w3 4774ck3d 7h3 pr0613m 0f 501v1ng cr055w0rd pu22135 6y c0mpu73r: g1v3n 4 537 0f c1u35 4nd 4 cr055w0rd gr1d, 7ry 70 m4x1m123 7h3 num63r 0f w0rd5 c0rr3c71y f1113d 1n. 4f73r 4n 4n41y515 0f 4 14rg3 c0113c710n 0f pu22135, w3 d3c1d3d 70 u53 4n 0p3n 4rch173c7ur3 1n wh1ch 1nd3p3nd3n7 pr0gr4m5 5p3c141123 1n 501v1ng 5p3c1f1c 7yp35 0f c1u35, dr4w1ng 0n 1d345 fr0m 1nf0rm4710n r37r13v41, d4746453 534rch, 4nd m4ch1n3 134rn1ng. 34ch 3xp3r7 m0du13 g3n3r4735 4 (p055161y 3mp7y) c4nd1d473 1157 f0r 34ch c1u3, 4nd 7h3 11575 4r3 m3rg3d 70g37h3r 4nd p14c3d 1n70 7h3 gr1d 6y 4 c3n7r41123d 501v3r. w3 u53d 4 pr0646111571c r3pr353n74710n 7hr0ugh0u7 7h3 5y573m 45 4 c0mm0n 1n73rch4ng3 14ngu4g3 637w33n 5u65y573m5 4nd 70 dr1v3 7h3 534rch f0r 4n 0p71m41 501u710n. 13773r5 c0rr3c7 1n und3r 15 m1nu735 p3r pu2213 0n 4 54mp13 0f 370 pu22135 74k3n fr0m 7h3 n3w y0rk 71m35 4nd 53v3r41 07h3r pu2213 50urc35. 7h15 c0rr35p0nd5 70 m1551ng r0ugh1y 3 w0rd5 0r 4 13773r5 0n 4 cruc1v3r641157 (cr055w0rd 501v3r). w0rd5 0f 7ru7h... cr055w0rd pu22135 4r3 4773mp73d d411y 6y m11110n5 0f p30p13, 4nd r39u1r3 0f 7h3 501v3r 607h 4n 3x73n51v3 kn0w13dg3 0f 14ngu4g3, h1570ry 4nd p0pu14r cu17ur3, 4nd 4 534rch 0v3r p0551613 4n5w3r5 70 f1nd 4 537 7h47 f175 1n 7h3 gr1d. 7h15 du41 745k, 0f 4n5w3r1ng n47ur41 14ngu4g3 9u35710n5 r39u1r1ng 5h4110w, 6r04d kn0w13dg3, 4nd 0f 534rch1ng f0r 4n 0p71m41 537 0f 4n5w3r5 f0r 7h3 gr1d, m4k35 7h353 pu22135 4n 1n73r3571ng ch4113ng3 f0r 4r71f1c141 1n73111g3nc3. 1n 7h15 p4p3r, w3 501v3r f0r 6r1715h-57y13 cr055w0rd5 pu6115h3d 6y g3n1u5~2000 50f7w4r3. 17 15 1n73nd3d 45 4 501v1ng 41d, 4nd wh113 17 4pp34r5 9u173 g00d 47 7h354uru5-7yp3 c1u35, 1n 1nf0rm41 73575 17 d1d p00r1y 47 hum4n ch4mp10n5, 17 3xc33d5 7h47 0f c45u41 hum4n 501v3r5, 4v3r4g1ng w3 w111 f1r57 d35cr163 7h3 pr0613m 4nd pr0v1d3 50m3 0f 7h3 1n51gh75 w3 g41n3d fr0m 57udy1ng 4 14rg3 d4746453 0f cr055w0rd pu22135, wh1ch m071v473d 0ur d351gn ch01c35. w3 w111 7h3n d15cu55 0ur und3r1y1ng 4n5w3r5 70 c1u35 4r3 5ugg3573d 6y 3xp3r7 m0du135, 4nd h0w w3 534rch f0r 4n 0p71m41 f17 0f 7h353 p0551613 4n5w3r5 1n70 7h3 gr1d. f1n411y, w3 w111 pr353n7 7h3 5y573m'5 p3rf0rm4nc3 0n 4 14rg3 7357 5u173 0f d411y cr055w0rd pu22135, 45 w311 45 0n 1998 70urn4m3n7 pu22135. 7h3 501u710n 70 4 cr055w0rd pu2213 15 4 537 0f 1n73r10ck1ng w0rd5 15 pr353n73d w17h 4n 3mp7y gr1d 4nd 4 537 0f c1u35; 34ch c1u3 5ugg3575 175 c0rr35p0nd1ng 74rg37. 50m3 c1u3-74rg37 p41r5 4r3 r31471v31y f1x3d-w1d7h f0n7; 411 3x4mp135 4r3 74k3n fr0m 0ur c1u3 d4746453. w3 w111 n073 7h3 74rg37 13ng7h f0110w1ng 54mp13 c1u35 1n 7h15 p4p3r 70 06119u3 4nd 6453d 0n w0rd p14y: m057 4 d023n 0r 50 w0rd5 10ng, 4v3r4g1ng 460u7 2.5 w0rd5 1n 4 54mp13 0f c1u35 w3'v3 c0113c73d. 70 501v3 4 cr055w0rd pu2213 6y c0mpu73r, w3 455um3 7h47 w3 h4v3 607h 7h3 gr1d 4nd 7h3 c1u35 1n m4ch1n3 r34d4613 f0rm, 1gn0r1ng 7h3 5p3c141 f0rm4771ng 4nd unu5u41 m4rk5 7h47 50m371m35 4pp34r 1n cr055w0rd5. 