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228:
Algorithmic Number Theory: Lattices, Number Fields, Curves and
Cryptography
75:
1655:
1493:
456:
91:
47:
31:
528:
463:. Progress in Mathematics. Vol. 126 (second ed.). BirkhÀuser.
2141:
2100:
1952:
1650:
1511:
722:
597:
164:
136:
1834:
1819:
146:
1877:
27:
Study of algorithms for performing number theoretic computations
2040:
1814:
677:
419:
221:
606:
Algorithmic Number Theory, Volume 1: Efficient
Algorithms
493:
345:
Number Theory â Volume I: Tools and
Diophantine Equations
174:
Algorithmic Number Theory, Volume 1: Efficient
Algorithms
596:
163:
1239:
indicate that algorithm is for numbers of special forms
523:
2055:
2045:
461:
Prime
Numbers and Computer Methods for Factorization
385:
Number Theory â Volume II: Analytic and Modern Tools
198:
74:. Computational number theory has applications to
634:A Course In Computational Algebraic Number Theory
265:A Course In Computational Algebraic Number Theory
193:
2232:
718:
1278:
564:
305:Advanced Topics in Computational Number Theory
1893:
1264:
704:
487:
628:
455:
379:
339:
299:
259:
2195:
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1900:
1886:
1271:
1257:
711:
697:
590:
429:Prime Numbers: A Computational Perspective
50:for investigating and solving problems in
14:
2233:
1694:Clifford's theorem on special divisors
581:The Princeton Companion to Mathematics
1881:
1252:
692:
560:
558:
622:
125:
104:Birch and Swinnerton-Dyer conjecture
231:. MSRI Publications. Vol. 44.
201:Factorisation and Primality Testing
24:
1863:Vector bundles on algebraic curves
1786:Weber's theorem (Algebraic curves)
1383:Hasse's theorem on elliptic curves
1373:Counting points on elliptic curves
555:
225:; Peter Stevenhagen, eds. (2008).
157:
25:
2262:
1907:
920:Special number field sieve (SNFS)
914:General number field sieve (GNFS)
670:
533:. American Mathematical Society.
2214:
2204:
2194:
2184:
2175:
2174:
676:
98:in number theory, including the
1474:Hurwitz's automorphisms theorem
1953:analytic theory of L-functions
1931:non-abelian class field theory
1699:Gonality of an algebraic curve
1610:Differential of the first kind
152:Fast Library for Number Theory
118:, and explicit aspects of the
13:
1:
2251:Computational fields of study
1853:BirkhoffâGrothendieck theorem
1552:Nagata's conjecture on curves
1423:SchoofâElkiesâAtkin algorithm
1297:Five points determine a conic
638:Graduate Texts in Mathematics
574:"Computational Number Theory"
548:
389:Graduate Texts in Mathematics
349:Graduate Texts in Mathematics
309:Graduate Texts in Mathematics
269:Graduate Texts in Mathematics
132:Magma computer algebra system
90:, and is used to investigate
1977:Transcendental number theory
1413:Supersingular elliptic curve
878:Lenstra elliptic curve (ECM)
7:
2241:Computational number theory
2200:List of recreational topics
1972:Computational number theory
1957:probabilistic number theory
1620:Riemann's existence theorem
1547:Hilbert's sixteenth problem
1439:Elliptic curve cryptography
1352:Fundamental pair of periods
683:Computational number theory
84:elliptic curve cryptography
58:, including algorithms for
40:computational number theory
10:
2267:
1750:Moduli of algebraic curves
1185:Exponentiation by squaring
868:Continued fraction (CFRAC)
585:Princeton University Press
497:Cambridge University Press
233:Cambridge University Press
70:, and explicit methods in
2170:
2152:Diophantine approximation
2124:
2111:Chinese remainder theorem
2033:
1915:
1843:
1794:
1763:
1727:
1676:
1669:
1643:
1575:
1492:
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1334:
1325:
1287:
1232:
1167:
1129:
1096:
1053:
997:
954:
858:
820:
729:
650:10.1007/978-3-662-02945-9
437:10.1007/978-1-4684-9316-0
401:10.1007/978-0-387-49894-2
361:10.1007/978-0-387-49923-9
321:10.1007/978-1-4419-8489-0
281:10.1007/978-3-662-02945-9
88:post-quantum cryptography
44:algorithmic number theory
18:Algorithmic number theory
1996:Arithmetic combinatorics
1517:CayleyâBacharach theorem
1444:Elliptic curve primality
505:10.1017/CBO9781139165464
1967:Geometric number theory
1923:Algebraic number theory
1776:RiemannâHurwitz formula
1740:GromovâWitten invariant
1600:Compact Riemann surface
1388:Mazur's torsion theorem
1098:Greatest common divisor
525:Samuel S. Wagstaff, Jr.
