Meet-in-the-Middle Attack on QARMA Block Cipher

QARMA is a recently published lightweight tweakable block cipher, which has been used by the ARMv8 architecture to support a software protection feature. In this paper, using the method of MITM, we give the first distinguisher of QARMA block cipher. It is made up of the \emph{Pseudo-Reflector} construction with two forward rounds and three backward rounds. By adding two rounds on the top and three rounds on the bottom of the distinguisher, together with the idea of the differential enumeration technique and the key-dependent sieve skill, we achieve a 10-round (of 16-round) key recovery attack with memory complexity of $2^{116}$ 192-bit space, data complexity of $2^{53}$ chosen plaintexts and time complexity of $2^{70.1}$ encryption units. Furthermore, we use the same distinguisher to attack QARMA-128 which also includes 10 (of 24) round functions and the \emph{Pseudo-Refector} construction. The memory complexity is $2^{232}$ 384-bit space, the data complexity is $2^{105}$ chosen plaintexts and the time complexity is $2^{141.7}$ encryption units. These are the first attacks on QARMA and do not threaten the security of full round QARMA

Truncated Differential Attacks: New Insights and 10-round Attacks on QARMA

Truncated differential attacks were introduced by Knudsen in 1994 [1]. They are a well-known family that has arguably received less attention than some other variants of differential attacks. This paper gives some new insight on truncated differential attacks and provides the best-known attacks on both variants of the lightweight cipher QARMA, in the single tweak model, reaching for the first time 10 rounds while contradicting the security claims of this reduced version. These attacks use some new truncated distinguishers as well as some evolved key-recovery techniques

The QARMA Block Cipher Family. Almost MDS Matrices Over Rings With Zero Divisors, Nearly Symmetric Even-Mansour Constructions With Non-Involutory Central Rounds, and Search Heuristics for Low-Latency S-Boxes

This paper introduces QARMA, a new family of lightweight tweakable block ciphers targeted at applications such as memory encryption, the generation of very short tags for hardware-assisted prevention of software exploitation, and the construction of keyed hash functions. QARMA is inspired by reflection ciphers such as PRINCE, to which it adds a tweaking input, and MANTIS. However, QARMA differs from previous reflector constructions in that it is a three-round Even-Mansour scheme instead of a FX-construction, and its middle permutation is non-involutory and keyed. We introduce and analyse a family of Almost MDS matrices defined over a ring with zero divisors that allows us to encode rotations in its operation while maintaining the minimal latency associated to {0, 1}-matrices. The purpose of all these design choices is to harden the cipher against various classes of attacks. We also describe new S-Box search heuristics aimed at minimising the critical path. QARMA exists in 64- and 128-bit block sizes, where block and tweak size are equal, and keys are twice as long as the blocks. We argue that QARMA provides sufficient security margins within the constraints determined by the mentioned applications, while still achieving best-in-class latency. Implementation results on a state-of-the art manufacturing process are reported. Finally, we propose a technique to extend the length of the tweak by using, for instance, a universal hash function, which can also be used to strengthen the security of QARMA

Zero-Correlation Attacks on Tweakable Block Ciphers with Linear Tweakey Expansion

The design and analysis of dedicated tweakable block ciphers is a quite recent and very active research field that provides an ongoing stream of new insights. For instance, results of Kranz, Leander, and Wiemer from FSE 2017 show that the addition of a tweak using a linear tweak schedule does not introduce new linear characteristics. In this paper, we consider – to the best of our knowledge – for the first time the effect of the tweak on zero-correlation linear cryptanalysis for ciphers that have a linear tweak schedule. It turns out that the tweak can often be used to get zero-correlation linear hulls covering more rounds compared to just searching zero-correlation linear hulls on the data-path of a cipher. Moreover, this also implies the existence of integral distinguishers on the same number of rounds. We have applied our technique on round reduced versions of Qarma, Mantis, and Skinny. As a result, we can present – to the best of our knowledge – the best attack (with respect to number of rounds) on a round-reduced variant of Qarma

