HackTheBox Spooky RSA Challenge

Explore the basics of cybersecurity in the Spooky RSA Challenge on Hack The Box. This easy-level Challenge introduces encryption reversal and file handling concepts in a clear and accessible way, perfect for beginners.

https://app.hackthebox.com/challenges/418

Description

It was a Sunday evening when, after years, you managed to understand how RSA works. Unfortunately, that changed when the worst villain ever decided to dress up like RSA and scare people who wanted to learn more about cryptography. But his custom uniform has a hole in it. Can you find it?

Exploitation

#!/usr/bin/env python3
from math import gcd
from Crypto.Util.number import long_to_bytes

N = 23252667157599516940129524769090828719982590926217686828297820221246528288024986185770032891432071416316776607472816043745785945382619303771286924656092974519197669053189283351571920071432553222222811904112119520974410020093306071010335958643236508606549664330684556056421228904824554943559829654154540793885983689462338911148618911233437943092856313175212883771802928968521215461427230178865304889974060408714941809216551397552099050566216607216463931428967751885004128977314044993037370392135272264982092147566078177173327860726953745529225163314733863792635537495622731398807790511518482833382759873192115192207209
e1 = 13130317383799359924397818711045172877651070470639872331555061566871077024416132122821689879197166729443692993224787531055068053553245916779683406195947939469930710138275745308571705318328750438377477058341710049450433868075025011970534711610887418427142999431981800104300319735079412330836192720430158369804693687507459455621592955618266507196962663247417904680299143606004651444970274693793668715761929296821908860947834841947073379537992600397854852337772316114987249254395674689638512533430273885970458183044843553777077752747556298072797820716079692849044148071698585069757021266842594074685187380985522959676924
c1 = 3276033314700994933236715546269096681595964054694634317877930652961630783669009686295177734678226788913957176667505963284895192875563765999040362544244408645923937742131293085082421535485813399270056524297324864682622089578866968706269063489779845211872503005591066652086230371845356855417702566514946373846876609725394545339840695130518357770158558391396835218039249572390662833461220605497534710914935522013573314984887838699014465554643808438475560847600079478934259045848291858470555503523718530137358192672530066755416937024529536303824075068992110042077005432280129307864841939511235555989308133055235385105960
e2 = 20883594128285008437725229014478679601366127938823960100219581029154081635436411892478004501333834114219976189312792835720670788637746570550119467812230092062199251164946197959206350494458367692847308442685450722126282132876286895613925612558140177853699821618151096670620765409968557233259334756429446973833981043722454375455334033442236036896820634662734963958738789068654435207820624411915045062084652483285735900502029367176441696762291709434815865847363600312665970290960775666366786471564595838531305478536744797611070398211876965476639913075928103807981832916853895307250848232566714169131101439494532639396872
c2 = 18023359039022070922496207692467909272905633400500071646677663883848372907925575359795644502829612958089930556811098737564701111791300315722656180784065385762079524349557515732188405944474314448560602595952205309214787356604461723684793632495397765839132359663293143446639091410994479947265462557919856471699351934094395015205994443217852376256039110600437586852484006845325143039405449700872936218023776566918818003785468900212143526790175840288515458337112681822830546618062507825380629100313042086810588864941567987823223444256356108148388871548275890051441470007397336976314029406010035567308845594636823378393001
diff = (c2 - c1) % N
p = gcd(diff, N)
q = N // p
assert p * q == N
m = (c1 - pow(p, e1, N)) % N
flag = long_to_bytes(m)
print(flag.decode())

Summary

The Spooky RSA Challenge on Hack The Box is an easy-level cryptography challenge that involves exploiting common modulus attacks in RSA encryption. Participants analyze two ciphertexts encrypted with different public exponents but the same modulus, use the greatest common divisor (GCD) to factorize the modulus, and recover the plaintext by leveraging modular arithmetic. By decrypting the message and extracting the flag, the challenge demonstrates the critical weakness of reusing the same modulus with different exponents in RSA, highlighting the importance of proper key management in cryptographic systems.