{
  "abstract": "We provide the first evidence relative to a classical oracle that pseudorandom unitaries (PRUs) can exist without quantum-computable one-way functions. To obtain this result, we first prove that five independent random diagonal phase layers interleaved with Hadamard transforms \\[ U=F_5HF_4HF_3HF_2HF_1 \\] form a strong PRU with security under adaptive, controlled access to the unitary, its inverse, transpose, and complex conjugate. Our main result is that, when the phase layers are implemented using a classical random oracle O, the construction remains secure against uniform BQP adversaries with coherent access to suitable Boolean completions of classical-input $QMA^{PH}^{O}}$ decision problems. Such an adversary can invert (even quantum-computable) one-way functions and solve efficiently verifiable one-way puzzles defined relative to O. Our result therefore provides classical-oracle evidence that PRUs do not imply quantum-computable one-way functions, in the form of a black-box separation. We substantially strengthen the classical-oracle result of Kretschmer, Qian, and Tal (STOC 2025) by obtaining PRUs secure against these QMA-aided adversaries. Our construction also consists of a simple, efficient circuit that queries a random function, suggesting a route to concrete implementation via the random-oracle heuristic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03711",
  "author_total": 3,
  "authors": [
    {
      "name": "Aditya Gulati"
    },
    {
      "name": "Dakshita Khurana"
    },
    {
      "name": "Kabir Tomer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2nfzfncfy2k1a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03711",
  "fulltext_url": null,
  "id": "2nfzfncfy2k1a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03711",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220473512",
  "pdf_url": "https://arxiv.org/pdf/2610.03711",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2nfzfncfy2k1a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03711",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03711"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "How to Build Pseudorandom Unitaries in Microcrypt",
  "title_text": "How to Build Pseudorandom Unitaries in Microcrypt",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/2nfzfncfy2k1a",
  "venue": "arXiv",
  "versions": []
}