Interpolation Attacks on Round-Reduced Elephant, Kravatte and Xoofff

We introduce an interpolation attack using the \textsc{Moebius Transform}. This can reduce the time complexity to get a linear system of equations for specified intermediate state bits, which is general to cryptanalysis of some ciphers with update function of low algebraic degree. Along this line, we perform an interpolation attack against \textsc{Elephant-Delirium}, a round 2 submission of the ongoing NIST lightweight cryptography project. This is the first third-party cryptanalysis on this cipher. Moreover, we promote the interpolation attack by applying it to the \textbf{Farfalle} pseudo-random constructions \textsc{Kravatte} and \textsc{Xoofff}. Our attacks turn out to be the most efficient method for these ciphers thus far

Algebraic Key-Recovery Attacks on Reduced-Round Xoofff

Farfalle, a permutation-based construction for building a pseudorandom function (PRF), is really versatile. It can be used for message authentication code, stream cipher, key derivation function, authenticated encryption and so on. Farfalle construction relies on a set of permutations and on so-called rolling functions: it can be split into a compression layer followed by a two-step expansion layer. As one instance of Farfalle, Xoofff is very efficient on a wide range of platforms from low-end devices to high-end processors by combining the narrow permutation Xoodoo and the inherent parallelism of Farfalle. In this paper, we present key-recovery attacks on reduced-round Xoofff. After identifying a weakness in the expanding rolling function, we first propose practical attacks on Xoofff instantiated with 1-/2-round Xoodoo in the expansion layer. We next extend such attack on Xoofff instantiated with 3-/4-round Xoodoo in the expansion layer by making use of Meet-in-the-Middle algebraic attacks and the linearization technique. All attacks proposed here -- which are independent of the details of the compression and/or middle layer -- have been practically verified (either on the real Xoofff or on a toy-version Xoofff with block-size of 96 bits). As a countermeasure, we discuss how to slightly modified the rolling function for free to reduce the number of attackable rounds

New MILP Modeling: Improved Conditional Cube Attacks on Keccak-based Constructions

In this paper, we propose a new MILP modeling to find better or even optimal choices of conditional cubes, under the general framework of conditional cube attacks. These choices generally find new or improved attacks against the keyed constructions based on Keccak permutation and its variants, including Keccak-MAC, KMAC, Keyak, and Ketje, in terms of attack complexities or the number of attacked rounds. Interestingly, conditional cube attacks were applied to round-reduced Keccak-MAC, but not to KMAC despite the great similarity between Keccak-MAC and KMAC, and the fact that KMAC is the NIST standard way of constructing MAC from SHA-3. As examples to demonstrate the effectiveness of our new modeling, we report key recovery attacks against KMAC128 and KMAC256 reduced to 7 and 9 rounds, respectively; the best attack against Lake Keyak with 128-bit key is improved from 6 to 8 rounds in the nonce-respected setting and 9 rounds of Lake Keyak can be attacked if the key size is of 256 bits; attack complexity improvements are found generally on other constructions. Our new model is also applied to Keccak-based full-state keyed sponge and gives a positive answer to the open question proposed by Bertoni et al. whether cube attacks can be extended to more rounds by exploiting full-state absorbing. To verify the correctness of our attacks, reduced-variants of the attacks are implemented and verified on a PC practically. It is remarked that this work does not threaten the security of any full version of the instances analyzed in this paper

Preimage Attacks on Round-reduced Keccak-224/256 via an Allocating Approach

We present new preimage attacks on standard Keccak-224 and Keccak-256 that are reduced to 3 and 4 rounds. An allocating approach is used in the attacks, and the whole complexity is allocated to two stages, such that fewer constraints are considered and the complexity is lowered in each stage. Specifically, we are trying to find a 2-block preimage, instead of a 1-block one, for a given hash value, and the first and second message blocks are found in two stages, respectively. Both the message blocks are constrained by a set of newly proposed conditions on the middle state, which are weaker than those brought by the initial values and the hash values. Thus, the complexities in the two stages are both lower than that of finding a 1-block preimage directly. Together with the basic allocating approach, an improved method is given to balance the complexities of two stages, and hence, obtains the optimal attacks. As a result, we present the best theoretical preimage attacks on Keccak-224 and Keccak-256 that are reduced to 3 and 4 rounds. Moreover, we practically found a (second) preimage for 3-round Keccak-224 with a complexity of 2^{39.39}