Prime Numbers
Prime Numbers Prime Numbers
564 REFERENCES [Montgomery 1987] P. Montgomery. Speeding the Pollard and elliptic curve methods of factorization. Math. Comp., 48:243–264, 1987. [Montgomery 1992a] P. Montgomery. An FFT Extension of the Elliptic Curve Method of Factorization. PhD thesis, University of California, Los Angeles, 1992. [Montgomery 1992b] P. Montgomery. Evaluating recurrences of form Xm+n = f(Xm,Xn,Xm−n) via Lucas chains. Unpublished manuscript, 1992. [Montgomery 1994] P. Montgomery. Square roots of products of algebraic numbers. In W. Gautschi, editor, Mathematics of Computation 1943–1993, volume 48 of Proc. Sympos. Appl. Math., pages 567–571. Amer. Math. Soc., 1994. [Montgomery 1995] P. Montgomery. A block Lanczos algorithm for finding dependencies over GF (2). In Advances in Cryptology, Eurocrypt ’95, volume 921 of Lecture Notes in Computer Science, pages 106–120, 1995. [Montgomery and Silverman 1990] P. Montgomery and R. Silverman. An FFT extension to the P − 1 factoring algorithm. Math. Comp., 54:839–854, 1990. [Morain 1990] F. Morain. Courbes elliptiques et tests de primalité. PhD thesis, Université Claude Bernard-Lyon I, 1990. [Morain 1992] F. Morain. Building cyclic elliptic curves modulo large primes. Unpublished manuscript, 1992. [Morain 1995] F. Morain. Calcul du nombre de points sur une courbe elliptique dans un corps fini: aspects algorithmiques. J. Théor. Nombres Bordeaux, 7:255–282, 1995. Les Dix-huitèmes Journées Arithmétiques (Bordeaux, 1993). [Morain 1998] F. Morain. Primality proving using elliptic curves: an update. In [Buhler 1998], pages 111 –127. [Morain 2004] F. Morain. Implementing the asymptotically fast version of the elliptic curve primality proving algorithm. http://www.lix.polytechnique.fr/Labo/Francois.Morain. [Morrison and Brillhart 1975] M. Morrison and J. Brillhart. A method of factoring and the factorization of F7. Math. Comp., 29:183–205, 1975. Collection of articles dedicated to Derrick Henry Lehmer on the occasion of his seventieth birthday. [Müller 1998] V. Müller. Efficient algorithms for multiplication on elliptic curves. Proceedings of GI—Arbeitskonferenz Chipkarten, TU München, 1998. [Müller 2004] V. Müller. Publications Volker Müller, 2004. http://lecturer.ukdw.ac.id/vmueller/publications.php, 2004. [Murphy 1998] B. Murphy. Modelling the yield of number field sieve polynomials. In [Buhler 1998], pages 137–150. [Murphy 1999] B. Murphy. Polynomial selection for the number field sieve integer factorisation algorithm. PhD thesis, Australian National University, 1999.
