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The Bleichenbacher Attack
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In 1998, Daniel Bleichenbacher, a cryptographer at Bell Labs, came up with an attack against PKCS #1 Block 02 padding. This attack takes
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advantage of the fact that the decryptor looks for specific bytes in specific locations. After decryption, the recipient will see whether the first byte is 00 and the second byte is 02 and whether there is a 00 after some random values. Suppose that Ray, our attacker from 3, has an encrypted message from Pao-Chi to Gwen. If Ray can decrypt the RSA digital envelope portion of the communication, he will have the session key and can decrypt the message. Here s how the attack works. First, Ray computes a bogus RSA digital envelope that looks like Pao-Chi s envelope. To do that, Ray uses a special mathematical formula and uses as input Pao-Chi s correct envelope and a random or pseudo-random number (for details, see the RSA Labs Bulletin number 7, June 26, 1998, written by Daniel Bleichenbacher, Burt Kaliski, and Jessica Staddon). Ray then sends the substitute envelope to Gwen. If Gwen responds by saying that something went wrong, that the envelope didn t unwrap properly, Ray uses the same formula to create a new, different envelope using Pao-Chi s envelope and a different number (probably just the previous number plus 1) and sends the new envelope to Gwen. When an envelope unwraps improperly, it means that the first byte is not 00, or the second byte is not 02, or maybe there s no 00 to indicate the end of padding. Ray continues to send fake envelopes to Gwen until she responds by saying the envelope unwrapped properly. When Ray has a fake envelope that works, he can figure out what PaoChi s original envelope is. The fake envelope and Pao-Chi s are related; Ray created the fake one based on the correct one and a number he chose. He uses this relationship to break the encryption. This technique does not break the private key; rather, it recovers only one envelope. Ray s fake envelope, when decrypted, does not produce the same thing Pao-Chi encrypted; rather, the result is something that simply looks like a digital envelope. It has the leading 00 02, and somewhere along the line there s another 00 to indicate the end of the padding. Gwen (or rather the software she uses to open the envelope) simply assumes that the numbers following this second 00, whatever those numbers happen to be, make up a session key. They don t this is a bogus envelope but to Gwen it looks like a legitimate envelope because all the marker bytes are there in the correct location. Bleichenbacher s research indicates that Ray will probably need to send about 1,000,000 (one million) fake envelopes to recover one message. In some situations, he might even need to send 20,000,000 fake envelopes. This attack is not likely to work using e-mail because Ray would have to wait for Gwen to open the one million e-mails and send a response to
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Appendix C
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each one, and eventually Gwen would stop trying to open any e-mail from Ray. But it might work if the recipient is using an automated responder. An example is an SSL server that simply responds to hits, sending an error message when something goes wrong and opening a session when all goes right. There are simple ways to thwart this attack (see the bulletin previously cited), and in fact, the SSL specification has a built-in countermeasure. It is probably safe, in the real world, to continue using PKCS #1 Block 02 padding when you re creating digital envelopes. However, if you want to avoid this attack, you can use a different padding scheme. The next section describes a padding scheme that s immune to the Bleichenbacher attack.
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