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30 June 2018

DOGESTORE - Google CTF 2018

by pietroferretti, chqmatteo

Secret Cloud Storage System: This is a new system to store your end-to-end encrypted secrets. Now with SHA3 integrity checks! $ nc dogestore.ctfcompetition.com 1337

Attached we find:

Understanding the challenge

Let’s start by taking a look at the Rust source code we were provided.

const FLAG_SIZE: usize = 56;
const FLAG_DATA_SIZE: usize = FLAG_SIZE * 2;

#[derive(Debug, Copy, Clone)]
struct Unit {
    letter: u8,
    size: u8,
}

fn deserialize(data: &Vec<u8>) -> Vec<Unit> {
    let mut secret = Vec::new();
    for (letter, size) in data.iter().tuples() {
        secret.push(Unit {
            letter: *letter,
            size: *size,
        });
    }
    secret
}

fn decode(data: &Vec<Unit>) -> Vec<u8> {
    let mut res = Vec::new();
    for &Unit { letter, size } in data.iter() {
        res.extend(vec![letter; size as usize + 1].iter())
    }
    res
}

fn decrypt(data: &Vec<u8>) -> Vec<u8> {
    key = get_key();
    iv = get_iv();
    openssl::symm::decrypt(
        openssl::symm::Cipher::aes_256_ctr(),
        &key,
        Some(&iv),
        data
    ).unwrap()
}

fn store(data: &Vec<u8>) -> String {
    assert!(
        data.len() == FLAG_DATA_SIZE,
        "Wrong data size ({} vs {})",
        data.len(),
        FLAG_DATA_SIZE
    );
    let decrypted = decrypt(data);
    let secret = deserialize(&decrypted);
    let expanded = decode(&secret);
    base64::encode(&compute_sha3(&expanded)[..])
}

As suggested by the name (fragment.rs), the source code is partial, but we can nonetheless understand what it’s supposed to do.

store is the function that calls all the other functions, and works like this:

We try to interact with the service at dogestore.ctfcompetition.com to check if it works in a similar way.

The service reads exactly 110 bytes, and returns a base64-encoded string, which decodes to 32 bytes.

The service’s behaviour seems to match the source code, except for reading 110 bytes instead of 112. Close enough to be FLAG_SIZE*2, but we guess the organizers messed something up and FLAG_SIZE is actually 55. Among the SHA-3 variants, 32 bytes means SHA-3-256 is probably the one used by the service.

The challenge emulates a service taking some encrypted, serialized data, restoring it back to original, and returning a checksum.

Let’s dive more deeply in each function.

Decryption

This function decrypts the 110 bytes using AES-CTR (AES counter mode). We assume the IV and the key are fixed, since we can’t supply them and the service is supposed to be deterministic.

Deserialization

This function parses and deserializes the decrypted data.

tuples() is not defined, but we assume (looking at the Unit struct) that it iterates through the byte vector 2 bytes at a time. For each pair, the first byte is read as a “letter”, the second as a “size”.

Decoding

The deserialized data is then “expanded” back to original size like this: for each letter-size pair, repeat the letter size+1 times.

Let’s see an example:

input: 'A \x00 B \x04 C \x01' (these are contiguous bytes)

A repeated 0+1=1 times
B repeated 4+1=5 times
C repeated 1+1=2 times

output: 'ABBBBBCC'

We now know the format of the decrypted data: the data is like

1 byte: letter
1 byte: size - 1
... repeated 55 times
total length = 55*2 = 110 bytes

Example: 'A\x00B\x04C\x01w\x00t\x02...'

Since usually serialization tries to save as much space as possible, we expect each letter to be different from the previous one.

Approach

encrypted_secret is 110 bytes long, same size as the service input. Looking at the filename, this is probably the serialized, encrypted flag.

Let’s start by submitting the secret to the service. The service sends back the SHA-3 hash of the decrypted secret:

ff1e690dea4fa3384cfb151e95abe92fde33e57d69d8c1f97107d0bbccf8a1d6

We can’t do much with this, but it could be useful for some additional final checks.

