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International Workshop on Distributed Algorithms

WDAG 1994: Distributed Algorithms pp 28–38Cite as

Factoring

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 857))

Abstract

A brief survey of general purpose integer factoring algorithms and their implementations.

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References

  1. L. M. Adleman, Factoring numbers using singular integers, proc 23rd Annual ACM Symposium on Theory of Computing (STOC) (1991) 64–71

    Google Scholar 

  2. W. R. Alford, C. Pomerance, Implementing the self initializing quadratic sieve on a distributed network, manuscript, 1994

    Google Scholar 

  3. D. Atkins, M. Graff, A. K. Lenstra, P. C. Leyland, THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE (in preparation)

    Google Scholar 

  4. D. J. Bernstein, A. K. Lenstra, A general number field sieve implementation, 103–126 in: [26]

    Google Scholar 

  5. R. P. Brent, Factorization of the eleventh Fermat number (preliminary report), Abstracts Amer. Math. Soc. 10 (1989) 73

    Google Scholar 

  6. R. P. Brent, Parallel algorithms for integer factorisation, pp. 26–37 in: J. H. Loxton (ed.), Number theory and cryptography, London Math. Soc. Lecture Note Series 154, Cambridge University Press, Cambridge, 1990

    Google Scholar 

  7. R. P. Brent, J. M. Pollard, Factorization of the eighth Fermat number, Math. Comp. 36 (1981) 627–630

    Google Scholar 

  8. J. Buchmann, J. Loho, J. Zayer, An implementation of the general number field sieve, Advances in Cryptology, Crypto '93, Lecture Notes in Comput. Sci. 773 (1994) 159–165.

    Google Scholar 

  9. T. R. Caron, R. D. Silverman, Parallel implementation of the quadratic sieve, The Journal of Supercomputing 1 (1988) 273–290

    Article  Google Scholar 

  10. S. Coppersmith, Solving linear equations over GF(2): block Lanczos algorithm, Linear algebras and its applications 192 (1993) 33–60

    Article  Google Scholar 

  11. S. Coppersmith, Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm, Math. Comp. 62 (1994) 333–350

    Google Scholar 

  12. J. A. Davis, D. B. Holdridge, Factorization using the quadratic sieve algorithm, Tech. Report SAND 83-1346, Sandia National Laboratories, Albuquerque, NM, 1983

    Google Scholar 

  13. T. Denny, B. Dodson, A. K. Lenstra, M. S. Manasse, On the factorization of RSA-120, Advances in Cryptology, Crypto '93, Lecture Notes in Comput. Sci. 773 (1994) 166–174

    Google Scholar 

  14. A. Díaz, M. Hitz, E. Kaltofen, A. Lobo, T. Valente, Process scheduling in DCS and the large sparse linear systems challenge, J. Symbolic Computation (submitted)

    Google Scholar 

  15. B. Dixon, A. K. Lenstra, Factoring integers using SIMD sieves, Advances in Cryptology, Eurocrypt '93, Lecture Notes in Comput. Sci. 765 (1994) 28–39

    Google Scholar 

  16. J. D. Dixon, Asymptotically fast factorization of integers, Math. Comp. 36 (1981) 255–260

    Google Scholar 

  17. B. Dodson, A. K. Lenstra, NFS with four large primes: an explosive experiment (in preparation)

    Google Scholar 

  18. M. Gardner, Mathematical games, A new kind of cipher that would take millions of years to break, Scientific American, August 1977, 120–124

    Google Scholar 

  19. J. L. Gerver, Factoring large numbers with a quadratic sieve, Math. Comp. 36 (1983) 287–294

    Google Scholar 

  20. R. Golliver, A. K. Lenstra, K. S. McCurley, Lattice sieving and trial division, Algorithmic number theory symposium, proceedings, Cornell, 1994 (to appear)

    Google Scholar 

  21. R. K. Guy, How to factor a number, Proc. Fifth Manitoba Conf. Numer. Math., Congressus Numerantium 16 (1976) 49–89

    Google Scholar 

  22. G. H. Hardy, E. M. Wright, An introduction to the theory of numbers, Oxford Univ. Press, Oxford, 5th ed., 1979

    Google Scholar 

  23. E. Kaltofen, Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems, Math. Comp. (to appear)

    Google Scholar 

  24. B. A. LaMacchia, A. M. Odlyzko, Computation of discrete logarithms in prime fields, Designs, Codes and Cryptography 1 (1991) 47–62

    Google Scholar 

  25. A. K. Lenstra, H. W. Lenstra, Jr., Algorithms in number theory, Chapter 12 in: J. van Leeuwen (ed.), Handbook of theoretical computer science, Volume A, Algorithms and complexity, Elsevier, Amsterdam, 1990

    Google Scholar 

  26. A. K. Lenstra, H. W. Lenstra, Jr. (eds), The development of the number field sieve, Lecture Notes in Math. 1554, Springer-Verlag, Berlin, 1993

