Programming the Demirci-Selçuk Meet-in-the-Middle Attack with Constraints

Danping Shi , Siwei Sun , Patrick Derbez (1) , Yosuke Todo (2) , Bing Sun , Lei Hu

1 EMSEC - EMbedded SEcurity and Cryptography
2 NTT Secure Platform Laboratories [Tokyo]

Cryptanalysis with SAT/SMT, MILP and CP has increased in popularity among symmetric-key cryptanalysts and designers due to its high degree of automation. So far, this approach covers differential, linear, impossible differential, zero-correlation, and integral cryptanaly-sis. However, the Demirci-Selçuk meet-in-the-middle (DS-MITM) attack is one of the most sophisticated techniques that has not been automated with this approach. By an in-depth study of Derbez and Fouque's work on DS-MITM analysis with dedicated search algorithms, we identify the crux of the problem and present a method for automatic DS-MITM attack based on general constraint programming, which allows the crypt-analysts to state the problem at a high level without having to say how it should be solved. Our method is not only able to enumerate distin-guishers but can also partly automate the key-recovery process. This approach makes the DS-MITM cryptanalysis more straightforward and easier to follow, since the resolution of the problem is delegated to off-the-shelf constraint solvers and therefore decoupled from its formulation. We apply the method to SKINNY, TWINE, and LBlock, and we get the currently known best DS-MITM attacks on these ciphers. Moreover, to demonstrate the usefulness of our tool for the block cipher designers, we exhaustively evaluate the security of 8! = 40320 versions of LBlock instantiated with different words permutations in the F functions. It turns out that the permutation used in the original LBlock is one of the 64 permutations showing the strongest resistance against the DS-MITM attack. The whole process is accomplished on a PC in less than 2 hours. The same process is applied to TWINE, and similar results are obtained.

Mots clés: Demirci-Selçuk meet-in-the-middle attack; Automated cryptanalysis; Constraint programming; MILP

Domaines: Cryptographie et sécurité [cs.CR]

Danping Shi, Siwei Sun, Patrick Derbez, Yosuke Todo, Bing Sun, et al.. Programming the Demirci-Selçuk Meet-in-the-Middle Attack with Constraints. ASIACRYPT 2018, Dec 2018, Brisbane, Australia. ⟨hal-02166675⟩