How to make a collection for the Meet-In-The-Middle attack?

Question

I want to create a collection, which can be used to find matches among the values. As you properly know, recovering the key for Double DES takes three steps. Having the plaintext and the ciphertext given:

Encrypting the plaintext with all 2^56 possible keys and storing the results
Decrypting the ciphertext with all 2^56 possible keys and storing the results
Checking where the results match to retrieve the key

What I am trying to do: I am currently working with Meet-in-the-middle attack on Double DES and I have reached the point where I have to encrypt/decrypt a plaintext/ciphertext 2^56 times and store the results in order to find any matches.

Right now, I have stored the results in two HashMaps where I store the key used and the result from the encryption/decryption. However, I am not able to figure out how I can compare the results from the two HashMaps and then decide which keys have been used.

So, my second idea is maybe to use ListMultimap instead where I can store the results from the encryption/decryption with the key used, but then again, I don't know how to find the matches. The matches are not necessarily on the same row.

EDIT:

I gave it a try with my two HashMaps, but I did not succeed i.e. I was not able to compare the Maps

for (int i = 0; i <  Math.pow(2, 20); i++) {

    for (int j = 0; j < Math.pow(2, 20); j++) {

        if(hmap1.values().toArray()[i].equals(hmap2.values().toArray()[j]) )    
             System.out.println(hmap1.keySet().toArray()[i] + " = " + hmap2.keySet().toArray()[i] );    
        }
 }

I forgot to mention that for the sake of testing, I am working with keys that have 20 effective bits. So, there will be 2^20 possible keys

I also forgot to mention what my HashMaps contain of. They contain of two byte arrays static Map<byte[], byte[]> hmap1 = new HashMap<byte[], byte[]>(); where the first byte array contains of the possible key and the second array contains of the result of the encryption/decryption

You need one loop not double. One loop iterates one hashmap inside search in the second. — kelalaka, Nov 21 '18 at 19:57
Use set intersection as [here](https://stackoverflow.com/questions/13180488/intersection-of-java-util-map) — kelalaka, Nov 21 '18 at 20:07
@JamesKPolk: Then how am I going to find the the key for the decryption? — Bab, Nov 21 '18 at 20:14
Unfortunately you have left off critical details on your implementation. You say you have HashMaps but you don't say what is the HashMap lookup key and its value. Since you have DES keys and DES encryption results it matters. — President James K. Polk, Nov 21 '18 at 20:44
My HashMaps contain of two byte arrays where the first byte array contains of the possible key and the second array contains of the result of the encryption/decryption — Bab, Nov 21 '18 at 20:53
Well, that's the wrong order of keys and output. See my answer. — President James K. Polk, Nov 21 '18 at 21:03

President James K. Polk · Answer 1 · 2018-11-21T23:18:31.753

Here is the basic outline:

You obtain a plaintext and ciphertext pair (P, C) which you know is the result of Double DES:

C = DES_k2(DES_k1(P))

Now going forward you create, say, a HashMap that maps DES intermediate output to the DES key k1 that created it. So this is important: don't get confused by the HashMap keys and the DES keys, this is just an unfortunate name overload. To avoid confusion I'll call the DES keys cryptokeys. So the HashMap is from 64-bit DES outputs to 56-bit (or 20 bit in the case of your toy) DES cryptokeys.

Java psuedo-code:

Map<Long, CryptoKey> forwardMap = new HashMap();
for (CryptoKey k1=0; k1 < (1 << 20); k1++) {
    Long intermediateCipher = DES-Encrypt(k1, P);
    forwardMap.put(intermediateCipher, k1);
}

Now to run the attack in Java psuedo-code:

for(CryptoKey k2=0; k2 < (1 << 20); k2++) {
    Long intermediateCipher = DES-Decrypt(k2, C);
    if (forwardMap.contains(intermediateCipher)) {
        k1 = forwardMap.get(intermediateCipher);
        System.out.printf("k1=%s, k2=%s work", k1.toString(), k2.toString());
    }
}

You can't use `byte[]` as the key, it doesn't implement `hashCode` and `equals`, so it won't work, i.e. `forwardMap.contains(intermediateCipher)` will always return `false` — fps, Nov 21 '18 at 21:26
@JamesKPolk; I just want to be sure about something. What is CryptoKeys in the for loop? I read that you have named the DES keys cryptokey, but how do I use them in a for loop? — Bab, Nov 24 '18 at 23:45

How to make a collection for the Meet-In-The-Middle attack?

1 Answers1