Crystal Ball

This system generates random numbers for its encryption keys. But how random is random, really? Watch the output long enough and you might see through the trick.

Below are 624 consecutive 32-bit outputs from the key generator. The next four outputs were used to derive the AES-128 key that encrypted the flag (4 x 32-bit words concatenated big-endian). Predict what comes next.

Generator outputs (624 x uint32):

82178386, 1831771319, 2017055984, 3864962434, 2573907513, 3997208305, 1830055415, 3839705926
2629337071, 1621923201, 3124994850, 3317367295, 2697172223, 4244780898, 4146086384, 1997577016
1423889158, 1695779503, 1566590341, 2984236442, 2870942905, 1751929166, 3104838656, 3966751670
3527303506, 3631812094, 1637798153, 3062105043, 2181908023, 2838534403, 1149697563, 1186548317
4262541068, 1078680453, 4177997269, 1078191273, 762698459, 2234402919, 1353584946, 1677528116
584259603, 2094176657, 1768470868, 1362946137, 2463075099, 4019312852, 2496295992, 2032736478
564458026, 4079533070, 4294781631, 3984634340, 2915469367, 2246854137, 32679994, 666969190
1683279381, 2842236941, 2955451305, 2355000720, 761415485, 2593983386, 4031846508, 1282596811
693067918, 1539851239, 3051516964, 2129078742, 1434249784, 1939606308, 1664614757, 3383630463
1897615024, 4193816130, 2424362046, 1112737424, 3535131173, 2322339283, 947626106, 2480917143
363549848, 1972227592, 3975447594, 1434182664, 2144123879, 3913561564, 823114709, 45770912
215999599, 657982666, 1195011210, 3468027773, 2541480138, 2293261761, 2973353201, 3195695871
2048981478, 1600783446, 2974455721, 2010969163, 184725281, 586627122, 2858030468, 1898467887
1025181292, 592448470, 1317454040, 3965324490, 544435114, 4013959785, 1885550281, 4137623871
1642481858, 2992946868, 689018636, 480290151, 1612262526, 2886318552, 2497735788, 151562091
1417247393, 764466865, 4182736268, 1792930890, 1188101424, 2801015553, 2289069366, 780369872
4162244029, 468978070, 229034945, 3269700837, 3270268263, 3698271009, 3046220160, 3617928455
2264949764, 1596990748, 1518686626, 642786858, 980183342, 2104354216, 469696995, 1840558166
4237367109, 1802099713, 3634405493, 1885714479, 1956900999, 3829653882, 2648005463, 2032752999
3975112703, 3211116977, 4098617070, 3503549651, 3189717999, 975353451, 1990912927, 2381523485
4220642754, 26893509, 1650140998, 665314080, 666028843, 3618904963, 1562770957, 2258548432
949906954, 1451534974, 3900476443, 3599409063, 801212677, 4109574978, 3147120161, 3732284930
3593362953, 2773592519, 1638593973, 2932375436, 1048363706, 380927288, 4238786088, 1371559763
4174097329, 3537696991, 1543702110, 4088086020, 3153232204, 3365488034, 3060974757, 3150621720
2686805022, 2492673363, 246350689, 2991234700, 2546534328, 2314453701, 2463516641, 4102261724
3660558951, 2344333610, 2280090663, 465796338, 2456063750, 1607367701, 532583095, 2262983439
3144719344, 1264688660, 2111017346, 543577409, 3614592049, 2060192896, 158860282, 2447043146
1728477061, 1404064980, 3922810874, 418546369, 3186624477, 912754827, 2773596532, 907368337
3652457422, 1357115234, 3773076187, 2440472721, 1659681529, 1699047979, 1821163953, 3129856321
1746613797, 2471797520, 3748805743, 4260408727, 3348820442, 2167854222, 3419529329, 1089356673
1715204679, 2045068071, 3409608289, 2804041711, 2689544427, 1574184993, 1167211477, 3809683646
2303924247, 3907414428, 3777156429, 739724797, 1520914756, 259523839, 3922768645, 3196109741
33608985, 332640596, 1798035144, 3671356727, 2118848326, 2090176901, 2708321743, 2352188030
1060979513, 3732777888, 3703475387, 1241937, 3397711590, 2122854871, 1836803400, 1524203040
3118707463, 2128791206, 906238909, 729714032, 3944069103, 1170387456, 4219439472, 3772258711
4083613577, 3509716782, 3987462391, 753963228, 1321097415, 250395216, 3612232716, 2433794147
4281176498, 2539990316, 2991950732, 1948064600, 2175305383, 3644527511, 1066532063, 1587686650
770216377, 3660090768, 439775495, 20301534, 1821460719, 185132862, 1046364381, 1281226273