7h3 0f 13773r5, g1v3n 7h3 num63r3d c1u35 4nd 4 146313d gr1d. 1n 7h15 w0rk, w3 f0cu5 0n 4m3r1c4n-57y13 cr055w0rd5, 45 0pp053d 70 6r1715h-57y13 0r cryp71c cr055w0rd5. 6y c0nv3n710n, 411 74rg375 4r3 47 13457 3 13773r5 1n 13ng7h 4nd 10ng 74rg375 c4n 63 c0n57ruc73d 6y p4r7 0f 4 d0wn 74rg37 4nd 4n 4cr055 74rg37. 45 7h15 15 14rg31y 4 n3w pr0613m d0m41n, d1571nc7 fr0m cr055w0rd 501v1ng r3411y w45. 70 g41n 50m3 1n51gh7 1n70 7h3 pr0613m, w3 57ud13d 4 14rg3 c0rpu5 0f 3x1571ng pu22135. w3 c0113c73d 5133 cr055w0rd pu22135 fr0m 4 v4r137y 0f 50urc35, 5umm4r123d 1n n3w5p4p3r pu22135 (7h3 n3w y0rk 71m35, 7h3 105 4ng3135 71m35, 7h3 u54 70d4y, 7v gu1d3), fr0m 0n11n3 51735 f347ur1ng pu22135 (d311, r1dd13r) 0r fr0m 5ynd1c4735 5p3c1f1c411y pr0duc1ng f0r 7h3 0n11n3 m3d1um (cr3470r'5 5ynd1c473, cr055yn3rgy 5ynd1c473). 7h353 pu22135 c0n5717u73 4 cr055w0rd d4746453 (cwd6) 0f 4r0und 350,000 c1u3-74rg37 p41r5, w17h 0v3r 250,000 0f 7h3m un19u3, wh1ch 53rv3d 45 4 p073n7 kn0w13dg3 50urc3 f0r 7h15 pr0j3c7. hum4n 501v3r5 1mpr0v3 w17h 3xp3r13nc3, 1n p4r7 63c4u53 p4r71cu14r c1u35 4nd 74rg375 73nd 70 r3cur. f0r 3x4mp13, m4ny hum4n 501v3r5 w111 ``07h3rw153,'' 4nd ``r3g10n''. 7h3 f1v3 m057 c0mm0n c1u3-74rg37 p41r5 0ur cwd6 c0rr35p0nd5 70 7h3 num63r 0f pu22135 7h47 w0u1d 63 3nc0un73r3d 6y 4 hum4n 0v3r 4 f0ur733n-y34r p3r10d, 47 4 r473 0f 0n3 pu2213 4 d4y. wh47 p3rc3n74g3 0f 74rg375 4nd c1u35 1n 4 n3w pu2213 pr353n73d 70 0ur 5y573m w111 63 1n 7h3 3x1571ng d4746453---h0w n0v31 4r3 cr055w0rd n0v31 74rg375, c1u35, c1u3-74rg37 p41r5, 4nd c1u3 w0rd5 45 w3 1ncr3453 7h3 num63r 0f 313m3n75 1n 7h3 d4746453. 4f73r r4nd0m121ng, w3 100k3d 47 5u65375 0f 7h3 d4746453 r4ng1ng fr0m 5,000 c1u35 70 41m057 350,000. f0r 34ch 5u6537, w3 c41cu1473d 7h3 p3rc3n74g3 0f 7h3 p4r71cu14r 173m (74rg37, c1u3, c1u3-74rg37, c1u3 w0rd) 7h47 4r3 un19u3. 7h15 15 4n 3571m473 f0r 7h3 11k311h00d 0f 7h3 n3x7 173m 631ng n0v31. g1v3n 7h3 c0mp1373 d4746453 (344,921 c1u35) c0n741n5 4 7r3m3nd0u5 4m0un7 0f u53fu1 d0m41n-5p3c1f1c 1nf0rm4710n. cwd6. g1v3n 411 350,000 c1u35, w3 w0u1d 3xp3c7 4 n3w pu2213 7h3 n3w y0rk 71m35 (ny7) cr055w0rd 15 c0n51d3r3d 6y m4ny 70 63 7h3 pr3m13r3 d411y pu2213. ny7 3d170r5 4773mp7 70 m4k3 7h3 pu22135 1ncr3453 1n d1ff1cu17y fr0m 345y 0n m0nd4y 70 v3ry d1ff1cu17 0n 547urd4y 4nd 5und4y. w3 h0p3d 7h47 57udy1ng 7h3 m0nd4y-70-547urd4y 7r3nd5 1n 7h3 pu22135 m1gh7 pr0v1d3 1n51gh7 1n70 wh47 m4k35 4 pu2213 h4rd f0r hum4n5. 