REFERENCES 565 [Namba 1984] M. Namba. Geometry of Projective Algebraic Curves, volume 88 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, 1984. [Narkiewicz 1986] W. Narkiewicz. Classical Problems in Number Theory. PWN-Polish Scientific Publishers, 1986. [Nathanson 1996] M. Nathanson. Additive Number Theory: The Classical Bases, volume 164 of Graduate Texts in Mathematics. Springer–Verlag, 1996. [Nguyen 1998] P. Nguyen. A Montgomery-like square root for the number field sieve. In [Buhler 1998], pages 151–168. [Nguyen and Liu 1999] N. Nguyen and Q. Liu. The Regular Fourier Matrices and Nonuniform Fast Fourier Transforms. SIAM J. Sci. Comput., 21:283–293, 1999. [Nicely 2004] T. Nicely. Prime constellations research project, 2004. http://www.trnicely.net/counts.html. [Niederreiter 1992] H. Niederreiter. Random Number Generation and Quasi-Monte-Carlo Methods, volume 63 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, 1992. [Niven et al. 1991] I. Niven, H. Zuckerman, and H. Montgomery. An Introduction to the Theory of Numbers. Fifth edition. John Wiley and Sons, 1991. [Nussbaumer 1981] H. Nussbaumer. Fast Fourier Transform and Convolution Algorithms. Springer–Verlag, 1981. [Odlyzko 1985] A. Odlyzko. Discrete logarithms in finite fields and their cryptographic significance. In Advances in Cryptology, Proc. Eurocrypt ’84, volume 209 of Lecture Notes in Computer Science, pages 224–313. Springer–Verlag, 1985. [Odlyzko 1987] A. Odlyzko. On the distribution of spacings between zeros of the zeta function. Math. Comp., 48:273–308, 1987. [Odlyzko 1992] A. Odlyzko. The 10 20 -th zero of the Riemann zeta function and 175 million of its neighbors, 1992. http://www.research.att.com/˜amo. [Odlyzko 1994] A. Odlyzko. Analytic computations in number theory. In W. Gautschi, editor, Mathematics of Computation 1943–1993, volume 48 of Proc. Sympos. Appl. Math., pages 441–463. Amer. Math. Soc., 1994. [Odlyzko 2000] A. Odlyzko. Discrete logarithms: The past and the future. Designs, Codes, and Cryptography, 19:129–145, 2000. [Odlyzko 2005] A. Odlyzko. The zeros of the Riemann zeta function: the 10 22 -nd zero and 10 billion of its neighbors. In preparation. [Odlyzko and te Riele 1985] A. Odlyzko and H. te Riele. Disproof of the Mertens conjecture. J. Reine Angew. Math., 357:138–160, 1985. [Odlyzko and Schönhage 1988] A. Odlyzko and A. Schönhage. Fast algorithms for multiple evaluations of the Riemann zeta-function. Trans. Amer. Math. Soc., 309:797–809, 1988.
- Page 522 and 523: 9.6 Polynomial arithmetic 513 where
- Page 524 and 525: 9.6 Polynomial arithmetic 515 such
- Page 526 and 527: 9.6 Polynomial arithmetic 517 Note
- Page 528 and 529: 9.7 Exercises 519 (3) Write out com
- Page 530 and 531: 9.7 Exercises 521 where “do” si
- Page 532 and 533: 9.7 Exercises 523 9.23. How general
- Page 534 and 535: 9.7 Exercises 525 two (and thus, me
- Page 536 and 537: 9.7 Exercises 527 0 2 +3 2 +0 2 is
- Page 538 and 539: 9.7 Exercises 529 9.49. In the FFT
- Page 540 and 541: 9.7 Exercises 531 adjustment step.
- Page 542 and 543: 9.7 Exercises 533 9.69. Implement A
- Page 544 and 545: 9.8 Research problems 535 less than
- Page 546 and 547: 9.8 Research problems 537 1.66), na
- Page 548 and 549: 9.8 Research problems 539 9.82. A c
- Page 550 and 551: 542 Appendix BOOK PSEUDOCODE Becaus
- Page 552 and 553: 544 Appendix BOOK PSEUDOCODE } ...;
- Page 554 and 555: 546 Appendix BOOK PSEUDOCODE Functi
- Page 556 and 557: 548 REFERENCES [Apostol 1986] T. Ap
- Page 558 and 559: 550 REFERENCES [Bernstein 2004b] D.
- Page 560 and 561: 552 REFERENCES [Buchmann et al. 199
- Page 562 and 563: 554 REFERENCES [Crandall 1997b] R.
- Page 564 and 565: 556 REFERENCES [Dudon 1987] J. Dudo
- Page 566 and 567: 558 REFERENCES [Goldwasser and Kili
- Page 568 and 569: 560 REFERENCES [Joe 1999] S. Joe. A
- Page 570 and 571: 562 REFERENCES [Lenstra 1981] H. Le
- Page 574 and 575: 566 REFERENCES [Oesterlé 1985] J.
- Page 576 and 577: 568 REFERENCES [Pomerance et al. 19
- Page 578 and 579: 570 REFERENCES [Schönhage and Stra
- Page 580 and 581: 572 REFERENCES [Sun and Sun 1992] Z
- Page 582 and 583: 574 REFERENCES [Weisstein 2005] E.
