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Are you referring to Joux here? Is the math for that really complicated? (I haven't tried to implement it.)

Later: I just read Ferguson, with the linear algebra.




Yeah. Joux's attack is conceptually simple. You have 2 tags T_0, T_1, obtained with distinct messages and the same IV. This means T_0 = S_0 ^ X and T_1 = S_1 ^ X, where X is the same value for both. So you have T_0 ^ T_1 = S_0 ^ S_1. S_0 and S_1 are the polynomial evaluation of the ciphertext at H, the authentication key (which is also the same).

Now, via a simple polynomial evaluation property, you have f(x) + g(x) = (f + g)(x). We know f and g --- those are the two ciphertexts being authenticated here, interpreted as polynomials --- and we know that the polynomial f + g - S_0 - S_1 must be 0 at H. From there it's a matter of finding the roots of this polynomial, one of which is H, and this is the mathematically complicated part of the attack. Though you can treat root-finding as a black-box, the keywords here are Berlekamp or Cantor-Zassenhaus.

(Hopefully I didn't get this too wrong, I'm handwaving here)


Can you imagine how much more insufferable I'm going to be once I have worked examples of these attacks? ;)




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