Book Review
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MathSciNet review:
1567658
Full text of review:
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Book Information:
Author:
Hans Riesel
Title:
Prime numbers and computer methods for factorization
Additional book information:
Progress in Mathematics, vol. 57, Birkhäuser, Boston, Basel and Stuttgart, 1985, xvi + 464 pp., $44.95. ISBN 0-8176-3291-3.
Leonard M. Adleman, Carl Pomerance, and Robert S. Rumely, On distinguishing prime numbers from composite numbers, Ann. of Math. (2) 117 (1983), no. 1, 173–206. MR 683806, DOI 10.2307/2006975
H. Cohen and A. K. Lenstra, Implementation of a new primality test, Math. Comp. 48 (1987), no. 177, 103–121, S1–S4. MR 866102, DOI 10.1090/S0025-5718-1987-0866102-2
3. S. Goldwasser and J. Kilian, Almost all primes can be quickly certified, Proc. 18th Annual ACM Symp. on Theory of Computing (1986), 316-329.
4. J. C. Lagarias and A. M. Odlyzko, Computing π(x): an analytic method, J. Algorithms 8 (1987), 173-191.
5. J. C. Lagarias, V. S. Miller and A. M. Odlyzko, Computing π(x): the Meissel-Lehmer method, Math. Comp. 44 (1985), 537-560.
D. H. Lehmer, Strong Carmichael numbers, J. Austral. Math. Soc. Ser. A 21 (1976), no. 4, 508–510. MR 417032, DOI 10.1017/s1446788700019364
7. A. K. Lenstra and H. W. Lenstra, Jr., Algorithms in number theory, Handbook of Theoretical Computer Science (to appear).
8. H. W. Lenstra, Jr., Factoring integers with elliptic curves, Ann. of Math. (to appear).
J. M. Pollard, Theorems on factorization and primality testing, Proc. Cambridge Philos. Soc. 76 (1974), 521–528. MR 354514, DOI 10.1017/s0305004100049252
C. Pomerance, Analysis and comparison of some integer factoring algorithms, Computational methods in number theory, Part I, Math. Centre Tracts, vol. 154, Math. Centrum, Amsterdam, 1982, pp. 89–139. MR 700260
Carl Pomerance, The quadratic sieve factoring algorithm, Advances in cryptology (Paris, 1984) Lecture Notes in Comput. Sci., vol. 209, Springer, Berlin, 1985, pp. 169–182. MR 825590, DOI 10.1007/3-540-39757-4_{1}7
Carl Pomerance, Fast, rigorous factorization and discrete logarithm algorithms, Discrete algorithms and complexity (Kyoto, 1986) Perspect. Comput., vol. 15, Academic Press, Boston, MA, 1987, pp. 119–143. MR 910929
Michael O. Rabin, Probabilistic algorithm for testing primality, J. Number Theory 12 (1980), no. 1, 128–138. MR 566880, DOI 10.1016/0022-314X(80)90084-0
J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64–94. MR 137689
René Schoof, Elliptic curves over finite fields and the computation of square roots mod $p$, Math. Comp. 44 (1985), no. 170, 483–494. MR 777280, DOI 10.1090/S0025-5718-1985-0777280-6
R. Solovay and V. Strassen, A fast Monte-Carlo test for primality, SIAM J. Comput. 6 (1977), no. 1, 84–85. MR 429721, DOI 10.1137/0206006
Volker Strassen, Einige Resultate über Berechnungskomplexität, Jber. Deutsch. Math.-Verein. 78 (1976/77), no. 1, 1–8. MR 438807
- 1.
- L. M. Adleman, C. Pomerance and R. S. Rumely, On distinguishing prime numbers from composite numbers, Ann. of Math. 117 (1983), 173-206. MR 0683806
- 2.
- H. Cohen and A. K. Lenstra, Implementation of a new primality test, Math. Comp. 48 (1987), 103-121. MR 866102
- 3.
- S. Goldwasser and J. Kilian, Almost all primes can be quickly certified, Proc. 18th Annual ACM Symp. on Theory of Computing (1986), 316-329.
- 4.
- J. C. Lagarias and A. M. Odlyzko, Computing π(x): an analytic method, J. Algorithms 8 (1987), 173-191.
- 5.
- J. C. Lagarias, V. S. Miller and A. M. Odlyzko, Computing π(x): the Meissel-Lehmer method, Math. Comp. 44 (1985), 537-560.
- 6.
- D. H. Lehmer, Strong Carmichael numbers, J. Austral. Math. Soc. Ser. A 21 (1976), 508-510. MR 417032
- 7.
- A. K. Lenstra and H. W. Lenstra, Jr., Algorithms in number theory, Handbook of Theoretical Computer Science (to appear).
- 8.
- H. W. Lenstra, Jr., Factoring integers with elliptic curves, Ann. of Math. (to appear).
- 9.
- J. M. Pollard, Theorems on factorization and primality testing, Proc. Cambridge Philos. Soc. 76 (1974), 521-528. MR 354514
- 10.
- C. Pomerance, Analysis and comparison of some integer factoring algorithms, Computational Methods in Number Theory (H. W. Lenstra, Jr. and R. Tijdeman, eds. ), Math. Centre Tracts 154/155, Mathematisch Centrum, Amsterdam, 1982, pp. 89-139. MR 700260
- 11.
- C. Pomerance, The quadratic sieve factoring algorithm, Advances in Cryptology (T. Beth, N. Cot and I. Ingemarsson, eds. ), Springer Lecture Notes in Computer Science 209 (1985), 169-182. MR 825590
- 12.
- C. Pomerance, Fast, rigorous factorization and discrete logarithm algorithms, Discrete Algorithms and Complexity (D. S. Johnson, T. Nishizeki, A. Nozaki and H. S. Wilf, eds. ), Academic Press, Orlando, Florida, 1987, pp. 119-143. MR 910929
- 13.
- M. O. Rabin, Probabilistic algorithms for testing primality, J. Number Theory 12 (1980), 128-138. MR 566880
- 14.
- J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94. MR 137689
- 15.
- R. J. Schoof, Elliptic curves over finite fields and the computation of square roots mod p, Math. Comp. 44 (1985), 483-494. MR 777280
- 16.
- R. Solovay and V. Strassen, A fast Monte-Carlo test for primality, SIAM J. Comput. 6 (1977), 84-85; erratum, ibid. 7 (1978), 118. MR 429721
- 17.
- V. Strassen, Einige Resultate über Berechnungskomplexität, Jahresber. Deutsch. Math.-Verein 78 (1976/77), 1-8. MR 438807
Review Information:
Reviewer:
Carl Pomerance
Journal:
Bull. Amer. Math. Soc.
18 (1988), 61-65
DOI:
https://doi.org/10.1090/S0273-0979-1988-15599-1