To move to the actual attack, some crypto basics are needed. Skip the next section if this stuff is old news for you.

Crypto Background

SHA-3

SHA-3 is a cryptographic hashing function, i.e. a function that maps a message of arbitrary length to a fixed-size digest.

One of the main properties of a cryptographic hash function is that it is non-invertible: we can’t recover the original message from a digest. We’ll have to find another way to find the secret.

AES-CTR

AES is a block cipher, but it can work in many different modes of operation.

AES-CTR specifically is a mode of operation which makes AES work like a stream cipher. Instead of encrypting a message block by block, we generate a continuous, unpredictable bitstream. The bitstream (also called keystream) is simply XOR-ed with the plaintext to generate the ciphertext.

AES-CTR

The keystream depends on both the IV (initialization vector, or nonce) and the key. In this challenge we assume the IV and the key are fixed, since we can’t provide them and we expect the service to be deterministic.

This means that in this specific case the keystream is fixed, and AES-CTR is reduced to a simple XOR cipher.

Let’s see an example. Consider as plaintext the string “Wiki” (01010111 01101001 01101011 01101001 in 8-bit ASCII).

Encryption with a XOR cipher and a sample keystream:

   01010111 01101001 01101011 01101001  // plaintext
 ⊕ 11110011 01100011 11101001 00110010  // keystream
 = 10100100 00001010 10000010 01011011  // ciphertext

Decryption is done by XOR-ing the ciphertext with the keystream again:

   10100100 00001010 10000010 01011011  // ciphertext
 ⊕ 11110011 01100011 11101001 00110010  // keystream
 = 01010111 01101001 01101011 01101001  // plaintext

Attacks on AES-CTR

Without integrity checks, AES-CTR is malleable. By manipulating the ciphertext, we can purposefully modify the plaintext it will be decrypted to, even if we don’t know the plaintext itself.

This is because, since aes-ctr is equivalent to a simple XOR cipher, when we flip a bit in the ciphertext the bit will be flipped in the plaintext too!

Let’s see an example. We take the same ciphertext as the previous example, and flip an arbitrary bit.

10100100 00001010 10000010 01011011 -> 10100100 00001010 1000001*1* 01011011

   10100100 00001010 10000011 01011011  // modified ciphertext
 ⊕ 11110011 01100011 11101001 00110010  // keystream
 = 01010111 01101001 01101010 01101001  // new plaintext

The plaintext bit in the same position was flipped.

01010111 01101001 01101011 01101001 -> 01010111 01101001 0110101*0* 01101001

Decrypted plaintext: “Wiji” instead of “Wiki”.

Since we know the format of the encrypted data, we can use this trick to our advantage to edit the plaintext in critical positions.

Finding the letters

Let’s think about it. The only output the service is willing to give us is the hash of the decoded plaintext. We can’t do much with it, except for checking if the hash is one we already know. We need to use this hash to guess the content of the plaintext.

We can use the fact that two different serializations can be decoded to the same message: if the same letter appears twice in a row in the serialized data, as long as the sum of the sizes of the two repeated letters is the same, the decoded message will also be the same (and the hash will be too).

Example:

'A\x02A\x02' is decoded as 'AAAAAA'
'A\x01A\x03' is also decoded as 'AAAAAA'

We will use this and some clever xor tricks to run automated tests on the plaintext values, and leak the content.

The attack:

When a match is found, we will have leaked the value M = letter 1 XOR letter 2.

Example:

original plaintext: A\x03D\x05
if the letter is xor-ed correctly, the second letter will be the same as the first in the new plaintext:
...
xor 2 -> A\x03C\x05

xor first size, xor second size -> result
0,0 -> A\x03C\x05 tot 10, decoded as AAAACCCCCC
0,1 -> A\x03C\x04 tot 9,  decoded as AAAACCCCC
1,0 -> A\x02C\x05 tot 9,  decoded as AAACCCCCC
1,1 -> A\x02C\x04 tot 8,  decoded as AAACCCCC
*no match*

xor 3 -> A\x03A\x05

xor first size, xor second size -> result
0,0 -> A\x03A\x05 tot 10, decoded as AAAAAAAAAA
0,1 -> A\x03A\x04 tot 9,  decoded as AAAAAAAAA *match*
1,0 -> A\x02A\x05 tot 9,  decoded as AAAAAAAAA *match*
1,1 -> A\x02A\x04 tot 8,  decoded as AAAAAAAA

