I've seen the ECB Penguin used to demonstrate why ECB is not a recommended method of encryption, but I do not understand how this translates to text or passwords.
Aren't the people who create these images comparing apples and oranges?
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It illustrates the point that the same plaintext going in to the cipher will result in the same ciphertext. It just happens to be a lot better example than showing someone
abc387af de7231ab abc387af abc387af a129867e
Now, what does this mean in the real world? If I gave you an email encrypted with AES-128 ECB, could you look at it and figure out the plaintext? Most likely not. If, however, I gave you a ciphertext from a long book and told you it is the encryption of one of 100 books, could you figure out which book it is? Probably.
So, comparing apples and oranges? In some ways yes, in others no. I think though that the point people who show this are driving home is that there are stronger modes which are much more likely to lead to a secure system. Sure ECB could be used to develop a system which is secure, but it would take a lot of analysis to convince an expert of that.
While there were several issues contributing to the scale of the compromise, one of them was that Adobe, instead of properly hashing the passwords, encrypted them using ECB mode instead. Even though the attackers apparently did not get the encryption key (or, if they did, they chose not to disclose it), this still exposed several weaknesses that made the passwords much easier to guess:
The length of the encrypted data revealed the length of the password, rounded up to the next 8 bytes. (This weakness is actually not specific to ECB mode, but I'm including it for completeness.)
Identical passwords produced identical ciphertexts, making it easy to locate frequently reused (and thus presumbaly weak) passwords, and also allowing multiple hints for the same passwords to be correlated as shown in the cartoon above. (This is a weakness of ECB mode; it would not have happened if the encryption had been done using a semantically secure mode with a proper IV.)
Passwords with the same 8-character prefix yielded ciphertexts with the same first block, making it easier to guess the prefix by comparing hints. Similarly, any multi-block passwords differing only in some of the blocks would yield partly matching ciphertexts, and any password that happened to contain repeating 8-character blocks (say, "passwordpassword" or "aaaaaaaaaaaaaaaa") would produce a repetitive ciphertext, just like in the Tux image example.