Generic Key Recovery Attack on Feistel Scheme

We propose new generic key recovery attacks on Feistel-type block ciphers. The proposed attack is based on the all subkeys recovery approach presented in SAC 2012, which determines all subkeys instead of the master key. This enables us to construct a key recovery attack without taking into account a key scheduling function. With our advanced techniques, we apply several key recovery attacks to Feistel-type block ciphers. For instance, we show 8-, 9- and 11-round key recovery attacks on n-bit Feistel ciphers with 2n-bit key employing random keyed F-functions, random F-functions, and SP-type F-functions, respectively. Moreover, thanks to the meet-in-the-middle approach, our attack leads to low-data complexity. To demonstrate the usefulness of our approach, we show a key recovery attack on the 8-round reduced CAST-128, which is the best attack with respect to the number of attacked rounds. Since our approach derives the lower bounds on the numbers of rounds to be secure under the single secret key setting, it can be considered that we unveil the limitation of designing an efficient block cipher by a Feistel scheme such as a low-latency cipher

Complementing Feistel Ciphers

In this paper, we propose related-key differential distinguishers based on the complementation property of Feistel ciphers. We show that with relaxed requirements on the complementation, i.e. the property does not have to hold for all keys and the complementation does not have to be on all bits, one can obtain a variety of distinguishers. We formulate criteria sufficient for attacks based on the complementation property. To stress the importance of our findings we provide analysis of the \textit{full-round} primitives: * For the hash mode of \camo without $FL,FL^{-1}$ layers, differential multicollisions with $2^{112}$ time * For GOST, practical recovery of the full key with 31 related keys and $2^{38}$ time/dat

Towards Understanding the Known-Key Security of Block Ciphers

Known-key distinguishers for block ciphers were proposed by Knudsen and Rijmen at ASIACRYPT 2007 and have been a major research topic in cryptanalysis since then. A formalization of known-key attacks in general is known to be difficult. In this paper, we tackle this problem for the case of block ciphers based on ideal components such as random permutations and random functions as well as propose new generic known-key attacks on generalized Feistel ciphers. We introduce the notion of known-key indifferentiability to capture the security of such block ciphers under a known key. To show its meaningfulness, we prove that the known-key attacks on block ciphers with ideal primitives to date violate security under known-key indifferentiability. On the other hand, to demonstrate its constructiveness, we prove the balanced Feistel cipher with random functions and the multiple Even-Mansour cipher with random permutations known-key indifferentiable for a sufficient number of rounds. We note that known-key indifferentiability is more quickly and tightly attained by multiple Even-Mansour which puts it forward as a construction provably secure against known-key attacks

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

International audienceCryptanalysis 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

Performance comparison between deep learning-based and conventional cryptographic distinguishers

While many similarities between Machine Learning and cryptanalysis tasks exists, so far no major result in cryptanalysis has been reached with the aid of Machine Learning techniques. One exception is the recent work of Gohr, presented at Crypto 2019, where for the first time, conventional cryptanalysis was combined with the use of neural networks to build a more efficient distinguisher and, consequently, a key recovery attack on Speck32/64. On the same line, in this work we propose two Deep Learning (DL) based distinguishers against the Tiny Encryption Algorithm (TEA) and its evolution RAIDEN. Both ciphers have twice block and key size compared to Speck32/64. We show how these two distinguishers outperform a conventional statistical distinguisher, with no prior information on the cipher, and a differential distinguisher based on the differential trails presented by Biryukov and Velichkov at FSE 2014. We also present some variations of the DL-based distinguishers, discuss some of their extra features, and propose some directions for future research

Meet-in-the-Middle Attacks on Classes of Contracting and Expanding Feistel Constructions

We show generic attacks on unbalanced Feistel ciphers based on the meet-in-the-middle technique. We analyze two general classes of unbalanced Feistel structures, namely contracting Feistels and expanding Feistels. In both of the cases, we consider the practical scenario where the round functions are keyless and known to the adversary. In the case of contracting Feistels with 4 branches, we show attacks on 16 rounds when the key length k (in bits) is as large as the block length n (in bits), and up to 24 rounds when k = 2n. In the case of expanding Feistels, we consider two scenarios: one, where different nonlinear functions without particular structures are used in the round function, and a more practical one, where a single nonlinear is used but different linear functions are introduced in the state update. In the former case, we propose generic attacks on 13 rounds when k = n, and up to 21 rounds when k = 2n. In the latter case, 16 rounds can be attacked for k = n, and 24 rounds for k = 2n

Improvements for Finding Impossible Differentials of Block Cipher Structures

We improve Wu and Wang’s method for finding impossible differentials of block cipher structures. This improvement is more general than Wu and Wang’s method where it can find more impossible differentials with less time. We apply it on Gen-CAST256, Misty, Gen-Skipjack, Four-Cell, Gen-MARS, SMS4, MIBS, Camellia⁎, LBlock, E2, and SNAKE block ciphers. All impossible differentials discovered by the algorithm are the same as Wu’s method. Besides, for the 8-round MIBS block cipher, we find 4 new impossible differentials, which are not listed in Wu and Wang’s results. The experiment results show that the improved algorithm can not only find more impossible differentials, but also largely reduce the search time

(Quantum) Collision Attacks on Reduced Simpira v2

Simpira v2 is an AES-based permutation proposed by Gueron and Mouha at ASIACRYPT 2016. In this paper, we build an improved MILP model to count the differential and linear active Sboxes for Simpira v2, which achieves tighter bounds of the minimum number of active Sboxes for a few versions of Simpira v2. Then, based on the new model, we find some new truncated differentials for Simpira v2 and give a series (quantum) collision attacks on two versions of reduced Simpira v2