Writeup T0t13nt | Cyber Grabs CTF | Catégorie crypto | [Electro/EN]

from sympy import totient
from tqdm import *

flag = "REDACTED"

def functor(n):
    val = 0
    for j in tqdm(range(1,n+1)):
        for i in range(1,j+1):
            val += j//i * totient(i)
            print(val,j//i,j,i,totient(i))
    return val

lest = []
for i in flag:
    print(i)
    lest.append(functor(ord(i)*6969696969))

print(lest)

import string

# Challenge's data
ct = [54751499983812600001595164999947606, 99964672809872376546137976728298625, 53109066146380481534971079770844564, 58137259942365444979479997549034855, 83599752542227961885740894770768516, 61659800043905527133538302215438384, 83599752542227961885740894770768516, 51499811650564080459894297372806965, 53109066146380481534971079770844564, 85819100646121058196943447618203070, 105003982813844976161353898313196914, 8400749730877624158255771399988559, 6240424741484609266392009977454864, 73075186383278314052649120872243371, 7485157899144949411682111055590430, 48379486424936974614387887472243260, 59881263192906899425738121667861480, 90374940243693329303922258576171375, 75104938249367345681206971604866080, 54751499983812600001595164999947606, 9388117281207654321254731172830840, 6638633268326718341544242944266781, 6240424741484609266392009977454864, 75104938249367345681206971604866080, 32264483340980969722020637386275054, 48379486424936974614387887472243260, 75104938249367345681206971604866080, 7485157899144949411682111055590430, 92712108866793232034695893485547544, 7485157899144949411682111055590430, 83599752542227961885740894770768516, 48379486424936974614387887472243260, 54751499983812600001595164999947606, 7485157899144949411682111055590430, 15496388930720047282261773301643045, 8400749730877624158255771399988559, 58137259942365444979479997549034855, 48379486424936974614387887472243260, 88077383691706059347171006086863620, 6240424741484609266392009977454864, 48379486424936974614387887472243260, 7934151132541799341665122998944580, 73075186383278314052649120872243371, 7934151132541799341665122998944580, 102463675364526450047988025312160540, 7485157899144949411682111055590430, 48379486424936974614387887472243260, 73075186383278314052649120872243371, 7485157899144949411682111055590430, 110209866655316842092627871164477875]


# Flag decoder function
def decoder(ct,guess):
	for elt in ct:
		_ = str(elt)
		if _ in guess.keys():
			print(guess[_],end="")
		else:
			print("-",end="")
	print("\n")


# Flag guessing support function
def guesser(ct,guess):
	pt =[]
	pt.extend(ct)
	pt.sort()
	for elt in pt:
		if str(elt) in guess.keys():
			print(elt,guess[str(elt)])
		else:
			print(elt)
# Clean solve
print("\n[+] Intended solution, sum_1_n (n//k)*phi(k)= n(n+1)/2 and sum of tringular number, from discord")
for elt in ct:
	for char in string.printable:
		n = ord(char)*6969696969
		res =  n*(n+1)*(n+2)//6
		if res == elt:
			print(char,end="")
			break		

print("\n")
print("[+] Unintended solution, cryptogaphic solving with known plaintext attack...")
print("[+] Assuming the flag format is cybergrabs{some_l337_words}")

guess = {

	"54751499983812600001595164999947606": "c",
	"99964672809872376546137976728298625":  "y",
	"53109066146380481534971079770844564":  "b",
	"58137259942365444979479997549034855":  "e",
	"83599752542227961885740894770768516":  "r",
	"61659800043905527133538302215438384":  "g",
	"51499811650564080459894297372806965":  "a",
	"85819100646121058196943447618203070":  "s",
	"105003982813844976161353898313196914": "{",
	"110209866655316842092627871164477875": "}"
}



decoder(ct,guess)

print("[+] After monitoring of functor(), functor() is an increasing function ...")
print("[+] Therefore ord('a') < ord('b') ==> functor(ord('a')) < functor(ord('b'))")
print()

steps = [
	("59881263192906899425738121667861480","f","Bound by 'e' and 'g'"),
	("102463675364526450047988025312160540","z","Bound by 'y' and '}'"),
	("48379486424936974614387887472243260","_","Just below 'a', as per ascii table"),
	("88077383691706059347171006086863620","t","Just after 's'"),
	("90374940243693329303922258576171375","u","Just after 't'"),
	("92712108866793232034695893485547544","v","Just after 'u'"),
	("75104938249367345681206971604866080","n","because the flag show fu-c"),
	("73075186383278314052649120872243371","m","Just below 'n'"),
	("7485157899144949411682111055590430","3","1337 speaks for matching 'e'"),
	("6240424741484609266392009977454864","0","133t speak for matching 'o' in 'to'"),
	("6638633268326718341544242944266781","1","Just after '0'"),
	("7934151132541799341665122998944580","4","Just after '3'"),
	("8400749730877624158255771399988559","5","Just after '4'"),
	("9388117281207654321254731172830840","7","Just after '5'"),
	("15496388930720047282261773301643045","A","To make cease"),
	("32264483340980969722020637386275054","S","to make functions")
]

for a,b,c in steps:
	print("-"*32)
	print("[+] Sorting ciphered element ...")
	guesser(ct,guess)
	print("[+] Guessed ", a , " is ", b , " because ", c )
	guess[str(a)]=b
	decoder(ct,guess)
	input("Show next guess ...")