A montgomery-like square root for the number field sieve

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1423, Issue , 1998, Pages 151-168

  Nguyen, Phong ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

NUMBER THEORY;

ALGEBRAIC NUMBERS; LAST STAGE; MONTGOMERY; NUMBER FIELD SIEVE; ORIGINAL ALGORITHMS; SQUARE ROOTS; WORLD RECORDS;

SIEVES;

EID: 84947781715     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0054859     Document Type: Conference Paper

References (18)

1. BATUT, C., BERNARDI, D., COHEN, H., AND OLIVIER, M. Pari-gp computer package. Can be obtained by ftp at megrez.math.u-bordeaux.fr.
2. BUCHMANN, J.A., AND LENSTRA, JR., H. W. Approximating rings of integers in number fields. J. Théor. Nombres Bordeaux 6, 2 (1994), 221-260.
3. BUHLER, J.P., LENSTRA, H.W., AND POMERANCE, C. Factoring integers with the number field sieve, pages 50-94 in [8].
4. COHEN, H. A course in computational algebraic number theory. Springer, 1993.
5. COUVEIGNES, J.-M. Computing a square root for the number field sieve, pages 95-102 in [8].
6. COWIE, J., DODSON, B., ELKENBRACHT-HUIZING, R.M., LENSTRA, A.K., MONTGOMERY, P.L., AND ZAYER, J. A world wide number field sieve factoring record: On to 512 bits. In Proceedings of ASIACRYPT’96 (1996), vol. 1163 of Lecture Notes in Computer Science, Springer-Verlag, pp. 382-394.
7. ELKENBRACHT-HUIZING, M. An implementation of the number field sieve. Experimental Mathematics 5, 3 (1996), 231-253.
8. LENSTRA, A.K., AND LENSTRA, JR., H. W. The development of the Number Field Sieve, vol. 1554 of Lecture Notes in Mathematics. Springer-Verlag, 1993.
9. LENSTRA, A.K., LENSTRA, JR., H.W., AND LOVÄSZ, L. Factoring polynomials with rational coefficients. Math. Ann. 261 (1982), 515-534.
10. LENSTRA, A.K., LENSTRA, JR., H.W., MANASSE, M.S., AND POLLARD, J. M. The number field sieve, pages 11-42 in [8].
11. LENSTRA, A.K., LENSTRA, JR., H.W., MANASSE, M.S., AND POLLARD, J. M. The factorization of the ninth fermat number. Math. Comp. 61 (1993), 319-349.
12. LENSTRA, JR., H. W. Factoring integers with elliptic curves. Ann. of Math. 126 (1987), 649-673.
13. LENSTRA, JR., H. W. Algorithms in algebraic number theory. Bull. Amer. Math. Soc. 26 (1992), 211-244.
14. MONTGOMERY, P. L. Square roots of products of algebraic numbers. Draft of June, 1995. Available at ftp://ftp.cwi.nl/pub/pmontgom/sqrt.ps.gz.
15. MONTGOMERY, P. L. Square roots of products of algebraic numbers. In Mathematics of Computation 1943-1993: a Half-Century of Computational Mathematics (1994), W. Gautschi, Ed., Proceedings of Symposia in Applied Mathematics, American Mathematical Society, pp. 567-571.
16. POHST, M., AND ZASSENHAUS, H. Algorithmic algebraic number theory. Cambridge University Press, 1989.
17. POLLARD, J. M. Factoring with cubic integers, pages 4-11 in [8].
18. REEVES, C. R. Modem Heuristic Techniques for Combinatorial Problems. Blackwell Scientific Publications, 1993.