Mersenne Factorization Factory View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2014

AUTHORS

Thorsten Kleinjung , Joppe W. Bos , Arjen K. Lenstra

ABSTRACT

We present work in progress to completely factor seventeen Mersenne numbers using a variant of the special number field sieve where sieving on the algebraic side is shared among the numbers. It is expected that it reduces the overall factoring effort by more than 50%. As far as we know this is the first practical application of Coppersmith’s “factorization factory” idea. Most factorizations used a new double-product approach that led to additional savings in the matrix step. More... »

PAGES

358-377

References to SciGraph publications

  • 1993-03. Modifications to the Number Field Sieve in JOURNAL OF CRYPTOLOGY
  • 2013. Universal Security in
  • 1993. The development of the number field sieve in NONE
  • 1994. Lattice sieving and trial division in ALGORITHMIC NUMBER THEORY
  • 2004. Proving the Primality of Very Large Numbers with fastECPP in ALGORITHMIC NUMBER THEORY
  • 2001-07-13. NFS with Four Large Primes: An Explosive Experiment in ADVANCES IN CRYPTOLOGY — CRYPT0’ 95
  • 2010. Factorization of a 768-Bit RSA Modulus in ADVANCES IN CRYPTOLOGY – CRYPTO 2010
  • 2007. A Kilobit Special Number Field Sieve Factorization in ADVANCES IN CRYPTOLOGY – ASIACRYPT 2007
  • 1998. A Montgomery-like square root for the Number Field Sieve in ALGORITHMIC NUMBER THEORY
  • Book

    TITLE

    Advances in Cryptology – ASIACRYPT 2014

    ISBN

    978-3-662-45607-1
    978-3-662-45608-8

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-662-45611-8_19

    DOI

    http://dx.doi.org/10.1007/978-3-662-45611-8_19

    DIMENSIONS

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