7yp35 ch4ng3 d4y 6y d4y. f0r 3x4mp13, n073 7h47 50m3 ``34513r'' 1355 4nd 1355 c0mm0n 45 7h3 w33k g035 0n. 1n 4dd1710n, c1u35 w17h 4 wh1ch 15 0f73n 4 51gn 0f 4 7h3m3d 0r pun c1u3, g37 m0r3 c0mm0n. 7h3 d157r16u710n 0f 74rg37 13ng7h5 4150 v4r135, w17h w0rd5 1n 7h3~6 70~10 13773r r4ng3 63c0m1ng much m0r3 c0mm0n fr0m m0nd4y 70 547urd4y. 5und4y 15 n07 1nc1ud3d 1n 7h3 74613 45 17 15 4 617 0f 4n 0u7113r 0n 50m3 0f 7h353 5c4135, p4r71y du3 70 7h3 f4c7 7h47 7h3 pu22135 4r3 5uch 45 f111-1n-7h3-614nk 4nd 9u073d phr4535, c1u3 57ruc7ur3 134d5 70 51mp13 w4y5 70 4n5w3r 7h053 c1u35. f0r 3x4mp13, g1v3n 7h3 c1u3 50urc35 100k1ng f0r 411 9-13773r phr4535 7h47 m47ch 0n w0rd 60und4r135 4nd kn0wn 13773r5. 1f 3nc0un73r 4 c1u3 5uch 45 466r3v14710n5. 7h3r3 4r3 4150 c1u35 7h47 d0 n07 f17 51mp13 p4773rn, 6u7 m1gh7 63 7h47 c4n 63 6r0ugh7 70 634r 70 501v3 d1ff3r3n7 7yp35 0f c1u35, 7h15 5ugg3575 4 7w0-574g3 4rch173c7ur3 f0r 0ur 501v3r: 0n3 c0n51571ng 0f 4 c0113c710n 0f 5p3c141-purp053 4nd g3n3r41 c4nd1d473-g3n3r4710n m0du135, 4nd 0n3 7h47 c0m61n35 7h3 r35u175 fr0m 7h353 m0du135 70 g3n3r473 4 501u710n 70 7h3 pu2213. 7h15 d3c3n7r41123d 4rch173c7ur3 4110w3d 4 r31471v31y 14rg3 gr0up 0f c0n7r16u70r5 (4ppr0x1m4731y 73n p30p13) 70 c0n7r16u73 m0du135 u51ng 73chn19u35 r4ng1ng fr0m g3n3r1c w0rd 11575 70 h1gh1y 5p3c1f1c m0du135, fr0m 57r1ng m47ch1ng 70 g3n3r41-purp053 1nf0rm4710n r37r13v41. 7h3 n3x7 53c710n d35cr1635 c4nd1d473 11575, 1n 15014710n fr0m 7h3 07h3r gr1d c0n57r41n75. 3xp3r7 m0du135 4r3 fr33 70 r37urn n0 c4nd1d4735 f0r 4ny c1u35, 0r 10,000 f0r 3v3ry 0n3. 7h3 c0113c710n 0f c4nd1d473 11575 15 7h3n r3w31gh73d 6y 4nd c0m61n3d 1n70 4 51ng13 1157 0f c4nd1d4735 f0r 34ch c1u3. f1n411y, 501u710n 17 c4n f1nd 7h47 4150 54715f135 7h3 gr1d c0n57r41n75. 4r3 d35cr163d 1n 4 1473r 53c710n. 70 un1fy 7h3 c4nd1d473-g3n3r4710n m0du135, 17 15 1mp0r74n7 70 f1r57 und3r574nd 0ur und3r1y1ng 455ump710n5 460u7 7h3 cr055w0rd-pu2213 pr0613m. f1r57, 455um3 7h47 cr055w0rd pu22135 4r3 cr3473d 6y r3p3473d1y ch0051ng w0rd5 f0r 7h3 51075 4cc0rd1ng 70 4 p4r71cu14r cr3470r'5 d157r16u710n (1gn0r3 c1u35 4nd cr0551ng c0n57r41n75 f0r n0w). 4f73r ch0051ng 7h3 w0rd5, 1f 7h3 cr0551ng c0n57r41n75 4r3 54715f13d, 7h3n 7h3 cr3470r k33p5 7h3 pu2213. 07h3rw153, 7h3 cr3470r dr4w5 4g41n. n0rm41121ng 70 4cc0un7 f0r 411 7h3 1113g41 pu22135 g3n3r473d g1v35 u5 4 pr06461117y d157r16u710n 0v3r 13g41 pu22135. n0w, 5upp053 7h47 f0r 34ch 5107 1n 4 pu2213, w3 h4d 4 pr06461117y d157r16u710n 0v3r p0551613 w0rd5 f0r 7h3 5107 g1v3n 7h3 c1u3. 7h3n, w3 c0u1d 7ry 70 501v3 0n3 0f 4 num63r 0f pr0646111571c 0p71m124710n pr0613m5 70 pr0duc3 7h3 ``6357'' f111 0f 7h3 gr1d. 1n 0ur w0rk, w3 d3f1n3 ``6357'' 45 7h3 pu2213 w17h 7h3 m4x1mum 3xp3c73d num63r 0f 74rg375 1n c0mm0n w17h 7h3 cr3470r'5 501u710n: 7h3 m4x1mum 3xp3c73d 0v3r14p. w3 w111 d15cu55 7h15 0p71m124710n m0r3 1n 4 f0110w1ng 53c710n, 6u7 f0r n0w 17 15 1mp0r74n7 0n1y 70 533 7h47 w3 w0u1d 11k3 70 7h1nk 0f c4nd1d473 g3n3r4710n 45 35746115h1ng pr06461117y d157r16u710n5 0v3r