66:, finding solutions to
2086:Transcendental numbers
2000:additive number theory
1949:Analytic number theory
1393:Modular elliptic curve
1209:Modular exponentiation
2157:Irrationality measure
2147:Diophantine equations
1990:HodgeâArakelov theory
1307:Rational normal curve
936:Shanks's square forms
860:Integer factorization
835:Sieve of Eratosthenes
142:Number Theory Library
112:modularity conjecture
68:diophantine equations
64:integer factorization
48:computational methods
2116:Arithmetic functions
1982:Diophantine geometry
1858:Stable vector bundle
1719:Weil reciprocity law
1709:RiemannâRoch theorem
1689:BrillâNoether theory
1625:RiemannâRoch theorem
1542:Genusâdegree formula
1403:MordellâWeil theorem
1378:Division polynomials
1214:Montgomery reduction
1088:Function field sieve
1063:Baby-step giant-step
909:Quadratic sieve (QS)
685:at Wikimedia Commons
530:The Joy of Factoring
116:Sato-Tate conjecture
2162:Continued fractions
2025:Arithmetic dynamics
2020:Arithmetic topology
2014:P-adic Hodge theory
2006:Arithmetic geometry
1939:IwasawaâTate theory
1670:Structure of curves
1562:Quartic plane curve
1484:Hyperelliptic curve
1464:De Franchis theorem
1408:NagellâLutz theorem
1224:Trachtenberg system
1190:Integer square root
1131:Modular square root
850:Wheel factorization
802:Quadratic Frobenius
782:LucasâLehmerâRiesel
431:. Springer-Verlag.
205:. Springer-Verlag.
72:arithmetic geometry
56:arithmetic geometry
46:, is the study of
2106:Modular arithmetic
2076:Irrational numbers
2010:anabelian geometry
1927:class field theory
1677:Divisors on curves
1469:Faltings's theorem
1418:Schoof's algorithm
1398:Modularity theorem
1116:Extended Euclidean
1055:Discrete logarithm
984:SchönhageâStrassen
840:Sieve of Pritchard
100:Riemann hypothesis
2228:
2227:
2125:Advanced concepts
2081:Algebraic numbers
2066:Composite numbers
1875:
1874:
1871:
1870:
1771:HasseâWitt matrix
1714:Weierstrass point
1661:Smooth completion
1630:TeichmĂŒller space
1532:Cubic plane curve
1452:
1451:
1366:Arithmetic theory
1347:Elliptic integral
1342:Elliptic function
1246:
1245:
845:Sieve of Sundaram
681:Media related to
640:. Vol. 138.
540:978-1-4704-1048-3
410:978-0-387-49893-5
391:. Vol. 240.
370:978-0-387-49922-2
351:. Vol. 239.
311:. Vol. 193.
271:. Vol. 138.
