Solving hidden number problem with one bit oracle and advice

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In the Hidden Number Problem (HNP), the goal is to find a hidden number s, when given p, g and access to an oracle that on query a returns the k most significant bits of . We present an algorithm solving HNP, when given an advice depending only on p and g; the running time and advice length are polynomial in logp. This algorithm improves over prior HNP algorithms in achieving: (1) optimal number of bits k ≥ 1 (compared with k ≥ Ω(loglogp)); (2) robustness to random noise; and (3) handling a wide family of predicates on top of the most significant bit. As a central tool we present an algorithm that, given oracle access to a function f over ℤN, outputs all the significant Fourier coefficients of f (i.e., those occupying, say, at least 1% of the energy). This algorithm improves over prior works in being: Local. Its running time is polynomial in logN and L1(f̂) (for L 1(f̂) the sum of f's Fourier coefficients, in absolute value). Universal. For any N, t, the same oracle queries are asked for all functions f over ℤN s.t. L1(f̂) ≤ t. Robust. The algorithm succeeds with high probability even if the oracle to f is corrupted by random noise.

Original languageEnglish
Title of host publicationAdvances in Cryptology - CRYPTO 2009 - 29th Annual International Cryptology Conference, Proceedings
Number of pages18
StatePublished - 2009
Externally publishedYes
Event29th Annual International Cryptology Conference, CRYPTO 2009 - Santa Barbara, CA, United States
Duration: 16 Aug 200920 Aug 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5677 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference29th Annual International Cryptology Conference, CRYPTO 2009
Country/TerritoryUnited States
CitySanta Barbara, CA

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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