    Google Scholar 

  27. A. K. Lenstra, H. W. Lenstra, Jr., M. S. Manasse, J. M. Pollard, The number field sieve, 11–42 in: [26]

    Google Scholar 

  28. A. K. Lenstra, H. W. Lenstra, Jr., M. S. Manasse, J. M. Pollard, The factorization of the ninth Fermat number, Math. Comp. 61 (1993) 319–349

    Google Scholar 

  29. A. K. Lenstra, M. S. Manasse, Factoring by electronic mail, Advances in Cryptology, Eurocrypt '89, Lecture Notes in Comput. Sci. 434 (1990) 355–371

    Google Scholar 

  30. A. K. Lenstra, M. S. Manasse, Factoring with two large primes, Advances in Cryptology, Eurocrypt '90, Lecture Notes in Comput. Sci., 473 (1990) 72–82; Math. Comp. (to appear)

    Google Scholar 

  31. H. W. Lenstra, Jr., Factoring integers with elliptic curves, Ann. of Math. 126 (1987) 649–673

    Google Scholar 

  32. H. W. Lenstra, Jr., C. Pomerance, A rigorous time bound for factoring integers, J. Amer. Math. Soc. 5 (1992) 483–516

    Google Scholar 

  33. H. W. Lenstra, Jr., R. Tijdeman (eds), Computational methods in number theory, Math. Centre Tracts 154/155, Mathematisch Centrum, Amsterdam, 1984

    Google Scholar 

  34. E. Messmer, Bellcore leads team effort to crack RSA encryption code, Network World, May 2, 1994

    Google Scholar 

  35. P. L. Montgomery, Record number field sieve factorizations, announcement on NmbrThry@VM1.NODAK.EDU, July 12, 1994

    Google Scholar 

  36. P. L. Montgomery, A block Lanczos algorithm for finding dependencies over GF(2), Draft manuscript, June 17, 1994

    Google Scholar 

  37. M. A. Morrison, J. Brillhart, A method of factoring and the factorization of F 7, Math. Comp. 29 (1975) 183–205

    Google Scholar 

  38. R. Peralta, A quadratic sieve on the n-dimensional hypercube, Advances in Cryptology, Crypto '92, Lecture Notes in Comput. Sci. 740 (1993) 324–332

    Google Scholar 

  39. J. M. Pollard, Theorems on factorization and primality testing, Proc. Cambr. Philos. Soc 76 (1974) 521–528

    Google Scholar 

  40. J. M. Pollard, A Monte Carlo method for factorization, BIT 15 (1975) 331–334

    Article  Google Scholar 

  41. J. M. Pollard, Factoring with cubic integers, 4–10 in [26]

    Google Scholar 

  42. C. Pomerance, Analysis and comparison of some integer factoring algorithms, pp. 89–139 in: [33]

    Google Scholar 

  43. C. Pomerance, J. W. Smith, Reduction of huge, sparse matrices over finite fields via created catastrophes, Experiment. Math. 1 (1992) 89–94

    MathSciNet  Google Scholar 

  44. C. Pomerance, J. W. Smith, R. Tuler, A pipe-line architecture for factoring large integers with the quadratic sieve algorithm, SIAM J. Comput. 17 (1988) 387–403

    Article  Google Scholar 

  45. R. L. Rivest, letter to Martin Gardner, 1977

    Google Scholar 

  46. R. L. Rivest, A. Shamir, L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Comm. ACM 21 (1978) 120–126

    Article  Google Scholar 

  47. R. J. Schoof, Quadratic fields and factorization, pp 235–286 in: [33]

    Google Scholar 

  48. R. C. Schroeppel, personal communication, May 1994

    Google Scholar 

  49. P. W. Shor, Algorithms for quantum computation: Discrete log and factoring, DIMACS Technical Report 94-37; to appear in Proc. 35th Symposium on Foundations of Computer Science, 1994

    Google Scholar 

  50. R. D. Silverman, The multiple polynomial quadratic sieve, Math. Comp. 48 (1987) 329–339

    Google Scholar 

  51. J. W. Smith, S. S. Wagstaff, Jr., An extended precision operand computer, Proc. 21st Southeast Region ACM Conf. (1983) 209–216

    Google Scholar 

  52. D. H. Wiedemann, Solving sparse linear equations over finite fields, IEEE Trans. Inform. Theory 32 (1986) 54–62

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Room MRE-2Q334, Bellcore, 445 South Street, 07960, Morristown, NJ, USA

    Arjen K. Lenstra

Authors
  1. Arjen K. Lenstra
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Editor information

Gerard Tel Paul Vitányi

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© 1994 Springer-Verlag Berlin Heidelberg

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Lenstra, A.K. (1994). Factoring. In: Tel, G., Vitányi, P. (eds) Distributed Algorithms. WDAG 1994. Lecture Notes in Computer Science, vol 857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020422

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  • DOI: https://doi.org/10.1007/BFb0020422

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58449-0

  • Online ISBN: 978-3-540-48799-9

  • eBook Packages: Springer Book Archive

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