# Broken Invitation
### Solution
So this is an RSA challenge where we are given 3 moduli and 3 ciphertexts.
We are also told that the public exponent used e=3.
Since the same plaintext is sent to 3 people the plaintext is susceptible to a Hastad's Broadcast attack.
Here is my implementation of the attack to get the flag.
```
import math
from sympy.functions.elementary.miscellaneous import cbrt
from Crypto.Util.number import long_to_bytes
from sympy.ntheory.modular import crt

def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(
lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)

def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise ValueError
return x % m

n1 = 924506488821656685683910901697171383575761384058997452768161613244316449994435541406042874502024337501621283644549497446327156438552952982774526792356194523541927862677535193330297876054850415513120023262998063090052673978470859715791539316871
n2 = 88950937117255391223977435698486265468789676087383749025900580476857958577458361251855358598960638495873663408330100969812759959637583297211068274793121379054729169786199319454344007481804946263873110263761707375758247409
n3 = 46120424124283407631877739918717497745499448442081604908717069311339764302716539899549382470988469546914660420190473379187397425725302899111432304753418508501904277711772373006543099077921097373552317823052570252978144835744949941108416471431004677
c1 = 388825822870813587493154615238012547494666151428446904627095554917874019374474234421038941934804209410745453928513883448152675699305596595130706561989245940306390625802518940063853046813376063232724848204735684760377804361178651844505881089386
c2 = 4132099145786478580573701281040504422332184017792293421890701268012883566853254627860193724809808999005233349057847375798626123207766954266507411969802654226242300965967704040276250440511648395550180630597000941240639594
c3 = 43690392479478733802175619151519523453201200942800536494806512990350504964044289998495399805335942227586694852363272883331080188161308470522306485983861114557449204887644890409995598852299488628159224012730372865280540944897915435604154376354144428
e = 3
N = n1 * n2 * n3
pt_cubed = crt([n3,n1,n2],[c3,c1,c2])[0]
pt = cbrt(pt_cubed)
flag = str(long_to_bytes(pt)[::-1])
flag = flag[2:-1]
print(flag)
```