From edf148cb957e6f58d11aebe2b69dddd8f4c3d8f2 Mon Sep 17 00:00:00 2001 From: Omar Santos Date: Mon, 11 May 2020 01:56:21 -0400 Subject: [PATCH] updating challenges --- .../challenges/heavy_computation/encrypt.py | 124 ++++++++++++++++++ .../challenges/heavy_computation/flag.enc | 4 + 2 files changed, 128 insertions(+) create mode 100644 capture_the_flag/challenges/heavy_computation/encrypt.py create mode 100644 capture_the_flag/challenges/heavy_computation/flag.enc diff --git a/capture_the_flag/challenges/heavy_computation/encrypt.py b/capture_the_flag/challenges/heavy_computation/encrypt.py new file mode 100644 index 0000000..e78d6a6 --- /dev/null +++ b/capture_the_flag/challenges/heavy_computation/encrypt.py @@ -0,0 +1,124 @@ +Heavy computation(400) +Question: +A friend of mine handed me this script and challenged me to recover the flag. However, I started running it on my school cluster and everything is burning now... Help me please! + +Given files: +encrypt.py +from Crypto.Util.number import bytes_to_long, long_to_bytes +from Crypto.Cipher import AES +from Crypto.Util.Padding import pad +from secret import password, flag +from hashlib import sha256 + +NB_ITERATIONS = 10871177237854734092489348927 +e = 65538 + +#Old N : N = 16725961734830292192130856503318846470372809633859943564170796604233648911148664645199314305393113642834320744397102098813353759076302959550707448148205851497665038807780166936471173111197092391395808381534728287101705 + +N = 14968794114523720195251887716913440457986979987674770429103169854116498198112478103466085455257317270930523061714030307370028304505577267672733143013124254253285088080041831478700041394909740024011681885623055622400205 + + +def derive_key(password): + start = bytes_to_long(password) + + #Making sure I am safe from offline bruteforce attack + + for i in range(NB_ITERATIONS): + start = start ** e + start %= N + + #We are never too cautious let's make it harder + + key = 1 + for i in range(NB_ITERATIONS): + key = key ** e + key %= N + key *= start + key %= N + + return sha256(long_to_bytes(key)).digest() + + +assert(len(password) == 2) +assert(password.decode().isprintable()) + +key = derive_key(password) +IV = b"random_and_safe!" +cipher = AES.new(key, AES.MODE_CBC,IV) +enc = cipher.encrypt(pad(flag,16)) + +with open("flag.enc","wb") as output_file: + output_file.write(enc) +flag.enc(dump) + 0000 f4 d8 e5 a2 ac 80 6c e9 dc c1 ef 1e d5 c4 51 7c ......l.......Q| + 0010 e3 d8 84 1a d7 c0 77 c9 9c b0 f6 f0 ab 13 63 b0 ......w.......c. + 0020 f9 5e 8d cd 87 ce c7 d3 88 7a 4a 68 de a9 6f 96 .^.......zJh..o. + 0030 77 cf 1e a7 95 a0 f8 1c be 3a 66 f0 aa 73 2c 3e w........:f..s,> +Solution: +Outline: +(1) For preparartion, we calcurate Euler's totient of N by FactorDb( http://www.factordb.com/ ): + +N=5*23*61*701*3043975283150884175290138965903193067634156680289693153778518185326633105971710936004483047892546798724665417739250476586249010832824560305913279982496088828053414799963361876618585076997170323631281630177651847 + +(2) First part of the functuon "derive_key": + +for i in range(NB_ITERATIONS): + start = start ** e + start %= N +It is easily simplificated by Euler's theorem. + +start = pow(bytes_to_long(password),pow(e,NB_ITERATIONS,phi_N), N) +where phi_N is the totient of N, + +phi_N=(5-1)* (23-1)* (61-1)* (701-1)* (3043975283150884175290138965903193067634156680289693153778518185326633105971710936004483047892546798724665417739250476586249010832824560305913279982496088828053414799963361876618585076997170323631281630177651847-1) + +(3) Second Part of the functuon "derive_key": + + key = 1 + for i in range(NB_ITERATIONS): + key = key ** e + key %= N + key *= start + key %= N +We can replace it with the following (using "invert" function of gmpy2). + + inv_e = gmpy2.invert(e-1,phi_N) + key = pow(start, (pow(e,NB_ITERATIONS,phi_N)-1) * inv_e, N) +(4) Finally, We brute force the password and get the flag! + +Solver: +solve.py +from Crypto.Util.number import bytes_to_long, long_to_bytes +from Crypto.Cipher import AES +from Crypto.Util.Padding import pad +from hashlib import sha256 +import gmpy2 + +NB_ITERATIONS = 10871177237854734092489348927 +e = 65538 +N = 14968794114523720195251887716913440457986979987674770429103169854116498198112478103466085455257317270930523061714030307370028304505577267672733143013124254253285088080041831478700041394909740024011681885623055622400205 + +#Using FactorDB, we have N=5*23*61*701*3043975283150884175290138965903193067634156680289693153778518185326633105971710936004483047892546798724665417739250476586249010832824560305913279982496088828053414799963361876618585076997170323631281630177651847 +phi_N = (5-1)*(23-1)*(61-1)*(701-1)*(3043975283150884175290138965903193067634156680289693153778518185326633105971710936004483047892546798724665417739250476586249010832824560305913279982496088828053414799963361876618585076997170323631281630177651847-1) + +def derive_key(password): + start = bytes_to_long(password) + start = pow(start,pow(e,NB_ITERATIONS,phi_N), N) + inv_e = gmpy2.invert(e-1,phi_N) + key = pow(start, (pow(e,NB_ITERATIONS,phi_N)-1) * inv_e, N) + return sha256(long_to_bytes(key)).digest() + +with open('flag.enc','rb') as f: + flag_enc = f.read() + for i in range(0x20, 0x100): + for j in range(0x20, 0x100): + password = long_to_bytes(i) + long_to_bytes(j) + key = derive_key(password) + IV = b"random_and_safe!" + cipher = AES.new(key, AES.MODE_CBC,IV) + flag = cipher.decrypt(flag_enc) + if(flag[0:6] == b'shkCTF'): + print(flag.decode('utf-8')[0:flag.decode('utf-8').find('}')+1]) + break +Flag: +shkCTF{M4ths_0v3r_p4t13Nce_b4453d1f9f5386a1846e57a3ec95678f} diff --git a/capture_the_flag/challenges/heavy_computation/flag.enc b/capture_the_flag/challenges/heavy_computation/flag.enc new file mode 100644 index 0000000..e2678ba --- /dev/null +++ b/capture_the_flag/challenges/heavy_computation/flag.enc @@ -0,0 +1,4 @@ + 0000 f4 d8 e5 a2 ac 80 6c e9 dc c1 ef 1e d5 c4 51 7c ......l.......Q| + 0010 e3 d8 84 1a d7 c0 77 c9 9c b0 f6 f0 ab 13 63 b0 ......w.......c. + 0020 f9 5e 8d cd 87 ce c7 d3 88 7a 4a 68 de a9 6f 96 .^.......zJh..o. + 0030 77 cf 1e a7 95 a0 f8 1c be 3a 66 f0 aa 73 2c 3e w........:f..s,>