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Our attacker (who we re calling Ray) has two ways to break PBE. First, he could break it like any symmetric-key encryption and use brute-force on the KEK. Second, he could figure out what the password is. Although the KEK is the result of mixing together the password and salt, Ray doesn t have to bother with those things; he could simply perform a brute-force attack on the KEK, use it to decrypt the session key, and then decrypt the data. This might be plausible if the session key is larger than the KEK. In 2, though, we saw that if a key is large enough, that s not going to happen. Hence, Ray will probably try the second way, which is to figure out what the password is. Once he has the password, he can reconstruct the key-generating process and have the KEK. How can Ray figure out what the password is One way would be to try every possible keystroke combination. This would be another flavor of the brute-force attack. If Pao-Chi entered the password from the keyboard, Ray could try every possible one-character password. Then he would try every two-character combination (AA, AB, AC, AD, . . . ), then three-character values, and so on. In this way, eight-character or less passwords (on a keyboard with 96 possible values) would be approximately equivalent to a 52-bit key. Ten-character passwords are equivalent to about 65-bit keys. Another attack is for Ray to build up a dictionary of likely passwords, such as every word in the English, German, French, and Spanish languages, along with common names, easy-to-type letter combinations, such as qwertyuiop. He could add to that dictionary lists of common passwords that are available from hacker sites and bulletin boards (if you ve thought of a password, someone else probably thought of it also). When confronted with PBE, he runs through the dictionary. For each entry, he mixes it with the salt and generates an alleged KEK. He tries that KEK on the chunk of PB-encrypted data. Did it produce the session key Because the original PBE probably has a check in it (such as the salt encrypted along with the session key), it s probably easy to determine. If the check passes, that was the correct password and it produced the correct KEK, which in turn will properly decrypt the session key, which will then decrypt the bulk data. This dictionary attack tries fewer passwords than does the brute force attack. Any password the dictionary attack tries, the brute force attack also tries, but the brute-force attack tries many additional passwords that the dictionary attack does not. As a result, the dictionary attack is faster than the brute force attack.
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Of course, if Pao-Chi comes up with a password not in Ray s dictionary, it will never succeed. If Ray is smart, he ll probably start with a dictionary attack and if that fails, move on to a modified brute-force attack.
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Slowing Down an Attack on a Password
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To check a password, Ray has to mix the salt and password the same way Pao-Chi did. Pao-Chi can slow Ray down by making that a lengthy task. His goal will be to make the process quick enough that it doesn t make his own encryption or decryption process too expensive, but slow enough to be a drain on Ray. He can do this by repeating the mixing over and over. First, mix the salt and password together. Then take the result of that and run it through the blender again. Then take the result of that and run it through the blender. And on and on, say 1,000 times. The blender is probably pretty fast, the mixing is almost certainly done with a message digest, and these algorithms are generally very fast, so for Pao-Chi to do 1,000 iterations of the mixing process won t be too time-consuming. In fact entering a password is going to be far more timeconsuming than 1,000 mixings. So relatively speaking, for Pao-Chi, the mixing takes up a very small portion of the total time. But Ray is going to have to do 1,000 mixings for every password he tries. That can add up. Let s say Pao-Chi has an eight-character password. In an earlier section we said that an eight-character password is equivalent to a 52-bit key. But actually, Ray cannot try one password as quickly as one key. If he tries the brute-force attack on a key, here s the process (BFK stands for brute-force on the key ): BFK1 BFK2 BFK3 BFK4 Get a candidate key. Do key setup (recall the key table from 2). Decrypt some ciphertext, yielding some purported plaintext. Check the plaintext.
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But for each password Ray checks, on the other hand, here s the process (BFP stands for brute-force on the password ): BFP1 BFP2 BFP3 Get a candidate password. Perform the mixing to build the candidate key. Do key setup.
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