242:978-0-521-20833-8
195:David M. Bressoud
126:Software packages
120:Langlands program
60:primality testing
16:(Redirected from
2258:
2218:
2208:
2198:
2197:
2188:
2187:
2178:
2177:
2071:Rational numbers
1902:
1895:
1888:
1879:
1878:
1704:Jacobian variety
1674:
1673:
1577:Riemann surfaces
1567:Real plane curve
1527:Cramer's paradox
1507:BĂ©zout's theorem
1332:
1331:
1281:algebraic curves
1273:
1266:
1259:
1250:
1249:
1195:Integer relation
1168:Other algorithms
1073:Pollard kangaroo
964:Ancient Egyptian
822:Prime-generating
807:SolovayâStrassen
720:Number-theoretic
713:
706:
699:
690:
689:
680:
664:
663:
626:
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421:Richard Crandall
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42:, also known as
36:computer science
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2256:
2255:
2231:
2230:
2229:
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2132:Quadratic forms
2120:
2095:P-adic analysis
2051:Natural numbers
2029:
1986:Arakelov theory
1911:
1906:
1876:
1867:
1839:
1830:Delta invariant
1808:
1790:
1759:
1723:
1684:AbelâJacobi map
1665:
1639:
1635:Torelli theorem
1605:Dessin d'enfant
1585:Belyi's theorem
1571:
1557:PlĂŒcker formula
1488:
1479:Hurwitz surface
1448:
1427:
1361:
1335:Analytic theory
1327:Elliptic curves
1321:
1302:Projective line
1289:Rational curves
1283:
1277:
1247:
1242:
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1163:
1125:
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993:
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789:Proth's theorem
731:Primality tests
725:
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642:Springer-Verlag
627:
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602:Jeffrey Shallit
595:
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393:Springer-Verlag
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353:Springer-Verlag
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169:Jeffrey Shallit
160:
158:Further reading
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2190:List of topics
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1083:Index calculus
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1078:PohligâHellman
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1030:Newton-Raphson
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956:Multiplication
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926:Rational sieve
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830:Sieve of Atkin
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671:External links
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566:Carl Pomerance
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108:ABC conjecture
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2137:Modular forms
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2061:Prime numbers
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1646:
1644:Constructions
1642:
1636:
1633:
1631:
1628:
1626:
1623:
1621:
1618:
1616:
1615:Klein quartic
1613:
1611:
1608:
1606:
1603:
1601:
1598:
1596:
1595:Bolza surface
1593:
1591:
1590:Bring's curve
1588:
1586:
1583:
1582:
1580:
1578:
1574:
1568:
1565:
1563:
1560:
1558:
1555:
1553:
1550:
1548:
1545:
1543:
1540:
1538:
1535:
1533:
1530:
1528:
1525:
1523:
1522:Conic section
1520:
1518:
1515:
1513:
1510:
1508:
1505:
1503:
1502:AF+BG theorem
1500:
1499:
1497:
1495:
1491:
1485:
1482:
1480:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1461:
1459:
1455:
1445:
1442:
1440:
1437:
1436:
1434:
1430:
1424:
1421:
1419:
1416:
1414:
1411:
1409:
1406:
1404:
1401:
1399:
1396:
1394:
1391:
1389:
1386:
1384:
1381:
1379:
1376:
1374:
1371:
1370:
1368:
1364:
1358:
1355:
1353:
1350:
1348:
1345:
1343:
1340:
1339:
1337:
1333:
1330:
1328:
1324:
1318:
1317:Twisted cubic
1315:
1313:
1310:
1308:
1305:
1303:
1300:
1298:
1295:
1294:
1292:
1290:
1286:
1282:
1274:
1269:
1267:
1262:
1260:
1255:
1254:
1251:
1238:
1235:
1234:
1231:
1225:
1222:
1220:
1217:
1215:
1212:
1210:
1207:
1204:
1200:
1196:
1193:
1191:
1188:
1186:
1183:
1181:
1178:
1176:
1173:
1172:
1170:
1166:
1160:
1157:
1155:
1152:
1150:
1147:
1145:
1144:Pocklington's
1142:
1140:
1137:
1136:
1134:
1132:
1128:
1122:
1119:
1117:
1114:
1112:
1109:
1107:
1104:
1103:
1101:
1099:
1095:
1089:
1086:
1084:
1081:
1079:
1076:
1074:
1071:
1069:
1066:
1064:
1061:
1060:
1058:
1056:
1052:
1046:
1043:
1041:
1038:
1036:
1033:
1031:
1028:
1026:
1023:
1021:
1018:
1016:
1013:
1011:
1008:
1007:
1005:
1003:
1000:
996:
990:
987:
985:
982:
980:
977:
975:
972:
970:
967:
965:
962:
961:
959:
957:
953:
947:
944:
942:
939:
937:
934:
932:
929:
927:
924:
922:
921:
917:
915:
912:
910:
907:
905:
903:
899:
897:
895:
891:
889:
888:Pollard's rho
886:
884:
881:
879:
876:
874:
871:
869:
866:
865:
863:
861:
857:
851:
848:
846:
843:
841:
838:
836:
833:
831:
828:
827:
825:
823:
819:
813:
810:
808:
805:
803:
800:
798:
797:
793:
791:
790:
786:
784:
783:
779:
777:
776:
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770:
767:
765:
762:
760:
757:
755:
752:
750:
747:
745:
742:
740:
737:
736:
734:
732:
728:
724:
721:
714:
709:
707:
702:
700:
695:
694:
691:
684:
679:
675:
674:
661:
659:0-387-55640-0
655:
651:
647:
643:
639:
635:
631:
625:
617:
615:0-262-02405-5
611:
608:. MIT Press.
