-
1
-
-
84872367309
-
On distinguishing prime numbers from composite numbers
-
IEEE, 21st FOCS, Syracuse, USA, Proceedings
-
L.M. ADLEMAN - «On distinguishing prime numbers from composite numbers», in Foundations of computer science, IEEE, 1980, 21st FOCS, Syracuse, USA, Proceedings, p. 387-406.
-
(1980)
Foundations of Computer Science
, pp. 387-406
-
-
Adleman, L.M.1
-
3
-
-
0001671902
-
On distinguishing prime numbers from composite numbers
-
L.M. ADLEMAN, C. POMERANCE & R.S. RUMELY - «On distinguishing prime numbers from composite numbers», Ann. of Math. (2) 117 (1983), p. 173-206.
-
(1983)
Ann. of Math. (2)
, vol.117
, pp. 173-206
-
-
Adleman, L.M.1
Pomerance, C.2
Rumely, R.S.3
-
4
-
-
0017930809
-
A method for obtaining digital signatures and public-key cryptosystems
-
L.M. ADLEMAN, R.L. RIVEST & A. SHAMIR - «A method for obtaining digital signatures and public-key cryptosystems», Comm. ACM 21 (1978), no. 2, p. 120-126.
-
(1978)
Comm. ACM
, vol.21
, Issue.2
, pp. 120-126
-
-
Adleman, L.M.1
Rivest, R.L.2
Shamir, A.3
-
7
-
-
0001725847
-
There are infinitely many Carmichael numbers
-
W.R. ALFORD, A. GRANVILLE & C. POMERANCE - «There are infinitely many Carmichael numbers», Ann. of Math. (2) 139 (1994), no. 3, p. 703-722.
-
(1994)
Ann. of Math. (2)
, vol.139
, Issue.3
, pp. 703-722
-
-
Alford, W.R.1
Granville, A.2
Pomerance, C.3
-
8
-
-
33748748598
-
Certain criteria for the primality of numbers connected with the little Fermat theorem (russian)
-
M. ARTJUHOV - «Certain criteria for the primality of numbers connected with the little Fermat theorem (russian)», Acta Arith. 12 (1966/67), p. 355-364.
-
(1966)
Acta Arith.
, vol.12
, pp. 355-364
-
-
Artjuhov, M.1
-
9
-
-
84966219173
-
Elliptic curves and primality proving
-
A.O.L. ATKIN & F. MORAIN. - «Elliptic curves and primality proving», Math. Comp. 61 (1993), no. 203, p. 29-68.
-
(1993)
Math. Comp.
, vol.61
, Issue.203
, pp. 29-68
-
-
Atkin, A.O.L.1
Morain, F.2
-
10
-
-
84966198660
-
Explicit bounds for primality testing and related problems
-
E. BACH - «Explicit bounds for primality testing and related problems», Math. Comp. 55 (1990), no. 191, p. 355-380.
-
(1990)
Math. Comp.
, vol.55
, Issue.191
, pp. 355-380
-
-
Bach, E.1
-
12
-
-
4444329922
-
The difference between consecutive primes. II
-
R.C. BAKER, G. HARMAN & J. PINTZ - «The difference between consecutive primes. II», Proc. London Math. Soc. (3) 83 (2001), no. 3, p. 532-562.
-
(2001)
Proc. London Math. Soc. (3)
, vol.83
, Issue.3
, pp. 532-562
-
-
Baker, R.C.1
Harman, G.2
Pintz, J.3
-
17
-
-
0003442756
-
-
London Math. Soc. Lecture Note Ser., Cambridge University Press
-
I. BLAKE, G. SEROUSSI & N. SMART - Elliptic curves in cryptography, London Math. Soc. Lecture Note Ser., vol. 265, Cambridge University Press, 1999.
-
(1999)
Elliptic Curves in Cryptography
, vol.265
-
-
Blake, I.1
Seroussi, G.2
Smart, N.3
-
20
-
-
84859288166
-
-
Contemporary Mathematics, AMS
-
n ± 1, b = 2, 3, 5, 6, 7, 10, 11, 12 up to high powers, 2 éd., Contemporary Mathematics, no. 22, AMS, 1988.
-
(1988)
n ± 1, B = 2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers, 2 Éd.
, Issue.22
-
-
Brillhart, J.1
Lehmer, D.H.2
Selfridge, J.L.3
Tuckerman, B.4
Wagstaff Jr., S.S.5
-
21
-
-
0011040582
-
Formal and efficient primality proofs by use of computer algebra oracles
-
O. CAPROTTI & M. OOSTDIJK - «Formal and efficient primality proofs by use of computer algebra oracles», J. Symbolic Comput. 32 (2001), p. 55-70.