2803834052, 1475238828, 1986428356, 1763569476, 2059459842, 2215449691, 3923343604, 2718661255
2343292147, 1187197816, 2234044381, 2434287033, 80846042, 1412000575, 1341802978, 373674021
4130787214, 3002416418, 3480735521, 2727818417, 140774118, 2895011853, 1594986959, 2257123749
4146220640, 1240053956, 1072597367, 630228904, 2110988398, 3579935318, 766073830, 1215574943
1245165691, 2111073014, 1043575640, 928109321, 4289768032, 3113322023, 3387189262, 1645913241
421565086, 2142464853, 2698465631, 3272573519, 2386598603, 4199177685, 4103359028, 2249330670
641578739, 517329281, 3873271974, 2092980930, 1592469460, 2115694217, 3884085240, 2955596961
3383720214, 2628918795, 115758207, 149297541, 2467454725, 2838111070, 442041376, 3591503241
3295268633, 2937726626, 1581677983, 2182346213, 2094970052, 119843372, 134046730, 431457112
2870745856, 599727582, 3077144215, 4121960288, 3359791351, 3755925887, 293703265, 3996568647
4176897487, 1920281379, 1255546138, 2791691817, 1631551897, 2219433014, 1672450773, 938849973
3418760483, 2584546159, 514758921, 1790956318, 2664248260, 1495175903, 3460163879, 1168841641
3731374290, 3906192761, 1932561746, 982432073, 1682129158, 3799083723, 716704035, 1644669053
987917313, 3755670738, 2986092948, 1126705507, 3993909658, 2828984343, 3428174073, 2556691846
3191192250, 1855362384, 398905508, 93868049, 3689275544, 1716879059, 1266104942, 3304981015
4077074573, 4140830921, 3743716251, 1772856690, 255045889, 1854872929, 3473532997, 3794919645
4007523162, 1546116197, 1253932476, 3002797995, 292795185, 958870050, 2892708479, 2788124211
2527071800, 1098440444, 399562937, 2214730285, 463815537, 2801924814, 3114449549, 44076497
2405652521, 1848147887, 3035348956, 3415068130, 3664990369, 2186313646, 1348750009, 84656220
1599989200, 1108141464, 1932159502, 1248772014, 800991879, 3144409918, 618187961, 2352627574
1084354733, 552708154, 3914687024, 73247526, 2442729476, 4270522502, 2209311636, 2661751110
2421540861, 917062254, 1065201103, 4165218765, 2666495381, 855900841, 1405711663, 62571314
3705148093, 2437347574, 762372603, 709994023, 3758803894, 89888331, 3077045121, 2207997151
1816378231, 1819983697, 1056957249, 2751415090, 549984854, 4238257311, 163907615, 26409096
3964249423, 41477929, 3328105772, 2148548872, 1325347054, 2782170891, 233599775, 1975464757
3215636868, 1959183192, 186462152, 3626020708, 1178405135, 1594882377, 1486768094, 4167066670
169343788, 3396200742, 1963979078, 3041555181, 4049162785, 3239437650, 426518024, 3951608084
3356742597, 4043430461, 2483293163, 4272340230, 2396704834, 3800908507, 369195836, 160975329
1127802820, 2008772505, 3536021253, 875279204, 3914144355, 415848104, 2475513811, 676096588
4020963970, 3587916023, 1230439017, 204408731, 2318883813, 730044748, 820469936, 238520504
3323440094, 575357331, 1858194560, 3521593828, 2230431888, 4281990816, 4152959661, 3966511867
3114813949, 2773199177, 300405294, 3217075522, 3992979652, 254751171, 3532838133, 924605903
3481115374, 699279379, 3710699405, 1451902452, 1972151795, 1518625292, 3462852694, 757225513
3054074174, 3649025133, 3749575452, 966834512, 3669294178, 3766941554, 3898535767, 407994562
885384734, 105898013, 2917130982, 1069793997, 730640080, 1769410951, 228523783, 3058837196
1640648808, 262757403, 3309421208, 2330911028, 3993964449, 2524076907, 1874740885, 1277703113
2116420634, 3085325642, 774499369, 769442402, 2367994246, 711503482, 3514115709, 661035689
1220340200, 2885731460, 879674657, 2761111681, 1709085055, 3446002925, 2145675458, 2947849412
3478014827, 554611566, 107710287, 4229263445, 2593509047, 1239967170, 2359502393, 2757438312
3611904715, 2065112977, 2250889345, 419189454, 2133399976, 993648906, 3564982319, 2564289207

Encrypted flag (AES-128-ECB, PKCS#7 padded, hex):

1704779e3fff727d40ac0187ecb48e572e82d8292306b0ed68ba58c182488172a47d1e0895a80ef0954dbfdf5b58d04b

Note: This challenge requires manual analysis. Automated tools will not help you solve it.