Quantum Pseudorandom Primitives Beyond Pseudorandom States
Guardado en:
| Publicado en: | ProQuest Dissertations and Theses (2025) |
|---|---|
| Autor principal: | |
| Publicado: |
ProQuest Dissertations & Theses
|
| Materias: | |
| Acceso en línea: | Citation/Abstract Full Text - PDF |
| Etiquetas: |
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
MARC
| LEADER | 00000nab a2200000uu 4500 | ||
|---|---|---|---|
| 001 | 3247618049 | ||
| 003 | UK-CbPIL | ||
| 020 | |a 9798293814688 | ||
| 035 | |a 3247618049 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 084 | |a 66569 |2 nlm | ||
| 100 | 1 | |a Lu, Chuhan | |
| 245 | 1 | |a Quantum Pseudorandom Primitives Beyond Pseudorandom States | |
| 260 | |b ProQuest Dissertations & Theses |c 2025 | ||
| 513 | |a Dissertation/Thesis | ||
| 520 | 3 | |a Quantum pseudorandomness is an emerging research area. Ji, Liu, and Song defined pseudorandom states (PRSs) and pseudorandom unitaries (PRUs) as quantum analogs of pseudorandom generators and pseudorandom functions. A unitary oracle separation result between one-way functions and PRSs/PRUs, established by Kretschmer, suggests that certain quantum primitives may remain secure even if classical cryptography is compromised. This insight has spurred extensive work on quantum pseudorandomness and its applications in quantum cryptography.Many constructions of PRSs have been established under standard assumptions, yet building a secure PRU was a long-standing open problem. This dissertation aims to narrow the gap between PRSs and PRUs and presents results that go beyond PRSs.We introduce Pseudorandom State Scramblers (PRSSs), a new primitive that lies between PRSs and PRUs. A PRSS maps any pure state to a pseudorandom state, a property shared with PRUs but not with PRSs. We present a construction of PRSSs inspired by the well-known Kac’s walk, and in particular, we develop a parallel variant that significantly accelerates the mixing time, enabling an efficient construction. PRSSs support cryptographic tasks not known to be achievable from PRSs alone, including a quantum encryption scheme and a succinct quantum state commitment. Additionally, when suitable classical randomness is provided, our construction exhibits a special dispersing property not known to be satisfied by any existing construction of quantum pseudorandom primitives.Our subsequent work shows that, without asymptotically increasing the number of steps, our construction based on the parallel Kac’s walk yields PRUs with standard or even strong security. The proof builds on a recently developed technique for establishing adaptive security, known as the path-recording method. This result provides an alternative construction of PRUs and further showcases the power of this proof technique.In addition, this dissertation includes two side projects. The first revisits the Hidden Subgroup Problem over Zn, providing a simplified analysis of a known quantum algorithm using elementary lattice tools. The second establishes a quantum analogue of a classical impossibility result for statistical non-interactive zero-knowledge arguments, showing limitations of black-box reductions under classical-query quantum adversaries. | |
| 653 | |a Computer science | ||
| 653 | |a Computer engineering | ||
| 653 | |a Statistics | ||
| 773 | 0 | |t ProQuest Dissertations and Theses |g (2025) | |
| 786 | 0 | |d ProQuest |t ProQuest Dissertations & Theses Global | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3247618049/abstract/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3247618049/fulltextPDF/embedded/75I98GEZK8WCJMPQ?source=fedsrch |