p0551613 501u710n5. w3 w111 n3x7 d15cu55 h0w 1nd1v1du41 m0du135 c4n cr3473 4ppr0x1m4710n5 70 7h353 d157r16u710n5, h0w w3 c4n c0m61n3 7h3m 1n70 4 un1f13d d157r16u710n5, 4nd 7h3n f1n411y h0w w3 c4n 534rch 70 f1nd 4 g00d 501u710n 70 7h3 0p71m124710n pr0613m. 7h3 f1r57 573p 15 70 h4v3 34ch m0du13 g3n3r473 c4nd1d4735 f0r 34ch c1u3, g1v3n 7h3 74rg37 13ng7h. 34ch m0du13 r37urn5 4 c0nf1d3nc3 5c0r3 (h0w 5ur3 17 15 7h47 7h3 4n5w3r 1135 1n 175 1157), 4nd 4 w31gh73d 1157 7h3 m0du13 r37urn5 4 1.0 c0nf1d3nc3 1n 175 1157, 4nd g1v35 h1gh3r w31gh7 70 7h3 p3r50n 0n 7h3 5h0w w17h 7h3 g1v3n 1457 n4m3, wh113 g1v1ng 10w3r w31gh7 70 07h3r c457 m3m63r5. n073 7h47 m057 0f 7h3 m0du135 w111 n07 63 4613 70 g3n3r473 4c7u41 pr06461117135 d157r16u710n5 f0r 7h3 74rg375, 4nd w111 n33d 70 m4k3 4ppr0x1m4710n5. 7h3 m3rg1ng 573p d15cu553d n3x7 w111 4773mp7 70 4cc0un7 f0r 7h3 3rr0r 1n 7h353 3571m4735 6y 73571ng 0n 7r41n1ng d474, 4nd 4dju571ng 5c411ng p4r4m373r5 70 c0mp3n5473. 17 15 1mp0r74n7 f0r m0du135 70 63 c0n51573n7, 4nd 70 g1v3 m0r3 11k31y c4nd1d4735 m0r3 w31gh7. 4150, 7h3 63773r c0n7r01 4 m0du13 3x3r75 0v3r 7h3 0v3r411 c0nf1d3nc3 5c0r3 wh3n unc3r741n, 7h3 m0r3 7h3 m3rg3r w111 ``7ru57'' 7h3 m0du13'5 pr3d1c710n5. 1n 411, w3 6u117 30 d1ff3r3n7 m0du135, m4ny 0f wh1ch 4r3 d35cr163d 6r13f1y 6310w. 70 g37 50m3 53n53 0f 7h3 c0n7r16u710n 0f 7h3 m4j0r c0n741n1ng 5374 c1u35. 7h353 pu22135 w3r3 dr4wn fr0m 7h3 54m3 50urc35 45 7h3 7357 pu22135, 73n fr0m 34ch. f0r 34ch m0du13, w3 1157 53v3r41 m345ur35 0f p3rf0rm4nc3: 7h3 p3rc3n74g3 0f c1u35 7h47 7h3 m0du13 gu3553d 47, 7h3 p3rc3n74g3 0f 7h3 71m3 7h3 74rg37 w45 1n 7h3 m0du13'5 c4nd1d473 1157, 7h3 4v3r4g3 13ng7h 0f 7h3 r37urn3d 11575, 4nd 7h3 p3rc3n74g3 0f c1u35 7h3 m0du13 ``w0n''---17 h4d 7h3 c0rr3c7 4n5w3r w31gh73d h1gh3r 7h4n 411 07h3r m0du135. 7h15 f1n41 57471571c 15 4n 1mp0r74n7 m345ur3 0f 7h3 m0du13'5 c0n7r16u710n 70 7h3 5y573m. f0r 3x4mp13, 7h3 w0rd1157-61g m0du13 g3n3r4735 0v3r 100,000 w0rd5 f0r 50m3 71m3). h0w3v3r, 51nc3 17 g3n3r4735 50 m4ny, 7h3 1nd1v1du41 w31gh7 g1v3n 70 7h3 74rg37 15 u5u411y h1gh3r 7h4n 7h47 4551gn3d 6y 07h3r 4n07h3r w4y 0f 100k1ng 47 7h3 c0n7r16u710n 0f 7h3 m0du135 15 70 c0n51d3r 7h3 pr06461117y 4551gn3d 70 34ch 74rg37 g1v3n 7h3 c1u35. 1d3411y, w3 w0u1d 11k3 411 74rg375 70 h4v3 pr06461117y 1. 1n g3n3r41, w3 w4n7 70 m4x1m123 7h3 pr0duc7 0f 7h3 pr06461117135 4551gn3d 70 7h3 74rg375, 51nc3 7h15 9u4n717y 15 d1r3c71y r31473d 70 wh47 7h3 r3pr353n75 7h3 pr06461117y 4551gn3d 6y 7h3 61gr4m m0du13 (d35cr163d 1473r). 7h15 pr06461117y 15 10w f0r 411 74rg375, 6u7 v3ry 10w f0r 7h3 h4rd 74rg375. 