- Page 584 and 585: Index ABC conjecture, 417, 434 abel
- Page 586 and 587: INDEX 579 Catalan problem, ix, 415,
- Page 588 and 589: INDEX 581 discrete arithmetic-geome
- Page 590 and 591: INDEX 583 complex-field, 477 Cooley
- Page 592 and 593: INDEX 585 Hajratwala, N., 23 Halber
- Page 594 and 595: INDEX 587 Lehmer, D., 149, 152, 155
- Page 596 and 597: INDEX 589 432, 447-450, 453, 458, 5
- Page 598 and 599: INDEX 591 Preneel, B. (with De Win
- Page 600 and 601: INDEX 593 Salomaa, A. (with Paun et
- Page 602 and 603: INDEX 595 te Riele, H. (with van de
- Page 604: INDEX 597 Yagle, A., 259, 499, 539
564 REFERENCES<br />
[Montgomery 1987] P. Montgomery. Speeding the Pollard and elliptic curve<br />
methods of factorization. Math. Comp., 48:243–264, 1987.<br />
[Montgomery 1992a] P. Montgomery. An FFT Extension of the Elliptic Curve<br />
Method of Factorization. PhD thesis, University of California, Los<br />
Angeles, 1992.<br />
[Montgomery 1992b] P. Montgomery. Evaluating recurrences of form<br />
Xm+n = f(Xm,Xn,Xm−n) via Lucas chains. Unpublished manuscript,<br />
1992.<br />
[Montgomery 1994] P. Montgomery. Square roots of products of algebraic<br />
numbers. In W. Gautschi, editor, Mathematics of Computation<br />
1943–1993, volume 48 of Proc. Sympos. Appl. Math., pages 567–571.<br />
Amer. Math. Soc., 1994.<br />
[Montgomery 1995] P. Montgomery. A block Lanczos algorithm for finding<br />
dependencies over GF (2). In Advances in Cryptology, Eurocrypt ’95,<br />
volume 921 of Lecture Notes in Computer Science, pages 106–120, 1995.<br />
[Montgomery and Silverman 1990] P. Montgomery and R. Silverman. An FFT<br />
extension to the P − 1 factoring algorithm. Math. Comp., 54:839–854,<br />
1990.<br />
[Morain 1990] F. Morain. Courbes elliptiques et tests de primalité. PhD thesis,<br />
Université Claude Bernard-Lyon I, 1990.<br />
[Morain 1992] F. Morain. Building cyclic elliptic curves modulo large primes.<br />
Unpublished manuscript, 1992.<br />
[Morain 1995] F. Morain. Calcul du nombre de points sur une courbe elliptique<br />
dans un corps fini: aspects algorithmiques. J. Théor. Nombres Bordeaux,<br />
7:255–282, 1995. Les Dix-huitèmes Journées Arithmétiques (Bordeaux,<br />
1993).<br />
[Morain 1998] F. Morain. Primality proving using elliptic curves: an update. In<br />
[Buhler 1998], pages 111 –127.<br />
[Morain 2004] F. Morain. Implementing the asymptotically fast version of the<br />
elliptic curve primality proving algorithm.<br />
http://www.lix.polytechnique.fr/Labo/Francois.Morain.<br />
[Morrison and Brillhart 1975] M. Morrison and J. Brillhart. A method of factoring<br />
and the factorization of F7. Math. Comp., 29:183–205, 1975. Collection of<br />
articles dedicated to Derrick Henry Lehmer on the occasion of his<br />
seventieth birthday.<br />
[Müller 1998] V. Müller. Efficient algorithms for multiplication on elliptic curves.<br />
Proceedings of GI—Arbeitskonferenz Chipkarten, TU München, 1998.<br />
[Müller 2004] V. Müller. Publications Volker Müller, 2004.<br />
http://lecturer.ukdw.ac.id/vmueller/publications.php, 2004.<br />
[Murphy 1998] B. Murphy. Modelling the yield of number field sieve polynomials.<br />
In [Buhler 1998], pages 137–150.<br />
[Murphy 1999] B. Murphy. Polynomial selection for the number field sieve integer<br />
factorisation algorithm. PhD thesis, Australian National University, 1999.
Change language