Frameworks for efficient quantum oblivious transfer in the QROM

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Kumar, Nishant

Contributors dc:contributor

• Khurana, Dakshita

• cryptography
• quantum
• random oracles
• oblivious transfer
• entanglement

Statement dc:rights

• Copyright 2022 Nishant Kumar

Language dc:language

en, eng

Handle dc:identifier

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

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115635