[1] Adleman, L. M.: Factoring numbers using singular integers. Proc. 23rd Annual ACM Sympos. Theory of Computing (STOC) 1991, 64–71.
[2] 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.
MR 1377748
[3] Brillhart, J., Lehmer, D. H., Selfridge, J. L., Tuckerman, B., Jr., S. S. Wagstaff:
Factorizations of $b^n\pm 1$, $b=2,3,5,6,7,10,11,12$, up to high powers. second ed., vol. 22, Contemp. Math., Amer. Math. Soc., Providence, RI 1988.
MR 0996414
[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
[5] Coppersmith, D.:
Modifications to the number field sieve. J. Cryptology 6 (1993), 169–180.
MR 1233462 |
Zbl 0806.11071
[6] Coppersmith, D., Odlyzko, A. M., Schroeppel, R.:
Discrete logarithms in $GF(p)$. Algorithmica 1 (1986), 1–15.
MR 0833115
[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.
[8] Elkenbracht-Huizing, M.:
A multiple polynomial general number field sieve. In: Algorithmic Number Theory, Second Internat. Sympos., ANTS-II, to appear.
MR 1446502 |
Zbl 0899.11060
[9] Gerver, J.:
Factoring large numbers with a quadratic sieve. Math. Comp. 41 (1983), 287–294.
MR 0701639 |
Zbl 0527.10003
[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
[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
[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
[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.
MR 1367513 |
Zbl 0973.11520
[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
[16] Morrison, M. A., Brillhart, J.:
A method of factorization and the factorization of $F_7$. Math. Comp. 29 (1975), 183–205.
MR 0371800
[17] Odlyzko, A. M.: The future of integer factorization. CryptoBytes (The technical newsletter of RSA Laboratories), 1 (1995) 2, 5–12.
[18] Pomerance, C.:
Cryptology and computational number theory. Proc. Sympos. Appl. Math., vol. 42, Amer. Math. Soc., Providence, RI 1990.
MR 1095547 |
Zbl 0734.11072
[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
[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
[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.
MR 0935347 |
Zbl 0644.10002
[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.
MR 1446523 |
Zbl 0895.11054
[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