45 w3 4dd gr0up5 0f m0du135, 7h3 3ff3c7 0n 7h3 pr06461117135 4551gn3d 70 74rg375 c4n 63 533n 45 4 10w3r1ng 0f 7h3 curv3, wh1ch c0rr35p0nd5 70 4551gn1ng m0r3 4nd m0r3 pr06461117y 70 7h3 74rg37. n073 7h3 14rg3 1ncr3453 du3 70 7h3 3x4c7 m47ch m0du13. f1n411y, n071c3 7h47 7h3r3 15 4 5m411 53gm3n7 7h47 w3 d0 v3ry p00r1y 0n---7h3 74rg375 7h47 n0 m0du13 07h3r 7h4n 61gr4m r37urn5. w3 w111 1473r 1n7r0duc3 3x73n510n5 70 7h3 5y573m 7h47 h31p w17h 7h15 r4ng3. 4dd3d 5h0w5 7h47 d1ff3r3n7 7yp35 0f m0du135 m4k3 d1ff3r3n7 r37urn 411 w0rd5 0f 7h3 c0rr3c7 13ng7h fr0m 53v3r41 d1c710n4r135. w0rd1157 c0n741n5 4 1157 0f 655,000 73rm5 fr0m 4 w1d3 v4r137y 0f 50urc35, 1nc1ud1ng 0n11n3 73x75, 3nc1y0p3d145 4nd d1c710n4r135. w0rd1157-61g c0n741n5 3v3ry7h1ng 1n w0rd1157, 45 w311 45 m4ny c0n57ruc73d `73rm5', pr0duc3d 6y c0m61n1ng r31473d 3n7r135 1n d47464535. 7h15 1nc1ud35 c0m61n1ng f1r57 4nd 1457 n4m35, 45 w311 45 m3rg1ng 4dj4c3n7 w0rd5 fr0m c1u35 1n 7h3 cwd6. w0rd1157-61g c0n741n5 0v3r 2.1 m11110n 73rm5. w0rd1157-cwd6 c0n741n5 7h3 58,000 un19u3 74rg375 1n 7h3 cwd6, 4nd r37urn5 411 74rg375 0f 7h3 4ppr0pr1473 13ng7h, r3g4rd1355 0f 7h3 c1u3. 17 w31gh75 7h3m w17h 3571m4735 0f 7h31r ``pr10r'' pr06461117135 45 74rg375 0f 4r617r4ry c1u35. 13ng7h 4550c1473d w17h 7h15 c1u3 1n 7h3 cwd6. c0nf1d3nc3 15 6453d 0n 4 64y3514n c41cu14710n 1nv01v1ng 7h3 num63r 0f 3x4c7 m47ch35 0f c0rr3c7 4nd 1nc0rr3c7 13ng7h5. 7r4n5f0rm4710n5 wh1ch, wh3n 4pp113d 70 c1u3-74rg37 p41r5 1n 7h3 cwd6, g3n3r4735 07h3r c1u3-74rg37 p41r5 1n 7h3 d4746453. wh3n f4c3d w17h 4 n3w c1u3, 17 4pp1135 411 4pp11c4613 7r4n5f0rm4710n5 4nd r37urn5 7h3 r35u175, w31gh73d 6453d 0n 7h3 pr3v10u5 pr3c1510n/r3c411 0f 7h353 7r4n5f0rm4710n5. 7r4n5f0rm4710n5 1n 7h3 d4746453 1nc1ud3 51ng13-w0rd 5u65717u710n, r3m0v1ng 0n3 phr453 fr0m 7h3 63g1nn1ng 0r 3nd 0f 4 c1u3 4nd 4dd1ng 4n07h3r phr453 70 7h3 63g1nn1ng 0r 3nd 0f 7h3 c1u3, d3p1ur41121ng 4 w0rd 1n 7h3 c1u3 4nd p1ur41121ng 7h3 4550c1473d 74rg37, 4nd 07h3r5. 7h3 f0110w1ng 15 4 1157 0f 53v3r41 n0n-7r1v141 3x4mp135 fr0m 7h3 73n5 0f 7h0u54nd5 0f 7r4n5f0rm4710n5 134rn3d: cr055w0rd c1u35 pr353n7 4n 1n73r3571ng ch4113ng3 70 7r4d1710n41 1nf0rm4710n r37r13v41 (1r) 73chn19u35. wh113 9u3r135 0f 51m114r 13ng7h 70 c1u35 h4v3 633n 57ud13d, 7h3 ``d0cum3n75'' 70 63 r37urn3d 4r3 9u173 d1ff3r3n7 (w0rd5 0r 5h0r7 539u3nc35 0f w0rd5). 1n 4dd1710n, 7h3 9u3r135 7h3m531v35 4r3 0f73n purp0531y phr453d 70 63 4m61gu0u5, 4nd n3v3r 5h4r3 w0rd5 w17h 7h3 ``d0cum3n75'' 70 63 r37urn3d. d35p173 7h353 d1ff3r3nc35, 17 533m3d n47ur41 70 7ry 4 v4r137y 0f 3x1571ng 1r 73chn19u35 0v3r 53v3r41 d0cum3n7 c0113c710n5. 7h15 m0du13 15 6453d 0n 4n 1nd3x3d 537 0f 3ncyc10p3d14 4r71c135. f0r 34ch 9u3ry 73rm, w3 c0mpu73 4 d157r16u710n 0f 73rm5 ``c1053'' 70 7h3 9u3ry 73rm 1n 7h3 73x7. 4 73rm 15 c0un73d $10-k$ 71m35 1n 7h15 d157r16u710n f0r 3v3ry 71m3 17 4pp34r5 47 4 d1574nc3 0f $k<10$ w0rd5 4w4y fr0m 7h3 9u3ry 73rm. 4 73rm 15 4150 c0un73d 0nc3 1f 17 4pp34r5 1n 4n 4r71c13 f0r wh1ch 7h3 9u3ry 73rm 15 1n 7h3 71713, 0r v1c3 v3r54. 