-
(2001)
J. Symbolic Comput.
, vol.32
, pp. 55-70
-
-
Caprotti, O.1
Oostdijk, M.2
-
22
-
-
0031531029
-
Primality test via quantum factorization
-
H.F. CHAU & H.-K. Lo - «Primality test via quantum factorization», Internat. J. Modern Phys. C 8 (1997), no. 2, p. 131-138.
-
(1997)
Internat. J. Modern Phys. C
, vol.8
, Issue.2
, pp. 131-138
-
-
Chau, H.F.1
Lo, H.-K.2
-
23
-
-
33746736075
-
Primality proving via one round in ECPP and one iteration in AKS
-
D. Boneh, éd., Lecture Notes in Comput. Sci., Springer Verlag
-
Q. CHENG - «Primality proving via one round in ECPP and one iteration in AKS», in Advances in Cryptology - CRYPTO 2003 (D. Boneh, éd.), Lecture Notes in Comput. Sci., vol. 2729, Springer Verlag, 2003, p. 338-348.
-
(2003)
Advances in Cryptology - CRYPTO 2003
, vol.2729
, pp. 338-348
-
-
Cheng, Q.1
-
24
-
-
0003705361
-
-
Graduate Texts in Mathematics, Springer-Verlag, Third printing
-
H. COHEN - A course in algorithmic algebraic number theory, Graduate Texts in Mathematics, vol. 138, Springer-Verlag, 1996, Third printing.
-
(1996)
A Course in Algorithmic Algebraic Number Theory
, vol.138
-
-
Cohen, H.1
-
25
-
-
84968501760
-
Implementation of a new primality test
-
H. COHEN & A.K. LENSTRA - «Implementation of a new primality test», Math. Comp. 48 (1987), no. 177, p. 103-121.
-
(1987)
Math. Comp.
, vol.48
, Issue.177
, pp. 103-121
-
-
Cohen, H.1
Lenstra, A.K.2
-
26
-
-
84968518187
-
Primality testing and Jacobi sums
-
H. COHEN & H.W. LENSTRA, JR. - «Primality testing and Jacobi sums», Math. Comp. 42 (1984), no. 165, p. 297-330.
-
(1984)
Math. Comp.
, vol.42
, Issue.165
, pp. 297-330
-
-
Cohen, H.1
Lenstra Jr., H.W.2
-
27
-
-
0004171569
-
-
Presses Universitaires de France
-
L. COMTET - Analyse combinatoire, Presses Universitaires de France, 1970.
-
(1970)
Analyse Combinatoire
-
-
Comtet, L.1
-
28
-
-
0003484756
-
-
John Wiley & Sons
-
2, John Wiley & Sons, 1989.
-
(1989)
2
-
-
Cox, D.A.1
-
30
-
-
0001963070
-
Elliptic and modular curves over finite fields and related computational issues
-
(D.A. Buell & J.T. Teitelbaum, éds.), AMS/IP Studies in Advanced Mathematics, American Mathematical Society, International Press
-
N.D. ELKIES - «Elliptic and modular curves over finite fields and related computational issues», in Computational Perspectives on Number Theory : Proceedings of a Conference in Honor of A.O.L. Atkin (D.A. Buell & J.T. Teitelbaum, éds.), AMS/IP Studies in Advanced Mathematics, vol. 7, American Mathematical Society, International Press, 1998, p. 21-76.
-
(1998)
Computational Perspectives on Number Theory : Proceedings of a Conference in Honor of A.O.L. Atkin
, vol.7
, pp. 21-76
-
-
Elkies, N.D.1
-
31
-
-
0013506173
-
Théorème do brun-titschmarsh; application au théorème de fermat
-
E. FOUVRY - «Théorème do Brun-Titschmarsh; application au théorème de Fermat», Invent. Math. 79 (1985), p. 383-407.
-
(1985)
Invent. Math.
, vol.79
, pp. 383-407
-
-
Fouvry, E.1
-
32
-
-
84859292015
-
Proving the primality of very large numbers with fastECPP
-
(D. Buell, éd.), Lecture Notes in Comput. Sci., Springer Verlag, 6th International Symposium, ANTS-IV, Burlington, June 2004, Proceedings
-
J. FRANKE, T. KLEINJUNG, F. MORAIN & T. WIRTH - «Proving the primality of very large numbers with fastECPP», in Algorithmic Number Theory (D. Buell, éd.), Lecture Notes in Comput. Sci., Springer Verlag, 2004, 6th International Symposium, ANTS-IV, Burlington, June 2004, Proceedings.
