation of QMA and AvgBQP.Comment: 20 pages; Computational Complexity, Cryptography and Quantum Physics;
Published version, main results unchanged, presentation improve
Quantum-enhanced Secure Delegated Classical Computing
We present a quantumly-enhanced protocol to achieve unconditionally secure
delegated classical computation where the client and the server have both
limited classical and quantum computing capacity. We prove the same task cannot
be achieved using only classical protocols. This extends the work of Anders and
Browne on the computational power of correlations to a security setting.
Concretely, we present how a client with access to a non-universal classical
gate such as a parity gate could achieve unconditionally secure delegated
universal classical computation by exploiting minimal quantum gadgets. In
particular, unlike the universal blind quantum computing protocols, the
restriction of the task to classical computing removes the need for a full
universal quantum machine on the side of the server and makes these new
protocols readily implementable with the currently available quantum technology
in the lab
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