On the factorization of RSA-120 (original) (raw)

Abstract

We present data concerning the factorization of the 120-digit number RSA-120, which we factored on July 9, 1993, using the quadratic sieve method. The factorization took approximately 825 MIPS years and was completed within three months real time. At the time of writing RSA-120 is the largest integer ever factored by a general purpose factoring algorithm. We also present some conservative extrapolations to estimate the difficulty of factoring even larger numbers, using either the quadratic sieve method or the number field sieve, and discuss the issue of the crossover point between these two methods.

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References

  1. Bernstein, D. J., Lenstra, A. K.: A general number field sieve implementation. 103–126 in Lenstra, Jr. H. W. (eds): The development of the number field sieve. Lecture Notes in Math. 1554, Springer-Verlag, Berlin, 1993 [7]
    Chapter Google Scholar
  2. Buhler, J. P., Lenstra, Jr., H. W., Pomerance, C: Factoring integers with the number field sieve. 50–94 in Lenstra, Jr. H. W. (eds): The development of the number field sieve. Lecture Notes in Math. 1554, Springer-Verlag, Berlin, 1993 [7]
    Chapter Google Scholar
  3. Buchmann, J.A., Denny, T. F.: An implementation of the multiple polynomial quadratic sieve, University of Saarbrücken (to appear)
    Google Scholar
  4. Dixon, B., Lenstra, A. K.: Factoring integers using SIMD sieves. Advances in Cryptology, Eurocrypt’ 93, Lecture Notes in Comput. Sci. (to appear)
    Google Scholar
  5. LaMacchia, B.A., Odlyzko, A.M.: Computation of discrete logarithms in prime fields. Designs, Codes and Cryptography 1 (1991) 47–62
    Article MATH MathSciNet Google Scholar
  6. Lenstra, A.K.: Massively parallel computing and factoring. Proceedings Latin’92, Lecture Notes in Comput. Sci. 583 (1992) 344–355
    Google Scholar
  7. Lenstra, A. K., Lenstra, Jr. H. W. (eds): The development of the number field sieve. Lecture Notes in Math. 1554, Springer-Verlag, Berlin, 1993
    MATH Google Scholar
  8. Lenstra, A.K., Lenstra, Jr., H.W., Manasse, M.S., Pollard, J.M.: The number field sieve. 11–42 in Lenstra, Jr. H. W. (eds): The development of the number field sieve. Lecture Notes in Math. 1554, Springer-Verlag, Berlin, 1993 [7]
    Chapter Google Scholar
  9. Lenstra, A.K., Lenstra, Jr., H. W., Manasse, M. S., Pollard, J. M.: The factorization of the ninth Fermat number. Math. Comp. 61 (1993) 319–349
    Article MATH MathSciNet Google Scholar
  10. Lenstra, A.K., Manasse, M.S.: Factoring by electronic mail. Advances in Cryptology, Eurocrypt’ 89, Lecture Notes in Comput. Sci. 434 (1990) 355–371
    Google Scholar
  11. Lenstra, A. K., Manasse, M. S.: Factoring with two large primes. Math. Comp. (to appear); extended abstract in: Advances in Cryptology, Eurocrypt’ 90, Lecture Notes in Comput. Sci. 473 (1991) 72–82
    Google Scholar
  12. Pomerance, C: The quadratic sieve factoring algorithm. Lecture Notes in Comput. Sci. 209 (1985) 169–182
    Google Scholar
  13. Pomerance, C., Smith, J. W.: Reduction of huge, sparse matrices over finite fields via created catastrophes. Experiment. Math. 1 (1992) 89–94
    MATH MathSciNet Google Scholar
  14. RSA Data Security Corporation Inc., sci.crypt, May 18, 1991; information available by sending electronic mail to challenge-rsa-list@rsa.coia
    Google Scholar

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Authors and Affiliations

  1. Lehrstuhl Prof. Buchmann, Fachbereich Informatik, Uníversität des Saarlandes, Postfach 1150, 66041, Saarbrücken, Germany
    T. Denny
  2. Department of Mathematics, Lehigh University, Bethlehem, PA, 18015-3174, USA
    B. Dodson
  3. MRE-2Q334, Bellcore, 445 South Street, Morristown, NJ, 07960, USA
    A. K. Lenstra
  4. DEC SRC, 130 Lytton Avenue, Palo Alto, CA, 94301, USA
    M. S. Manasse

Authors

  1. T. Denny
  2. B. Dodson
  3. A. K. Lenstra
  4. M. S. Manasse

Editor information

Editors and Affiliations

  1. Computer Science and Engineering Department and Center for Communication and Information Science, University of Nebraska, 68588-01115, Lincoln, NE, USA
    Douglas R. Stinson

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© 1994 Springer-Verlag Berlin Heidelberg

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Denny, T., Dodson, B., Lenstra, A.K., Manasse, M.S. (1994). On the factorization of RSA-120. In: Stinson, D.R. (eds) Advances in Cryptology — CRYPTO’ 93. CRYPTO 1993. Lecture Notes in Computer Science, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48329-2\_15

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