-
(2004)
Algorithmic Number Theory
-
-
Franke, J.1
Kleinjung, T.2
Morain, F.3
Wirth, T.4
-
34
-
-
84946825131
-
Counting points on hyperelliptic curves over finite fields
-
W. Bosrna, éd., Lecture Notes in Comput. Sci., Springer Verlag, 4th International Symposium, ANTS-IV, Leiden, The Netherlands, July 2000, Proceedings
-
P. GAUDRY & R. HARLEY - «Counting points on hyperelliptic curves over finite fields», in Algorithmic Number Theory W. Bosrna, éd.), Lecture Notes in Comput. Sci., vol. 1838, Springer Verlag, 2000, 4th International Symposium, ANTS-IV, Leiden, The Netherlands, July 2000, Proceedings, p. 313-332.
-
(2000)
Algorithmic Number Theory
, vol.1838
, pp. 313-332
-
-
Gaudry, P.1
Harley, R.2
-
35
-
-
84971137261
-
On the number of primes p for which p + a has a large prime factor
-
M. GOLDFELD - «On the number of primes p for which p + a has a large prime factor», Mathematika 16 (1969), p. 23-27.
-
(1969)
Mathematika
, vol.16
, pp. 23-27
-
-
Goldfeld, M.1
-
36
-
-
0002574855
-
Almost all primes can be quickly certified
-
ACM, May 28-30, Berkeley
-
S. GOLDWASSER & J. KILIAN - «Almost all primes can be quickly certified», in Proc. 18th STOC, ACM, 1986, May 28-30, Berkeley, p. 316-329.
-
(1986)
Proc. 18th STOC
, pp. 316-329
-
-
Goldwasser, S.1
Kilian, J.2
-
37
-
-
0010697221
-
Primality testing using elliptic curves
-
_, «Primality testing using elliptic curves», Journal of the ACM 46 (1999), no. 4, p. 450-472.
-
(1999)
Journal of the ACM
, vol.46
, Issue.4
, pp. 450-472
-
-
-
38
-
-
0002897015
-
The differences between consecutive primes
-
D.R. HEATH-BROWN - «The differences between consecutive primes», J. London Math. Soc. (2) 18 (1978), no. 1, p. 7-13.
-
(1978)
J. London Math. Soc. (2)
, vol.18
, Issue.1
, pp. 7-13
-
-
Heath-Brown, D.R.1
-
40
-
-
0040093208
-
Primes in short intervals
-
H. IWANIEC & M. JUTILA - «Primes in short intervals», Ark. Mat. 17 (1979), no. 1, p. 167-176.
-
(1979)
Ark. Mat.
, vol.17
, Issue.1
, pp. 167-176
-
-
Iwaniec, H.1
Jutila, M.2
-
41
-
-
85039390522
-
Towards a deterministic polynomial-time primality test
-
IIT Kanpur
-
N. KAYAL & N. SAXENA - «Towards a deterministic polynomial-time primality test», Technical report, IIT Kanpur, 2002, http://www.cse.iitk. ac.in/research/btp2002/primality.html.
-
(2002)
Technical Report
-
-
Kayal, N.1
Saxena, N.2
-
43
-
-
0001645509
-
Complete systems of addition Laws on abelian variety
-
H. LANGE & W. RUPPERT - «Complete systems of addition Laws on abelian variety», Invent. Math. 79 (1985), p. 603-610.
-
(1985)
Invent. Math.
, vol.79
, pp. 603-610
-
-
Lange, H.1
Ruppert, W.2
-
45
-
-
0000931680
-
Algorithms in number theory
-
(J. van Leeuwen, éd.), Algorithms and Complexity, North Holland
-
A.K. LENSTRA & H.W. LENSTRA, JR. - «Algorithms in number theory», in Handbook of Theoretical Computer Science (J. van Leeuwen, éd.), vol. A : Algorithms and Complexity, North Holland, 1990, p. 674-715.
-
(1990)
Handbook of Theoretical Computer Science
, vol.A
, pp. 674-715
-
-
Lenstra, A.K.1
Lenstra Jr., H.W.2
-
46
-
-
0003638131
-
-
éds., Lecture Notes in Math., Springer
-
_(éds.) - The development of the number field sieve, Lecture Notes in Math., vol. 1554, Springer, 1993.
