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What's cool about this paper is the CCA2 attack on unpadded RSA in the middle of it. What's cool about that attack is how simple it is.

The setting, simplified: you send RSA(aes-key), AES(key, message). The server replies if the AES key it recovers from the RSA message successfully decrypts the AES ciphertext; the server is an oracle for whether the message is valid.

The attack is stupid simple: the attacker shifts 127 of the AES key bits off of the RSA message --- the attacker can do this, because RSA is homomorphic with respect to multiplication and thus malleable --- and then sends the bit-shifted RSA message along with an AES ciphertext encrypted with the 0b1000...0 AES key. If that elicits a server response, the attacker knows the bottom bit of the real AES key is 1. The attacker repeats with a 126 bit shift, then the math teachers and so on until everyone is eaten.

As I like to say, I know enough about crypto to know that I should never ever trust my knowledge about how to build a secure crypto protocol.

The more I learn the more I realize everything is a cat and mouse game. Commitment comes when you believe you've invested enough that you have more to lose if you stop than to keep going.

I appreciate your summary, and especially the way you ended it.

Interesting, I never thought of rsa being multiplicatively homomorphic.

That's the basis of several other classic attacks on RSA.

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