73rm5 0f 7h3 c0rr3c7 74rg37 13ng7h 4r3 4551gn3d 5c0r35 pr0p0r710n41 70 7h31r fr39u3nc135 1n 7h3 ``c1053'' d157r16u710n, d1v1d3d 6y 7h31r fr39u3ncy 1n 7h3 c0rpu5. 7h3 d157r16u710n 0f 5c0r35 15 n0rm41123d 70 1. 1f 4 9u3ry c0n741n5 mu171p13 73rm5, 7h3 5c0r3 d157r16u710n5 4r3 c0m61n3d 11n34r1y 4cc0rd1ng 70 7h3 10g 1nv3r53 fr39u3ncy 0f 7h3 9u3ry 73rm5 1n 7h3 c0rpu5. 1f 7h3 9u3ry c0n741n5 v3ry c0mm0n 73rm5 5uch 45 ``45'' 4nd ``4nd,'' 7h3y 4r3 1gn0r3d. 4 v3c70r 5p4c3 w17h 0n3 d1m3n510n f0r 3v3ry w0rd 1n 7h3 d1c710n4ry. 4 c1u3 15 r3pr353n73d 45 4 v3c70r 1n 7h15 5p4c3. f0r 34ch w0rd $w$ 4 c1u3 c0n741n5, 17 g375 4 c0mp0n3n7 1n d1m3n510n $w$ 0f m4gn17ud3 f0r 4 c1u3 $c$, w3 f1nd 411 c1u35 1n 7h3 cwd6 7h47 5h4r3 w0rd5 w17h $c$. f0r 34ch 5uch c1u3, w3 g1v3 175 74rg37 4 w31gh7 6453d 0n 7h3 d07 pr0duc7 0f 7h3 c1u3 w17h $c$. 7h3 4551gn3d w31gh7 15 g30m37r1c411y 7h15 d07 pr0duc7. v3c70r 5p4c3 m0d31 7h47 u535 51ngu14r v41u3 d3c0mp051710n 70 1d3n71fy c0rr314710n5 637w33n w0rd5. 151 h45 633n 5ucc355fu11y 4pp113d 70 7h3 wh1ch 15 c10531y r31473d 70 501v1ng cr055w0rd c1u35. 0ur 151 m0du135 w3r3 7r41n3d 0n cwd6 (411 c1u35 w17h 7h3 54m3 74rg37 w3r3 7r3473d 45 4 d0cum3n7) 4nd 53p4r4731y 0n 4n 0n11n3 3ncyc10p3d14 4nd r37urn3d 7h3 c105357 w0rd5 (6y c051n3) w17h 34ch c1u3. 7h3 d1jk57r4 m0du135 w3r3 1n5p1r3d 6y 7h3 1n7u1710n 7h47 r31473d w0rd5 317h3r c0-0ccur w17h 0n3 4n07h3r 0r c0-0ccur w17h 51m114r w0rd5. 7h15 5ugg3575 4 m345ur3 0f r31473dn355 6453d 0n gr4ph d1574nc3. fr0m 4 5313c73d 537 0f 73x7 d47464535, 7h3 m0du13 6u11d5 4 w31gh73d d1r3c73d gr4ph 0n 7h3 537 0f 411 73rm5. f0r 34ch d4746453 $d$ 4nd 34ch p41r 0f 73rm5 $(7,u)$ 7h47 c0-0ccur 1n 7h3 54m3 d0cum3n7, w3 p14c3 4n 3dg3 fr0m $7$ 70 $u$ 1n 7h3 gr4ph w17h w31gh7, f0r 4 0n3-w0rd c1u3 $7$, w3 4551gn 4 73rm $u$ 4 5c0r3 0f w3 f1nd 7h3 h1gh357 5c0r1ng 73rm5 w17h 4 5h0r7357-p47h-11k3 534rch. f0r 4 mu171-w0rd c1u3, w3 6r34k 7h3 c1u3 1n70 1nd1v1du41 73rm5 4nd 4dd 7h3 5c0r35 45 c0mpu73d 460v3. 7h3 f0ur d1jk57r4 m0du135 1n 0ur 5y573m u53 v4r14n75 0f 7h15 73chn19u3. f0r d47464535, w3 u53d 4n 3ncyc10p3d14 1nd3x, 7w0 7h354ur1, 4 d4746453 0f w0rdf0rm5 4nd 7h3 cwd6. 5h0w5. 7h15 m0du13 100k5 f0r 4 num63r 0f p4773rn5 1n 7h3 c1u3 (3.g. 9u073d 717135 45 1n c0py 0f 7h3 d4746453 1n 4 v4r137y 0f f0rm5. 7h353 m0du135 u53 51mp13 p4773rn m47ch1ng 0f 7h3 c1u3 (100k1ng f0r k3yw0rd5 ``c17y'', ``4u7h0r'',``64nd'' 4nd 07h3r5 45 1n d4746453. 7h3 1173r4ry d4746453 15 cu113d fr0m 607h 0n11n3 4nd 3ncyc10p3d14 r350urc35. 7h3 g30gr4phy d4746453 15 fr0m 7h3 g377y 1nf0rm4710n 1n5717u73, w17h 4dd1710n41 d474 5upp113d fr0m 0n11n3 11575. 