A tale of two sieves
Pokroky matematiky, fyziky a astronomie (1998)
- Volume: 43, Issue: 1, page 9-29
- ISSN: 0032-2423
Access Full Article
topHow to cite
topPomerance, Carl. "Vyprávění o dvou sítech." Pokroky matematiky, fyziky a astronomie 43.1 (1998): 9-29. <http://eudml.org/doc/36134>.
@article{Pomerance1998,
author = {Pomerance, Carl},
journal = {Pokroky matematiky, fyziky a astronomie},
keywords = {quadratic sieve; number field sieve; factorization; complexity; algorithm; continued fraction},
language = {cze},
number = {1},
pages = {9-29},
publisher = {Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists},
title = {Vyprávění o dvou sítech},
url = {http://eudml.org/doc/36134},
volume = {43},
year = {1998},
}
TY - JOUR
AU - Pomerance, Carl
TI - Vyprávění o dvou sítech
JO - Pokroky matematiky, fyziky a astronomie
PY - 1998
PB - Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists
VL - 43
IS - 1
SP - 9
EP - 29
LA - cze
KW - quadratic sieve; number field sieve; factorization; complexity; algorithm; continued fraction
UR - http://eudml.org/doc/36134
ER -
References
top- Adleman, L. M., Factoring numbers using singular integers, Proc. 23rd Annual ACM Sympos. Theory of Computing (STOC) 1991, 64–71. (1991)
- Alford, W. R., Pomerance, C., Implementing the self initializing quadratic sieve on a distributed network, In: Number Theoretic and Algebraic Methods in Computer Science, Proc. Internat. Moscow Conf., June–July 1993 (A. J. van der Poorten, I. Shparlinski, H. G. Zimmer, eds.), World Scientific 1995, 163–174. (1993) Zbl0939.11038MR1377748
- Brillhart, J., Lehmer, D. H., Selfridge, J. L., Tuckerman, B., Jr., S. S. Wagstaff, Factorizations of , , up to high powers, second ed., vol. 22, Contemp. Math., Amer. Math. Soc., Providence, RI 1988. (1988) MR0996414
- Canfield, E. R., Erdős, P., Pomerance, C., On a problem of Oppenheim concerning “Factorisatio Numerorum”, J. Number Theory 17 (1983), 1–28. (1983) Zbl0513.10043MR0712964
- Coppersmith, D., Modifications to the number field sieve, J. Cryptology 6 (1993), 169–180. (1993) Zbl0806.11071MR1233462
- Coppersmith, D., Odlyzko, A. M., Schroeppel, R., Discrete logarithms in , Algorithmica 1 (1986), 1–15. (1986) Zbl0631.12010MR0833115
- Cowie, J., Dodson, B., Elkenbracht-Huizing, R. Marije, Lenstra, A. K., Montgomery, P. L., Zayer, J., A world wide number field sieve factoring record: On to bits, Advances in Cryptology – Asiacrypt ’96, to appear. Zbl1028.11500
- Elkenbracht-Huizing, M., A multiple polynomial general number field sieve, In: Algorithmic Number Theory, Second Internat. Sympos., ANTS-II, to appear. Zbl0899.11060MR1446502
- Gerver, J., Factoring large numbers with a quadratic sieve, Math. Comp. 41 (1983), 287–294. (1983) Zbl0527.10003MR0701639
- Lenstra, A. K., Integer factoring, Preprint. Zbl0964.11057MR1758972
- Lenstra, A. K., Lenstra, H. W., Jr., The development of the number field sieve, Lecture Notes in Math., vol. 1554, Springer-Verlag, Berlin, Heidelberg 1993. (1554) Zbl0777.00017MR1321216
- Lenstra, A. K., Manasse, M. S., Factoring by electronic mail, In: Advances in Cryptology – Eurocrypt ’89 (J.-J. Quisquater, J. Vandewalle, eds.), Springer-Verlag, Berlin, Heidelberg 1990, 355–371. (1990) MR1083962
- Jr., H. W. Lenstra, Elliptic curves and number theoretic algorithms, In: Proc. Internat. Congr. Math., Berkeley, CA, 1986, vol. 1 (A. M. Gleason, ed.), Amer. Math. Soc., Providence, RI 1987, 99–120. (1986) MR0934218
- Montgomery, P. L., A block Lanczos algorithm for finding dependencies over , In: Advances in Cryptology – Eurocrypt ’95 (L. C. Guillou, J.-J. Quisquater, eds.), Springer-Verlag, Berlin, Heidelberg 1995, 106–120. (1995) Zbl0973.11520MR1367513
- Montgomery, P. L., Square roots of products of algebraic integers, In: Mathematics of Computation 1943-1993, Fifty Years of Computational Mathematics (W. Gautschi, ed.), Proc. Sympos. Appl. Math., vol. 48, Amer. Math. Soc., Providence, RI 1994, 567–571. (1943) MR1314892
- Morrison, M. A., Brillhart, J., A method of factorization and the factorization of , Math. Comp. 29 (1975), 183–205. (1975) Zbl0302.10010MR0371800
- Odlyzko, A. M., The future of integer factorization, CryptoBytes (The technical newsletter of RSA Laboratories), 1 (1995) 2, 5–12. (1995)
- Pomerance, C., Cryptology and computational number theory, Proc. Sympos. Appl. Math., vol. 42, Amer. Math. Soc., Providence, RI 1990. (1990) Zbl0734.11072MR1095547
- Pomerance, C., The number field sieve, In: Mathematics of Computation 1943-1993, Fifty Years of Computational Mathematics (W. Gautschi, ed.), Proc. Sympos. Appl. Math., vol. 48, Amer. Math. Soc., Providence, RI 1994, 465–480. (1943) Zbl0821.11064MR1314884
- Pomerance, C., On the role of smooth numbers in number theoretic algorithms, In: Proc. Internat. Congr. Math., Zurich, Switzerland, 1994, vol. 1 (S. D. Chatterji, ed.), Birkhauser-Verlag, Basel 1995, 411–422. (1994) Zbl0854.11047MR1403941
- Pomerance, C., Smith, J. W., Tuler, R., A pipeline architecture for factoring large integers with the quadratic sieve algorithm, SIAM J. Comput. 17 (1988), 387–403. (1988) Zbl0644.10002MR0935347
- Schirokauer, O., Weber, D., Denny, T., Discrete logarithms: The effectiveness of the index calculus method, Algorithmic Number Theory, Second Internat. Sympos., ANTS-II, to appear. Zbl0895.11054MR1446523
- Williams, H. C., Shallit, J. O., Factoring integers before computers, In: Mathematics of Computation 1943–1993, Fifty Years of Computational Mathematics (W. Gautschi, ed.), Proc. Sympos. Appl. Math. 48, Amer. Math. Soc., Providence, RI 1994, 481–531. (1943) Zbl0847.11002MR1314885
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.