We can prove that, if the next letter is xor-ed to be the same as the current, at least two of the four hashes will be the same. There is always a combination that makes the size increase or decrease by the same amount. Size variation for each xor bit combination:

  0,0 0,1 1,0 1,1
0,0 +0 +1 +1 +2
0,1 +0 -1 +1 +0
1,0 +0 +1 -1 +0
1,1 +0 -1 -1 -2

On the y axis, we have the lsb of the size bytes for the first and second letter. On the x axis, the possible xor combinations.

Using this attack we can find all the bitwise differences between adjacent letters. Since we don’t know the value of the first letter, we will have to try all of them and guess which is the one that makes more sense. All the other letters can be found using the first value and the differences.

The exploit:

#!/usr/bin/env python3
from socket import socket
from hashlib import sha3_256 as sha3

def bxor(b1, b2):
    parts = []
    for b1, b2 in zip(b1, b2):
        parts.append(bytes([b1 ^ b2]))
    return b''.join(parts)

def gethash(text):
    # send text
    sock = socket()
    sock.connect((host, port))
    sock.send(text)
    # get base64 encoded hash
    data = sock.recv(1024)
    sock.close()
    return data

host = 'dogestore.ctfcompetition.com'
port = 1337

# load encrypted flag
with open('encrypted_secret', 'rb') as f:
    ctext = f.read()
print('Encrypted:')
print(ctext.hex())
print(len(ctext), 'bytes')

nletters = len(ctext) // 2

differences = []
for i in range(0, nletters - 1):
    print('index:', i)
    for c in range(256):
        print('diff:', c)
        hashes = []
        for x, y in ((0, 0), (0, 1), (1, 0), (1, 1)):
            # a) xor next letter to make it the same as the current one
            # b) xor least significant bit of the sizes to create two messages
            # with varying sizes for the current and following letter,
            # but same total size
            mask = b'\x00\x00' * i + \
                   b'\x00' + (x).to_bytes(1, 'little') + \
                   (c).to_bytes(1, 'little') + (y).to_bytes(1, 'little') + \
                   b'\x00\x00' * (nletters - i - 2)
            assert len(mask) == len(ctext)
            h = gethash(bxor(ctext, mask))
            hashes.append(h)
        # if we found a match among the hashes, the letters were the same, and
        # we guessed the bit difference between this letter and the next one
        if len(set(hashes)) < 4:
            print()
            print('Nice!', c)
            differences.append(c)
            print(differences)
            print()
            break

for c in range(256):
    s = chr(c)
    for x in differences:
        s += chr(ord(s[-1]) ^ x)
    print(c)
    print(s)

Among the possible candidates, we notice one that follows the ctf flag format:

...
72
HFHFHDHDHDSAaACTF{SADASDSDCTF{L_E_R_OY_JENKINS}ASDCTF{
...

Sadly we still don’t know how many times each letter is repeated in the actual decoded data.

Finding the sizes

We can mount an attack similar to the previous, but this time we have the advantage of knowing the value of the letters themselves.

Again, we exploit the case where two different serializations are decoded to the same message.

The attack:

With this attack we can recover M’ = size 1 XOR size 2, one bit at a time.

Example:

original plaintext: A\x03D\x02
xor to make the letters match -> A\x03A\x02

bit 1:
-> A\x02A\x02, tot 6, decoded as AAAAAA
-> A\x03A\x03, tot 8, decoded as AAAAAAAA
*no match*
the bits are different

bit 2:
-> A\x01A\x02, tot 5, decoded as AAAAA
-> A\x03A\x00, tot 5, decoded as AAAAA
*match*
the bits are the same
...

