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Self-witnessing polynomial-time complexity and prime factorization

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Abstract

For a number of computational search problems, the existence of a polynomial-time algorithm for the problem implies that a polynomial-time algorithm for the problem is constructively known. Some instances of such self-witnessing polynomial-time complexity are presented. Our main result demonstrates this property for the problem of computing the prime factorization of a positive integer, based on a lemma which shows that a certificate for primality or compositeness can be constructed for a positive integer p in deterministic polynomial time given a complete factorization of p - 1.

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Authors and Affiliations

  1. Department of Computer Science, University of Victoria, V8W 3P6, Victoria, B.C., Canada

    Michael R. Fellows

  2. Department of Mathematics, University of Washington, 98195, Seattle, WA, USA

    Neal Koblitz

Authors
  1. Michael R. Fellows
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  2. Neal Koblitz
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Communicated by S.A. Vanstone

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Fellows, M.R., Koblitz, N. Self-witnessing polynomial-time complexity and prime factorization. Des Codes Crypt 2, 231–235 (1992). https://doi.org/10.1007/BF00141967

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  • DOI: https://doi.org/10.1007/BF00141967

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