Wednesday, December 17, 2014

Study Group: Attack on XLS

This week's study group, delivered by Guy, featured a paper by Mridul Nandi attacking the XLS domain completion method. This attack was initially given at DIAC in August, and was formally presented earlier this month at Asiacrypt 2014 in Taiwan. The idea of a domain completion method is to preserve length in an encryption scheme, so that the ciphertext is of the same length as the message. More formally, this means turning an encryption scheme that works on blocks of size n to a cipher that works on inputs of size mn. This contrasts to the strategy of padding (for example to the block length of a block cipher) that infers ciphertext expansion, which is used in many applications and standards. A number of approaches have appeared in the literature including ciphertext stealing, hash-then-counter (XCB, HCTR, HCH) and applying a block cipher twice to create a one-time pad for the final block (EME, TET, HEH) - but these methods are not applicable to generic blockciphers and lack formal security analysis.

At FSE 2007, Ristenpart and Rogaway presented XLS (eXtended Latin Squares), a domain completion method that inherits the assumed strong pseudorandom permutation property of the underlying blockcipher. The method is conceptually straightforward, utilising a (linear) mixing permutation and bit-flipping and the security proof is, as you would expect from the authors, relatively easy to follow despite its numerous intricacies. No fewer than six teams have incorporated XLS into their CAESAR submissions.

Despite this acquired confidence, Nandi presents an attack to demonstrate that XLS is in fact not a strong pseudorandom permutation (SPRP), giving an attack that makes just three encryption/decryption oracle queries and succeeds with probability 1/2. In addition, the author shows that replacing the mixing function defined in the original paper with some other stronger linear permutation(s) does not help, and gives a distinguishing attack (with success probability 1/4) against this generalised version of XLS.

Nandi does not precisely pinpoint any incorrect assertions in the proof nor provide any indication to give hope that XLS is fixable, and it will be interesting to see how the authors of the original paper (and the teams relying on XLS in their CAESAR submissions) respond in the coming months.

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