Key-Recovery Attacks on Full Kravatte ★
This paper presents a cryptanalysis of full Kravatte, an instantiation of the Farfalle construction of a pseudorandom function (PRF) with variable input and output length. This new construction, proposed by Bertoni et al., introduces an efficiently parallelizable and extremely versatile building block for the design of symmetric mechanisms, e.g. message authentication codes or stream ciphers. It 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. The key is expanded and used to mask the inputs and outputs of the construction. Kravatte instantiates Farfalle using linear rolling functions and permutations obtained by iterating the Keccak round function.We develop in this paper several attacks against this PRF, based on three different attack strategies that bypass part of the construction and target a reduced number of permutation rounds. A higher order differential distinguisher exploits the possibility to build an affine space of values in the cipher state after the compression layer. An algebraic meet-in-the-middle attack can be mounted on the second step of the expansion layer. Finally, due to the linearity of the rolling function and the low algebraic degree of the Keccak round function, a linear recurrence distinguisher can be found on intermediate states of the second step of the expansion layer. All the attacks rely on the ability to invert a small number of the final rounds of the construction. In particular, the last two rounds of the construction together with the final masking by the key can be algebraically inverted, which allows to recover the key.The complexities of the devised attacks, applied to the Kravatte specifications published on the IACR ePrint in July 2017, or the strengthened version of Kravatte recently presented at ECC 2017, are far below the security claimed.
Cryptanalysis of NORX v2.0
NORX is an authenticated encryption scheme with associated data being publicly scrutinized as part of the ongoing CAESAR competition, where 14 other primitives are also competing. It is based on the sponge construction and relies on a simple permutation that allows efficient and versatile implementations. Thanks to research on the security of the sponge construction, the design of NORX, whose permutation is inspired from the permutations used in BLAKE and ChaCha, has evolved throughout three main versions (v1.0, v2.0 and v3.0). In this paper, we investigate the security of the full NORX v2.0 primitive that has been accepted as third-round candidate in the CAESAR competition. We show that some non-conservative design decisions probably motivated by implementation efficiency considerations result in at least one strong structural distinguisher of the underlying sponge permutation that can be turned into an attack on the full primitive. This attack yields a ciphertext-only forgery with time and data complexity 266 (resp. 2130) for the variant of NORX v2.0 using 128-bit (resp. 256-bit) keys and breaks the designers’ claim of a 128-bit, resp. 256-bit security. Furthermore, we show that this forgery attack can be extended to a key-recovery attack on the full NORX v2.0 with the same time and data complexities. We have implemented and experimentally verified the correctness of the attacks on a toy version of NORX. We emphasize that the scheme has recently been tweaked to NORX v3.0 at the beginning of the third round of the CAESAR competition: the main change introduces some key-dependent internal operations, which make NORX v3.0 immune to our attacks. However, the structural distinguisher of the permutation persists.
Is AEZ v4.1 Sufficiently Resilient Against Key-Recovery Attacks?
AEZ is a parallelizable, AES-based authenticated encryption algorithm that is well suited for software implementations on processors equipped with the AES-NI instruction set. It aims at offering exceptionally strong security properties such as nonce and decryption-misuse resistance and optimal security given the selected ciphertext expansion. AEZ was submitted to the authenticated ciphers competition CAESAR and was selected in 2015 for the second round of the competition. In this paper, we analyse the resilience of the latest algorithm version, AEZ v4.1 (October 2015), against key-recovery attacks. While AEZ modifications introduced in 2015 were partly motivated by thwarting a key-recovery attack of birthday complexity against AEZ v3 published at Asiacrypt 2015 by Fuhr, Leurent and Suder, we show that AEZ v4.1 remains vulnerable to a key-recovery attack of similar complexity and security impact. Our attack leverages the use, in AEZ, of an underlying tweakable block cipher based on a 4-round version of AES. Although the presented key-recovery attack does not violate the security claims of AEZ since the designers made no claim for beyond-birthday security, it can be interpreted as an indication that AEZ does not fully meet the objective of being an extremely conservative and misuse-resilient algorithm.