Re: My attempt to break Rijndael (SAT-attack)

Thorsten Kiefer <toki782@xxxxxxxxxxxxxxxx> wrote:
I added the clauses for the plaintext, ciphertext and all 128 clauses of the key.
It takes 24 seconds to solve this.
Then I remove the key-clauses and insert only 126 clauses of the key.
This takes 30 seconds to solve.
Then I remove the key-clauses and insert only 116 clauses of the key.
This takes 617 seconds to solve.

If you assume the formula a*b^n for the time complexity, then you can find:
time(n) = 24 * 1.2^n, where n is the number of missing key-clauses(/bits).

This would be completely devastating for Rijndael, since the time
for recovery of 128 bit key should be approximately 2^127 ~ 10^40. It
would also be _very_ surprising (not to mention embarrassing for the
cryptographic community).

time(128) = 3.27*10^11 second, which is about 10000 years (on my computer).
So if you could accelerate the solver e.g. by parallel computing by a factor 10000,
you could crack a Rijndael key in 1 year.

Unfortunately my favorite SAT-solver is stochastic an therefore the time(n)-formula
is not totally reliable.

Is this more interesting now ?

Not really. You need to show that your formula really describes the
behaviour of the system when n increases. I don't see anything that
suggests this is the case.

Kristian Gjøsteen