Frameworks for efficient quantum oblivious transfer in the QROM
Kumar, Nishant
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https://hdl.handle.net/2142/115635
Description
Title
Frameworks for efficient quantum oblivious transfer in the QROM
Author(s)
Kumar, Nishant
Issue Date
2022-06-01
Director of Research (if dissertation) or Advisor (if thesis)
Khurana, Dakshita
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
cryptography
quantum
random oracles
oblivious transfer
entanglement
Abstract
We propose new general frameworks for constructing round efficient and concretely efficient
quantum oblivious transfer (OT) in the quantum random oracle model (QROM). We obtain
the following unconditionally secure protocols in the QROM, satisfying simulation-based
security against malicious adversaries.
• Non-interactive (i.e., one-message) bit OT between two parties that initially share a
set of EPR pairs. This realizes an ideal functionality that obtains two chosen bits
(m0,m1) from a sender and outputs (b,mb) to a receiver, for uniformly random b.
• Two-message bit OT without setup, realizing the same functionality as above. This is
obtained by showing that the above protocol remains secure even if the receiver is the
one that sets up the entanglement.
• Three-message chosen-input string OT without entanglement or setup.
Our conceptual contribution is a new template for quantum OT, that we call the “fixed basis
framework”. In this framework, the correct choice of basis used by one player to polarize
qubits is largely fixed and public at the time of measurement, except for some hidden trap
qubits that are intentionally polarized in a conjugate basis. To analyze some of our protocols,
we develop new techniques that enable seedless extraction from quantum sources of entropy.
Finally, we also construct three-message random-input and four-message chosen-input
OT assuming non-interactive idealized (i.e. extractable and equivocal) bit commitments.
In fact, all our protocols use such commitments, for which we provide simple and efficient
constructions in the QROM. These may be of independent interest.
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