7h3r3 4r3 f0ur d1571nc7 5yn0nym m0du135, 6453d 0n 7hr33 d1ff3r3n7 100k5 f0r r007 f0rm5 0f w0rd5 1n 7h3 c1u3, 4nd 7h3n f1nd5 4 v4r137y 0f 0f r313v4nc3 f33d64ck 15 u53d 70 g3n3r473 11575 0f 5yn0nym5 0f 5yn0nym5. f1n411y, 1f n3c3554ry, 7h3 f0rm5 0f 7h3 r31473d w0rd5 4r3 c0v3r73d 64ck 70 7h3 f0rm 0f 7h3 0r1g1n41 c1u3 w0rd (num63r, 73n53, 0v3r f1v3 p3rc3n7 0f 411 c1u35 1n cwd6 h4v3 4 614nk 1n 7h3m. w3 534rch3d 4 v4r137y 0f d47464535 70 f1nd c1u3 p4773rn5 w17h 4 m1551ng w0rd (mu51c, g30gr4phy, m0v135, 1173r4ry 4nd 9u0735). f0r 3x4mp13, 4ny f0ur ch4r473r5 70 f111 7h3 614nk5, 1nc1ud1ng mu171p13 w0rd5. 1n 50m3 0f 0ur pr373575 w3 4150 r4n 7h353 534rch35 0v3r m0r3 g3n3r41 50urc35 0f 73x7 11k3 3ncyc10p3d145 4nd 4rch1v3d n3w5 f33d5, 6u7 f0r 3ff1c13ncy, w3 13f7 7h353 0u7 0f 7h3 f1n41 run5. ``k1nd 0f'' c1u35 4r3 51m114r 70 f111-1n-7h3-614nk c1u35 1n 7h47 7h3y 1nv01v3 p4773rn m47ch1ng 0v3r 5h0r7 phr4535. w3 1d3n71f13d 0v3r 50 cu35 7h47 1nd1c473 4 c1u3 0f 7h15 7yp3, f0r 3x4mp13, 4nd 4f73r 34ch 3xp3r7 m0du13 h45 g3n3r473d 4 w31gh73d c4nd1d473 1157, w3 mu57 50m3h0w m3rg3 7h353 1n70 4 un1f13d c4nd1d473 1157 w17h 4 c0mm0n w31gh71ng 5ch3m3 f0r 7h3 501v3r. 7h15 pr0613m 15 51m114r 70 7h3 pr0613m f4c1ng m374-cr4w13r 534rch 3ng1n35 1n 7h47 53p4r4731y w31gh73d r37urn 11575 mu57 63 c0m61n3d 1n 4 53n51613 w4y. 4n 4dv4n74g3 0f 7h15 d0m41n 15 r34dy 4cc355 70 pr3c153 4nd 46und4n7 7r41n1ng d474. f0r 4 g1v3n c1u3, 34ch 3xp3r7 m0du13 $m$ r37urn5 4 w31gh73d 537 0f c4nd1d4735 4nd 4 num3r1c41 13v31 0f c0nf1d3nc3 7h47 7h3 c0rr3c7 74rg37 15 1n 7h15 537. f0r 34ch 3xp3r7 m0du13 $m$, w3 537 7hr33 r341 c1u3, w3 r3w31gh7 7h3 c4nd1d473 537 6y r4151ng 34ch w31gh7 70 7h3 pr06461117y d157r16u710n 0v3r c4nd1d4735, w3 11n34r1y c0m61n3 7h3 m0d1f13d c4nd1d473 5375 0f 411 7h3 m0du135 w31gh73d 6y 7h31r m0d1f13d c0nf1d3nc3 13v315, 4nd n0rm41123 7h3 5um 70 1. c0n7r01 0v3r h0w 7h3 1nf0rm4710n r37urn3d 6y 4n 3xp3r7 m0du13 15 1nc0rp0r473d 1n70 7h3 f1n41 c4nd1d473 1157. w3 537 7h353 p4r4m373r5 u51ng 4 n41v3 h111-c11m61ng 73chn19u3. 7h3 06j3c71v3 func710n f0r 0p71m124710n 15 7h3 4v3r4g3 10g pr06461117y 4551gn3d 70 7h3 c0rr3c7 74rg37. 7h15 c0rr35p0nd5 70 m4x1m121ng 7h3 4v3r4g3 10g pr06461117y 4551gn3d 6y 7h3 501v3r 70 7h3 c0rr3c7 pu2213 f111-1n, 51nc3 1n 0ur m0d31 7h3 pr06461117y 0f 4 pu2213 501u710n 15 pr0p0r710n41 70 7h3 pr0duc7 0f 7h3 pr10r pr06461117135 0n 7h3 4n5w3r5 1n 34ch 0f 7h3 51075. 7h3 0p71m41 v41u3 w3 4ch13v3 0n 7h3 70 pu2213 4f73r r341121ng h0w much r3p371710n 0ccur5 1n cr055w0rd5, 1n 607h 74rg375 4nd c1u35, 4nd 7h3r3f0r3 h0w w311 7h3 cwd6 c0v3r5 7h3 d0m41n, 0n3 m1gh7 w0nd3r wh37h3r 7h15 c0v3r4g3 15 3n0ugh 70 c0n57r41n 7h3 d0m41n 70 5uch 4n 3x73n7 7h47 7h3r3 15 n07 much f0r 7h3 gr1d-f1111ng 41g0r17hm 70 d0. w3 d1d n07 f1nd 7h15 70 63 7h3 c453. 51mp11571c gr1d f1111ng y131d3d 0n1y m3d10cr3 r35u175. 