| Title:
|
Vyprávění o dvou sítech (Czech) |
| Title:
|
A tale of two sieves (English) |
| Author:
|
Pomerance, Carl |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
9-29 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11Y05 |
| MSC:
|
11Y16 |
| MSC:
|
11Y65 |
| idZBL:
|
Zbl 1042.11528 |
| Note:
|
Z Notices Amer. Math. Soc. 43 (1996), 1473-1485. přeložili J. Chleboun, M. Křížek a K. Segeth. (Czech) |
| Note:
|
From Notices Amer. Math. Soc. 43 (1996), 1473-1485, translated by J. Chleboun, M. Křížek and K. Segeth. (English) |
| . |
| Date available:
|
2010-12-11T15:56:52Z |
| Last updated:
|
2012-08-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/138468 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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[4] Canfield, E. R., Erdős, P., Pomerance, C.: On a problem of Oppenheim concerning “Factorisatio Numerorum”.J. Number Theory 17 (1983), 1–28. MR 0712964 |
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[6] Coppersmith, D., Odlyzko, A. M., Schroeppel, R.: Discrete logarithms in $GF(p)$.Algorithmica 1 (1986), 1–15. MR 0833115 |
| Reference:
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[7] 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 $512$ bits.Advances in Cryptology – Asiacrypt ’96, to appear. |
| Reference:
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[8] Elkenbracht-Huizing, M.: A multiple polynomial general number field sieve.In: Algorithmic Number Theory, Second Internat. Sympos., ANTS-II, to appear. Zbl 0899.11060, MR 1446502 |
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[9] Gerver, J.: Factoring large numbers with a quadratic sieve.Math. Comp. 41 (1983), 287–294. Zbl 0527.10003, MR 0701639 |
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[10] Lenstra, A. K.: Integer factoring.Preprint. Zbl 0964.11057, MR 1758972 |
| Reference:
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[11] 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. MR 1321216 |
| Reference:
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[12] 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. MR 1083962 |
| Reference:
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[13] 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. MR 0934218 |
| Reference:
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[14] Montgomery, P. L.: A block Lanczos algorithm for finding dependencies over $GF(2)$.In: Advances in Cryptology – Eurocrypt ’95 (L. C. Guillou, J.-J. Quisquater, eds.), Springer-Verlag, Berlin, Heidelberg 1995, 106–120. Zbl 0973.11520, MR 1367513 |
| Reference:
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[15] 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. MR 1314892 |
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[16] Morrison, M. A., Brillhart, J.: A method of factorization and the factorization of $F_7$.Math. Comp. 29 (1975), 183–205. MR 0371800 |
| Reference:
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[17] Odlyzko, A. M.: The future of integer factorization.CryptoBytes (The technical newsletter of RSA Laboratories), 1 (1995) 2, 5–12. |
| Reference:
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[18] Pomerance, C.: Cryptology and computational number theory.Proc. Sympos. Appl. Math., vol. 42, Amer. Math. Soc., Providence, RI 1990. Zbl 0734.11072, MR 1095547 |
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[19] 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. MR 1314884 |
| Reference:
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[20] 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. MR 1403941 |
| Reference:
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[21] 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. Zbl 0644.10002, MR 0935347 |
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[22] 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. Zbl 0895.11054, MR 1446523 |
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[23] 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. MR 1314885 |
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