-
(1993)
The Development of the Number Field Sieve
, vol.1554
-
-
-
47
-
-
0040716208
-
Miller's primality test
-
H.W. LENSTRA, JR. - «Miller's primality test», Inform. Process. Lett. 8 (1979), no. 2, p. 86-88.
-
(1979)
Inform. Process. Lett.
, vol.8
, Issue.2
, pp. 86-88
-
-
Lenstra Jr., H.W.1
-
48
-
-
84859292760
-
Primality testing algorithms (after Adleman, Rumely, Williams)
-
Lecture Notes in Math., Springer-Verlag, exposé no 576
-
_, «Primality testing algorithms (after Adleman, Rumely, Williams)», in Séminaire Bourbaki (1080/81), Lecture Notes in Math., vol. 901, Springer-Verlag, 1981, exposé no 576.
-
(1981)
Séminaire Bourbaki (1080/81)
, vol.901
-
-
-
49
-
-
0007418889
-
Primality testing
-
Math. Centrum, Amsterdam
-
_, «Primality testing», in Computational methods in number theory, Part I, Math. Centrum, Amsterdam, 1982, p. 55-77.
-
(1982)
Computational Methods in Number Theory, Part I
, pp. 55-77
-
-
-
50
-
-
84859285818
-
Primality testing with Artin symbols
-
Progr. Math., Birkhäuser Boston, Mass.
-
_, «Primality testing with Artin symbols», in Number theory related to Format's last theorem (Cambridge, Mass., 1981), Progr. Math., vol. 26, Birkhäuser Boston, Mass., 1982, p. 341-347.
-
(1982)
Number Theory Related to Format's Last Theorem (Cambridge, Mass., 1981)
, vol.26
, pp. 341-347
-
-
-
51
-
-
0345899244
-
Galois theory and primality testing
-
(I. Reiner & K. W. Roggenkamp, éds.), Lecture Notes in Math., Springer, Proc. of a conference, Oberwolfach, June 3-9, 1984
-
_, «Galois theory and primality testing», in Orders and their applications (I. Reiner & K. W. Roggenkamp, éds.), Lecture Notes in Math., vol. 1142, Springer, 1984, Proc. of a conference, Oberwolfach, June 3-9, 1984, p. 169-189.
-
(1984)
Orders and Their Applications
, vol.1142
, pp. 169-189
-
-
-
52
-
-
0346017864
-
Elliptic curves and number-theoretic algorithms
-
(Providence, RI), Amer. Math. Soc.
-
_, «Elliptic curves and number-theoretic algorithms», in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) (Providence, RI), Amer. Math. Soc., 1987, p. 99-120.
-
(1987)
Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986)
, vol.1-2
, pp. 99-120
-
-
-
53
-
-
0001258323
-
Factoring integers with elliptic curves
-
_, «Factoring integers with elliptic curves», Ann. of Math. (2) 126 (1987), p. 649-673.
-
(1987)
Ann. of Math. (2)
, vol.126
, pp. 649-673
-
-
-
57
-
-
85015281689
-
Riemann's hypothesis and tests for primality
-
G.L. MILLER - «Riemann's hypothesis and tests for primality», in Proc. 7th STOC, 1975, p. 234-239.
-
(1975)
Proc. 7th STOC
, pp. 234-239
-
-
Miller, G.L.1
-
58
-
-
0000673728
-
Calcul du nombre de points sur une courbe elliptique dans un corps fini : Aspects algorithmiques
-
F. MORAIN - «Calcul du nombre de points sur une courbe elliptique dans un corps fini : aspects algorithmiques», J. Théor. Nombres Bordeaux 7 (1995), p. 255-282.
-
(1995)
J. Théor. Nombres Bordeaux
, vol.7
, pp. 255-282
-
-
Morain, F.1
-
61
-
-
0005599967
-
Analysis and comparison of some integer factoring algorithms
-
(H.W. Lenstra, Jr. & R. Tijdeman, éds.), Mathematisch Centrum, Amsterdam, Mathematical Center Tracts
-
C. POMERANCE - «Analysis and comparison of some integer factoring algorithms», in Computational methods in number theory (H.W. Lenstra, Jr. & R. Tijdeman, éds.), Mathematisch Centrum, Amsterdam, 1982, Mathematical Center Tracts 154/155, p. 89-140.
-
(1982)
Computational Methods in Number Theory
, vol.154-155
, pp. 89-140
-
-
Pomerance, C.1
-
62
-
-
84968475670
-
Very short primality proofs
-
_, «Very short primality proofs», Math. Comp. 48 (1987), no. 177, p. 315-322.
