{
  "annotation_id": "623371db-3db3-445e-a9a1-5347d5bebf21",
  "date_created": "2026-03-02T18:02:10.329000Z",
  "date_modified": "2026-03-02T18:02:10.329000Z",
  "file_hash": "153db8d1e1f834d4bb2d0d3b47d734aba535a26de4e024eb775893a08492d34f",
  "private": false,
  "record": {
    "abstract": "Boolean functions are important building blocks in cryptography for their\nwide application in both stream and block cipher systems. For cryptanalysis of\nsuch systems one tries to find out linear functions that are correlated to the\nBoolean functions used in the crypto system. Let $f$ be an $n$-variable Boolean\nfunction and its Walsh spectra is denoted by $W_f(\\omega)$ at the point $\\omega\n\\in \\{0, 1\\}^n$. The Boolean function is available in the form of an oracle. We\nlike to find an $\\omega$ such that $W_f(\\omega) \\neq 0$ as this will provide\none of the linear functions which are correlated to $f$. We show that the\nquantum algorithm proposed by Deutsch and Jozsa (1992) solves the above\nmentioned problem in constant time. However, the best known classical algorithm\nto solve this problem requires exponential time in $n$. We also analyse certain\nclasses of cryptographically significant Boolean functions and highlight how\nthe basic Deutsch-Jozsa algorithm performs on them.",
    "arxiv_id": "quant-ph/0410042",
    "authors": [
      "Subhamoy Maitra",
      "Partha Mukhopadhyay"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Deutsch-Jozsa Algorithm Revisited in the Domain of Cryptographically   Significant Boolean Functions",
    "url": "https://arxiv.org/abs/quant-ph/0410042"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "96d5dce8-1215-4944-9279-2bffb9507647",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}