607:
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332:
330:0-387-98727-4
326:
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306:
302:
298:
297:
292:
290:0-387-55640-0
286:
282:
278:
274:
270:
266:
262:
258:
257:
252:
248:
244:
238:
234:
230:
229:
224:
223:Joe P. Buhler
220:
219:
214:
212:0-387-97040-1
208:
203:
202:
196:
192:
191:
186:
184:0-262-02405-5
180:
177:. MIT Press.
176:
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96:open problems
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73:
69:
65:
61:
57:
53:
52:number theory
49:
45:
41:
37:
33:
19:
2034:Key concepts
1971:
1961:sieve theory
1804:
1781:Prym variety
1755:Stable curve
1745:Hodge bundle
1735:ELSV formula
1537:Fermat curve
1494:Plane curves
1457:Higher genus
1432:Applications
1357:Modular form
1236:
918:
901:
893:
812:MillerâRabin
794:
787:
780:
775:LucasâLehmer
773:
633:
624:
605:
592:
580:
529:
492:
489:Victor Shoup
460:
428:
384:
344:
304:
264:
227:
200:
173:
78:, including
76:cryptography
43:
39:
29:
2220:Wikiversity
2142:L-functions
1810:singularity
1656:Polar curve
1068:Pollard rho
1025:Goldschmidt
759:Pocklington
749:BaillieâPSW
630:Henri Cohen
457:Hans Riesel
381:Henri Cohen
341:Henri Cohen
301:Henri Cohen
261:Henri Cohen
92:conjectures
32:mathematics
2235:Categories
2101:Arithmetic
1651:Dual curve
1279:Topics in
1180:Cornacchia
1175:Chakravala
723:algorithms
549:References
479:0821.11001
251:1154.11002
1764:Morphisms
1512:Bitangent
1154:Berlekamp
1111:Euclidean
999:Euclidean
979:ToomâCook
974:Karatsuba
598:Eric Bach
165:Eric Bach
2210:Wikibook
2180:Category
1121:Lehmer's
1015:Chunking
1002:division
931:Fermat's
632:(1993).
604:(1996).
568:(2009),
527:(2013).
491:(2012).
459:(1994).
427:(2001).
383:(2007).
343:(2007).
303:(2000).
263:(1993).
197:(1989).
171:(1996).
137:SageMath
2041:Numbers
1835:Tacnode
1820:Crunode
1237:Italics
1159:Kunerth
1139:Cipolla
1020:Fourier
989:FĂŒrer's
883:Euler's
873:Dixon's
796:PĂ©pin's
572:(ed.),
147:PARI/GP
1916:Fields
1815:Acnode
1728:Moduli
1219:Schoof
1106:Binary
1010:Binary
946:Shor's
764:Fermat
656:
612:
537:
511:
477:
467:
443:
407:
367:
327:
287:
249:
239:
209:
181:
114:, the
110:, the
106:, the
102:, the
2056:Unity
1040:Short
769:Lucas
577:(PDF)
1825:Cusp
1035:Long
969:Long
654:ISBN
610:ISBN
535:ISBN
509:ISBN
465:ISBN
441:ISBN
405:ISBN
365:ISBN
325:ISBN
285:ISBN
237:ISBN
207:ISBN
179:ISBN
94:and
86:and
62:and
54:and
34:and
1199:LLL
1045:SRT
904:+ 1
896:â 1
744:APR
739:AKS
646:doi
501:doi
475:Zbl
433:doi
397:doi
357:doi
317:doi
277:doi
247:Zbl
80:RSA
30:In
2237::
2012:,
1988:,
1959:,
1955:,
1941:,
1937:,
1933:,
1929:,
1203:KZ
1201:;
652:.
644:.
636:.
600:;
583:,
579:,
557:^
507:.
499:.
495:.
473:.
439:.
423:;
403:.
395:.
387:.
363:.
355:.
347:.
323:.
315:.
307:.
283:.
275:.
267:.
245:.
235:.
167:;
122:.
82:,
38:,
2097:)
2093:(
2046:0
2016:)
2008:(
2002:)
1998:(
1992:)
1984:(
1963:)
1951:(
1945:)
1925:(
1901:e
1894:t
1887:v
1807:k
1805:A
1272:e
1265:t
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1205:)
1197:(
902:p
894:p
712:e
705:t
698:v
662:.
648::
618:.
543:.
517:.
503::
481:.
449:.
435::
413:.
399::
373:.
359::
333:.
319::
293:.
279::
253:.
215:.
187:.
20:)
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