45 4 m345ur3 0f 7h3 745k 13f7 70 7h3 gr1d-f1111ng 41g0r17hm, 0n 7h3 f1r57 173r4710n 0f 501v1ng, 0f 74rg375 4r3 1n 7h3 70p 0f 7h3 c4nd1d473 1157 f0r 7h31r 5107. h0w3v3r, 7h3 gr1d-f1111ng 41g0r17hm 15 4613 70 r4153 7h15 70 f1111ng 45 4n 0p71m124710n pr0613m. 1n p4r71cu14r, 7h3 4cr055 4nd d0wn 13773r 1n73r53c710n5 35746115h c0n57r41n75 0n h0w 7h3 gr1d c4n 63 f1113d, 4nd cr055w0rd-pu2213 f1111ng 15 0f73n c173d 45 4 c0n57r41n7 54715f4c710n pr0613m. h0w3v3r, 1n 0ur c453, w3 d0n'7 ju57 w4n7 70 f1nd ``6357'' f17. w3 c4n d3f1n3 ``6357'' 1n 53v3r41 d1ff3r3n7 w4y5, 6u7 1n 7h353 73575 w3 4773mp73d 70 m4x1m123 7h3 3xp3c73d 0v3r14p w17h 7h3 cr3470r'5 501u710n, 1n 73rm5 0f w0rd5 c0rr3c7. 07h3r d3f1n1710n5 0f ``6357'' 1nc1ud3 m4x1m121ng 7h3 pr06461117y 0f g3771ng 7h3 3n71r3 pu2213 c0rr3c7, 0r m4x1m121ng 3xp3c73d 13773r 0v3r14p. 7h3 d3c1510n 70 u53 3xp3c73d w0rd 0v3r14p 15 m071v473d 6y 7h3 5c0r1ng 5y573m u53d 1n hum4n 70urn4m3n75 (533 6310w). 51nc3 f1nd1ng 7h3 0p71m41 501u710n 70 7h15 pr0613m 15 1n7r4c74613, w3 3mp10y 4 v4r137y 0f 3ff1c13n7 4ppr0x1m4710n5. 0ur pr06461117y m345ur3 4551gn5 pr06461117y 23r0 70 4 74rg37 7h47 15 5ugg3573d 6y n0 m0du13 4nd pr06461117y 23r0 70 411 501u710n5 c0n741n1ng 7h47 74rg37. 7h3r3f0r3, w3 n33d 70 4551gn n0n-23r0 pr06461117y 70 411 13773r 539u3nc35. c134r1y, 7h3r3 4r3 700 m4ny 70 4c7u411y 1157 3xp11c171y. w3 4ugm3n73d 7h3 501v3r 70 r3450n w17h pr06461117y d157r16u710n5 0v3r c4nd1d473 11575 7h47 4r3 1mp11c171y 4dd1710n41 c4nd1d4735 0nc3 7h3 501v3r c4n g1v3 7h3m m0r3 1nf0rm4710n 460u7 13773r pr06461117y d157r16u710n5 0v3r 7h3 5107. 7h3 m057 1mp0r74n7 0f 7h353 15 4 13773r 61gr4m m0du13, wh1ch ``g3n3r4735'' 411 p0551613 13773r 539u3nc35 0f 7h3 g1v3n 13ng7h 6y r37urn1ng 4 13773r 61gr4m d157r16u710n 0v3r 411 p0551613 57r1ng5, 134rn3d fr0m 7h3 cwd6. 63c4u53 7h3 61gr4m pr06461117135 4r3 u53d 7hr0ugh0u7 7h3 501u710n pr0c355, 7h15 m0du13 15 4c7u411y 71gh71y 1n73gr473d 1n70 7h3 501v3r 17531f. n0 m0du13 3xc3p7 61gr4m 15 r37urn1ng 7h3 74rg37. 1n 4 pr37357 run 0n 70 pu22135, 7h3 c1u3-74rg37 w17h 7h3 10w357 pr06461117y w45 71m35, 4nd 17 g375 4 p4r71cu14r1y 10w pr06461117y 63c4u53 0f 7h3 m4ny un11k31y 13773r p41r5 1n 7h3 74rg37. 0nc3 7h3 gr1d-f1111ng pr0c355 15 und3rw4y, w3 h4v3 pr06461117y d157r16u710n5 f0r 34ch 13773r 1n 7h353 10ng3r 74rg375 4nd 7h15 c4n 11m17 0ur 534rch f0r c4nd1d4735. 70 4ddr355 10ng3r, mu171w0rd 74rg375, w3 cr3473d fr33-574nd1ng 1mp11c17 d157r16u710n m0du135. 34ch 1mp11c17 d157r16u710n m0du13 74k35 4 13773r pr06461117y d157r16u710n f0r 34ch 13773r 0f 7h3 5107 (c0mpu73d w17h1n 7h3 501v3r), 4nd r37urn5 w31gh73d c4nd1d473 11575. 7h353 11575 4r3 7h3n 4dd3d 70 7h3 pr3v10u5 c4nd1d473 11575, 4nd 7h3 gr1d-f1111ng 41g0r17hm c0n71nu35. 7h15 pr0c355 0f g3771ng n3w c4nd1d4735 c4n h4pp3n 53v3r41 71m35 dur1ng 7h3 501u710n 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