The exploit:

#!/usr/bin/env python3
from socket import socket
from hashlib import sha3_256 as sha3

def bxor(b1, b2):
    parts = []
    for b1, b2 in zip(b1, b2):
        parts.append(bytes([b1 ^ b2]))
    return b''.join(parts)

def gethash(text):
    # send text
    sock = socket()
    sock.connect((host, port))
    sock.send(text)
    # get base64 encoded hash
    data = sock.recv(1024)
    sock.close()
    return data

host = 'dogestore.ctfcompetition.com'
port = 1337

differences = [14, 14, 14, 14, 12, 12, 12, 12, 12, 23, 18, 32, 32, 2, 23, 18,
               61, 40, 18, 5, 5, 18, 23, 23, 23, 7, 23, 18, 61, 55, 19, 26, 26,
               13, 13, 16, 22, 6, 21, 15, 11, 5, 2, 7, 29, 46, 60, 18, 23, 7,
               23, 18, 61, 113]

# load encrypted flag
with open('encrypted_secret', 'rb') as f:
    ctext = f.read()
print('Encrypted:')
print(ctext.hex())
print(len(ctext), 'bytes')

nletters = len(ctext) // 2

sizes = []
for i in range(0, nletters - 1):
    print('index:', i)
    b = 0
    for j in range(8):
        print('bit', j)
        # check if this bit in the current size byte is different from the one
        # in the following size byte
        # first mask: make letters the same,
        #             change one bit in the size of the first letter
        mask1 = b'\x00\x00' * i + \
                b'\x00' + (1<<j).to_bytes(1, 'little') + \
                (differences[i]).to_bytes(1, 'little') + b'\x00' + \
                b'\x00\x00' * (nletters - i - 2)
        assert len(mask1) == 110
        h1 = gethash(bxor(ctext, mask1))
        # second mask: make letters the same,
        #              change one bit in the size of the second letter
        mask2 = b'\x00\x00' * i + \
                b'\x00\x00' + \
                (differences[i]).to_bytes(1, 'little') + \
                (1<<j).to_bytes(1, 'little') + \
                b'\x00\x00' * (nletters - i - 2)
        assert len(mask2) == 110
        h2 = gethash(bxor(ctext, mask2))
        # if the bits are the same, the size will be increased by the same
        # amount for both letters
        # -> same hash
        # otherwise  one size will be increased, the other decreased
        # -> different hashes
        if h1 == h2:
            print('same')
        else:
            print('different')
            b += (1 << j)
    print(hex(b))
    sizes.append(b)
    print(sizes)

Using this exploit we manage to find the bitwise differences between the sizes of each letter.

Again, we don’t know the first value, but we guess the one with the smallest values is the most probable.

Flag

With the leaked letters and sizes, we can recover the decoded secret, which is 'HFHFHHHDHDHDDDDDDSSSSSSSAAAAaAAAAAACTF{{{SADASDSDCTF{LLLLLLLLL___EEEEE____RRRRRRRRRRR_OYYYYYYYYYY_JEEEEEEENKKKINNSSS}ASDDDDDDDCTF{{{{{\n'.

The sha3 hash of the secret we found is ff1e690dea4fa3384cfb151e95abe92fde33e57d69d8c1f97107d0bbccf8a1d6, which matches with the one provided by the server! We’re all set.

The flag is the portion following this ctf’s flag format, i.e. CTF{LLLLLLLLL___EEEEE____RRRRRRRRRRR_OYYYYYYYYYY_JEEEEEEENKKKINNSSS}.

Additional notes

This challenge was fun, as there were many different way to leak the plaintext content.

For instance, an alternative way to leak the sizes came to our mind after the ctf was finished.

Once we knew the letters, we could just XOR all letters to the same one and get the resulting hash. We could then locally compute the hash of that letter repeated for all possible lengths, and look for a match to find the sum of all the sizes.

The single values could next be found by xoring a letter at a time, and again bruteforcing locally all possible combination of the repetitions of that letter, concatenated with the repetitions of the other letter.

This could have saved some requests to the challenge service, which was often slow while the ctf was running (probably due to high load).

tags: google - ctf - crypto - mhackeroni