After receiving two inquiries about the coldboot attack paper which were best answered by looking at the code or by comparing with our code, I figured it was about time I put it online. So here it is:
For this code to run you’ll need to apply this patch to Sage:
which adds an interface to SCIP. Unfortunately, this patch crashes on OSX and I didn’t figure out yet why. Anybody willing to help, please step forward 🙂
Also, I assume the code on bitbucket needs some patching to work with the most recent version of Sage. Patches very welcome!
Carlos and I finally managed to put our paper on polynomial system solving with noise and its application to the cold boot problem out.
Abstract: A method for extracting cryptographic key material from DRAM used in modern computers has been recently proposed in ; the technique was called Cold Boot attacks. When considering block ciphers, such as the AES and DES, simple algorithms were also proposed in  to recover the cryptographic key from the observed set of round subkeys in memory (computed via the cipher’s key schedule operation), which were however subject to errors due to memory bits decay. In this work we extend this analysis to consider key recovery for other ciphers used in Full Disk Encryption (FDE) products. Our algorithms are also based on closest code word decoding methods, however apply a novel method for solving a set of non-linear algebraic equations with noise based on Integer Programming. This method should have further applications in cryptology, and is likely to be of independent interest. We demonstrate the viability of the Integer Programming method by applying it against the Serpent block cipher, which has a much more complex key schedule than AES. Furthermore, we also consider the Twofish key schedule, to which we apply a dedicated method of recovery.
Btw. an older version of our code for Sage for solving polynomial systems with errors is available on bitbucket.org (… yes, I should update it to the most recent version). Here’s an example from my talk at the Tools for cryptanalysis workshop 2010:
sage: p = PRESENT(Nr=1,sbox_representation='lex')
sage: F = present_dc(,r=1,return_system=True,characteristic=True)
sage: H = F.gens()[:-64]
sage: S = F.gens()[-64:]
(Y00100 + Y10100, Y00101 + Y10101, Y00102 + Y10102, Y00103 + Y10103, Y00104 + Y10104, Y00105 + Y10105, Y00106 + Y10106, Y00107 + Y10107 + 1, Y00108 + Y10108)
sage: F_prob = ProbabilisticMPolynomialSystem(F.ring(),H,S)
sage: s,t = F_prob.solve_mip(solver='SCIP')
Writing problem data to '/home/malb/.sage//temp/road/16007//tmp_1.mps'6605 records were writtenCPU Time: 0.20 Wall time: 25.95, Obj: 3.00
Not that this was a good way of attacking a blockcipher, but you get the idea.
I passed my PhD defence on Friday. I’ve uploaded the final version of my thesis titled Algorithmic Algebraic Techniques and their Application to Block Cipher Cryptanalysis. Not much changed since the last draft, which I also posted on this blog, except a few typos and errors.
Continue reading “Final Version of my PhD thesis”
I’m giving four talks this week at the ECRYPT Tools for Cryptanalysis 2010 workshop and at the 2nd International Conference on Symbolic Computation and Cryptography (both at Royal Holloway). If you want to come prepared to ask the really tough questions but are too lazy to read the papers, here are the slides: