Frameworks for efficient quantum oblivious transfer in the QROM

Kumar, Nishant

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https://hdl.handle.net/2142/115635 Copy

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.

Graduation Semester

2022-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Nishant Kumar

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