Abstract
We describe a possible improvement to the Number Field Sieve. In theory we can reduce the time for the sieve stage by a factor comparable with log(B 1). In the real world, where much factoring takes place, the advantage will be less. We used the method to repeat the factorisation of F 7 on an 8-bit computer (yet again!).
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References
A. K. Lenstra, H. W. Lenstra, Jr., M. S. Manasse, J. M. Pollard, The number field sieve, this volume, pp. 11–42; extended abstract: Proc. 22nd Annual ACM Symp. on Theory of Computing (STOC), Baltimore, May 14–16, 1990, 564–572.
A. K. Lenstra, H. W. Lenstra, Jr., M. S. Manasse, J. M. Pollard, The factorization of the ninth Fermat number, Math. Comp. 61 (1993), to appear.
J. M. Pollard, Factoring with cubic integers, unpublished manuscript, 1988; this volume, pp. 4–10.
C. Pomerance, Factoring, pp. 27–47 in: C. Pomerance (ed.), Cryptology and computational number theory, Proc. Sympos. Appl. Math. 42, Amer. Math. Soc., Providence, 1990.
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© 1993 Springer-Verlag
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Pollard, J.M. (1993). The lattice sieve. In: Lenstra, A.K., Lenstra, H.W. (eds) The development of the number field sieve. Lecture Notes in Mathematics, vol 1554. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091538
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DOI: https://doi.org/10.1007/BFb0091538
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