Randomness

Basically, there is an LCG being used to generate the string of numbers. It takes a seed, multiplies it with "a", adds "b", and then takes that mod a prime "p".

We don't know any of these values however. It generates a list of numbers from a starting random seed this way, and then xors each character of the flag to get a new list.

We know the flag format is "FwordCTF{", so we can start by XORing these characters to get the actual string of LCG generated numbers: [6680465291011788181, 5100570103593250306, 5906808313299165163, 1965917782737693404, 9056785591048864532, 1829758495155458643, 6790868899161600099, 1596515234863242753, 1542626304251881944] Now, we do some modular maths stuff:

6680465291011788181 a + b = 5100570103593250306 5906808313299165163 a + b = 1965917782737693404(all of these are taken mod p of course) 1596515234863242753 * a + b = 154262630425188194

We can subtract the equations from each other to get rid of the b: (6680465291011788181 - 5906808313299165163)a = 5100570103593250306 - 1965917782737693404 (5906808313299165163 - 1596515234863242753)a = 1965917782737693404 - 1542626304251881944

Simplifying:

773656977712623018a = 3134652320855556902
4310293078435922410a = 423291478485811460

Im using these from now because idk why the others arent working

5194353664298357346a = 53888930611360809
2265916691887264433a = 233243260292215890

Solve script:

p = 9444729917070668893
a = 7762244320486225184
b = 731234830430177597
X=[6680465291011788181]
c=0
while c<73:
    X.append((a*X[c]+b)%p)
    c+=1
o = ""
bleh = [6680465291011788243, 5100570103593250421, 5906808313299165060, 1965917782737693358, 9056785591048864624, 1829758495155458576, 6790868899161600055, 1596515234863242823, 1542626304251881891, 8104506805098882719, 1007224930233032567, 3734079115803760073, 7849173324645439452, 8732100672289854567, 5175836768003400781, 1424151033239111460, 1199105222454059911, 1664215650827157105, 9008386209424299800, 484211781780518254, 2512932525834758909, 270126439443651096, 3183206577049996011, 3279047721488346724, 3454276445316959481, 2818682432513461896, 1198230090827197024, 6998819122186572678, 9203565046169681246, 2238598386754583423, 467098371562174956, 5653529053698720276, 2015452976526330232, 2551998512666399199, 7069788985925185031, 5960242873564733830, 8674335448210427234, 8831855692621741517, 6943582577462564728, 2159276184039111694, 8688468346396385461, 440650407436900405, 6995840816131325250, 4637034747767556143, 3074066864500201630, 3089580429060692934, 2636919931902761401, 5048459994558771200, 6575450200614822046, 666932631675155892, 3355067815387388102, 3494943856508019168, 3208598838604422062, 1651654978658074504, 1031697828323732832, 3522460087077276636, 6871524519121580258, 6523448658792083486, 127306226106122213, 147467006327822722, 3241736541061054362, 8781435214433157730, 7267936298215752831, 3411059229428517472, 6597995245035183751, 1256684894889830824, 6272257692365676430, 303437276610446361, 8730871523914292433, 6472487383860532571, 5022165523149187811, 4462701447753878703, 1590013093628585660, 4874224067795612706]
for i in range(len(bleh)):
    o += chr(bleh[i] ^^ X[i])
print(o)

Flag: FwordCTF{LCG_easy_to_break!That_was_a_mistake_choosing_it_as_a_secure_way}