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Factoring Integers by CVP Algorithms

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Number Theory and Cryptography

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8260))

Abstract

We use pruned enumeration algorithms to find lattice vectors close to a specific target vector for the prime number lattice. These algorithms generate multiplicative prime number relations modulo N that factorize a given integer N. The algorithm New Enum performs the stages of exhaustive enumeration of close lattice vectors in order of decreasing success rate. For example an integer N ≈ 1014 can be factored by about 90 prime number relations modulo N for the 90 smallest primes. Our randomized algorithm generated for example 139 such relations in 15 minutes. This algorithm can be further optimized. The optimization for larger integers N is still open.

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Authors and Affiliations

  1. Fachbereich Informatik und Mathematik, Goethe-Universität Frankfurt, PSF 111932, 60054, Frankfurt am Main, Germany

    Claus Peter Schnorr

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  1. Claus Peter Schnorr
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Editors and Affiliations

  1. Technische Universität Darmstadt & CASED, Mornewegstraße 30, 64293, Darmstadt, Germany

    Marc Fischlin

  2. Technische Universität Darmstadt & CASED, Mornewegstraße 32, 64293, Darmstadt, Germany

    Stefan Katzenbeisser

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Schnorr, C.P. (2013). Factoring Integers by CVP Algorithms. In: Fischlin, M., Katzenbeisser, S. (eds) Number Theory and Cryptography. Lecture Notes in Computer Science, vol 8260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-42001-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-42001-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-42000-9

  • Online ISBN: 978-3-642-42001-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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