-
(1987)
Math. Comp.
, vol.48
, Issue.177
, pp. 315-322
-
-
-
64
-
-
0011521703
-
Every prime has a succint certificate
-
V.R. PRATT - «Every prime has a succint certificate», SIAM J. Comput. 4 (1975), p. 214-220.
-
(1975)
SIAM J. Comput.
, vol.4
, pp. 214-220
-
-
Pratt, V.R.1
-
65
-
-
33845432604
-
Probabilistic algorithms for testing primality
-
M. RABIN - «Probabilistic algorithms for testing primality», J. Number Theory 12 (1980), p. 128-138.
-
(1980)
J. Number Theory
, vol.12
, pp. 128-138
-
-
Rabin, M.1
-
68
-
-
84972540003
-
Approximate formulas for some functions of prime numbers
-
J.B. ROSSER & L. SCHOENFELD - «Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), p. 64-94.
-
(1962)
Illinois J. Math.
, vol.6
, pp. 64-94
-
-
Rosser, J.B.1
Schoenfeld, L.2
-
69
-
-
84966233278
-
Elliptic curves over finite fields and the computation of square roots mod p
-
R. SCHOOF - «Elliptic curves over finite fields and the computation of square roots mod p», Math. Comp. 44 (1985), p. 483-494.
-
(1985)
Math. Comp.
, vol.44
, pp. 483-494
-
-
Schoof, R.1
-
70
-
-
0001219865
-
Counting points on elliptic curves over finite fields
-
_, «Counting points on elliptic curves over finite fields», J. Théor. Nombres Bordeaux 7 (1995), p. 219-254.
-
(1995)
J. Théor. Nombres Bordeaux
, vol.7
, pp. 219-254
-
-
-
71
-
-
85115374351
-
Algorithms for quantum conputation : Discrete logarithms and factoring
-
(Montreal, Canada), ACM
-
P.W. SHOR - «Algorithms for quantum conputation : Discrete logarithms and factoring», in Proceedings 26th Annual ACM Symposium on Theory of Computing (STOC) (Montreal, Canada), ACM, 1994, p. 124-134.
-
(1994)
Proceedings 26th Annual ACM Symposium on Theory of Computing (STOC)
, pp. 124-134
-
-
Shor, P.W.1
-
72
-
-
0001873077
-
A fast Monte-carlo test for primality
-
Erratum, ibid, volume 7, 1, 1978
-
R. SOLOVAY & V. STRASSEN - «A fast Monte-Carlo test for primality», SIAM J. Comput. 6 (1977), no. 1, p. 84-85, Erratum, ibid, volume 7, 1, 1978.
-
(1977)
SIAM J. Comput.
, vol.6
, Issue.1
, pp. 84-85
-
-
Solovay, R.1
Strassen, V.2
-
73
-
-
0042833057
-
Jacobi sums over finite fields
-
102.1
-
P. VAN WAMELEN - «Jacobi sums over finite fields», Acta Arith. 102.1 (2002), p. 1-20.
-
(2002)
Acta Arith.
, pp. 1-20
-
-
Van Wamelen, P.1
-
74
-
-
0001556633
-
Abelian varieties over finite fields
-
E. WATERHOUSE - «Abelian varieties over finite fields», Ann. Sci. École Norm. Sup. 2 (1969), p. 521-560.
-
(1969)
Ann. Sci. École Norm. Sup.
, vol.2
, pp. 521-560
-
-
Waterhouse, E.1
-
75
-
-
0037235338
-
Constructing hyperelliptic curves of genus 2 suitable for cryptography
-
A. WENG - «Constructing hyperelliptic curves of genus 2 suitable for cryptography», Math. Comp. 72 (2003), p. 435-458.
-
(2003)
Math. Comp.
, vol.72
, pp. 435-458
-
-
Weng, A.1
-
76
-
-
0039288455
-
Factoring integers before computers
-
Proc. Sympos. Appl. Math., Amer. Math. Soc., Providence, RI
-
H.C. WILLIAMS & J.O. SHALLIT - «Factoring integers before computers», in Mathematics of Computation 1943-1993 : a half-century of computational mathematics (Vancouver, BC, 1993), Proc. Sympos. Appl. Math., vol. 48, Amer. Math. Soc., Providence, RI, 1994, p. 481-531.
-
(1994)
Mathematics of Computation 1943-1993 : A Half-century of Computational Mathematics (Vancouver, BC, 1993)
, vol.48
, pp. 481-531
-
-
Williams, H.C.1
Shallit, J.O.2
|