Related-Tweak Statistical Saturation Cryptanalysis and Its Application on QARMA

Statistical saturation attack takes advantage of a set of plaintext with some bits fixed while the others vary randomly, and then track the evolution of a non-uniform plaintext distribution through the cipher. Previous statistical saturation attacks are all implemented under single-key setting, and there is no public attack models under related-key/tweak setting. In this paper, we propose a new cryptanalytic method which can be seen as related-key/tweak statistical saturation attack by revealing the link between the related-key/tweak statistical saturation distinguishers and KDIB (Key Difference Invariant Bias) / TDIB (Tweak Difference Invariant Bias) ones. KDIB cryptanalysis was proposed by Bogdanov et al. at ASIACRYPT’13 and utilizes the property that there can exist linear trails such that their biases are deterministically invariant under key difference. And this method can be easily extended to TDIB distinguishers if the tweak is also alternated. The link between them provides a new and more efficient way to find related-key/tweak statistical saturation distinguishers in ciphers. Thereafter, an automatic searching algorithm for KDIB/TDIB distinguishers is also given in this paper, which can be implemented to find word-level KDIB distinguishers for S-box based key-alternating ciphers. We apply this algorithm to QARMA-64 and give related-tweak statistical saturation attack for 10-round QARMA-64 with outer whitening key. Besides, an 11-round attack on QARMA-128 is also given based on the TDIB technique. Compared with previous public attacks on QARMA including outer whitening key, all attacks presented in this paper are the best ones in terms of the number of rounds

Parallel SAT Framework to Find Clustering of Differential Characteristics and Its Applications

The most crucial but time-consuming task for differential cryptanalysis is to find a differential with a high probability. To tackle this task, we propose a new SAT-based automatic search framework to efficiently figure out a differential with the highest probability under a specified condition. As the previous SAT methods (e.g., the Sun et al’s method proposed at ToSC 2021(1)) focused on accelerating the search for an optimal single differential characteristic, these are not optimized for evaluating a clustering effect to obtain a tighter differential probability of differentials. In contrast, our framework takes advantage of a method to solve incremental SAT problems in parallel using a multi-threading technique, and consequently, it offers the following advantages compared with the previous methods: (1) speedy identification of a differential with the highest probability under the specified conditions; (2) efficient construction of the truncated differential with the highest probability from the obtained multiple differentials; and (3) applicability to a wide class of symmetric-key primitives. To demonstrate the effectiveness of our framework, we apply it to the block cipher PRINCE and the tweakable block cipher QARMA. We successfully figure out the tight differential bounds for all variants of PRINCE and QARMA within the practical time, thereby identifying the longest distinguisher for all the variants, which improves existing ones by one to four more rounds. Besides, we uncover notable differences between PRINCE and QARMA in the behavior of differential, especially for the clustering effect. We believe that our findings shed light on new structural properties of these important primitives. In the context of key recovery attacks, our framework allows us to derive the key-recovery-friendly truncated differentials for all variants of QARMA. Consequently, we report key recovery attacks based on (truncated) differential cryptanalysis on QARMA for the first time and show these key recovery attacks are competitive with existing other attacks

SCARF: A Low-Latency Block Cipher for Secure Cache-Randomization

Randomized cache architectures have proven to significantly increase the complexity of contention-based cache side channel attacks and therefore pre\-sent an important building block for side channel secure microarchitectures. By randomizing the address-to-cache-index mapping, attackers can no longer trivially construct minimal eviction sets which are fundamental for contention-based cache attacks. At the same time, randomized caches maintain the flexibility of traditional caches, making them broadly applicable across various CPU-types. This is a major advantage over cache partitioning approaches. A large variety of randomized cache architectures has been proposed. However, the actual randomization function received little attention and is often neglected in these proposals. Since the randomization operates directly on the critical path of the cache lookup, the function needs to have extremely low latency. At the same time, attackers must not be able to bypass the randomization which would nullify the security benefit of the randomized mapping. In this paper we propose \cipher (\underline{S}ecure \underline{CA}che \underline{R}andomization \underline{F}unction), the first dedicated cache randomization cipher which achieves low latency and is cryptographically secure in the cache attacker model. The design methodology for this dedicated cache cipher enters new territory in the field of block ciphers with a small 10-bit block length and heavy key-dependency in few rounds

Probabilistic Related-Key Statistical Saturation Cryptanalysis

The related-key statistical saturation (RKSS) attack is a cryptanalysis method proposed by Li et al. at FSE 2019. It can be seen as the extension of previous statistical saturation attacks under the related-key setting. The attack takes advantage of a set of plaintexts with some bits fixed, while the other bits take all possible values, and considers the relation between the value distributions of a part of the ciphertext bits generated under related keys. Usually, RKSS distinguishers exploit the property that the value distribution stays invariant under the modification of the key. However, this property can only be deterministically verified if the plaintexts cover all possible values of a selection of bits. In this paper, we propose the probabilistic RKSS cryptanalysis which avoids iterating over all non-fixed plaintext bits by applying a statistical method on top of the original RKSS distinguisher. Compared to the RKSS attack, this newly proposed attack has a significantly lower data complexity and has the potential of attacking more rounds. As an illustration, for reduced-round Piccolo, we obtain the best key recovery attacks (considering both pre- and post-whitening keys) on both versions in terms of the number of rounds. Note that these attacks do not threaten the full-round security of Piccolo

The QARMAv2 Family of Tweakable Block Ciphers

We introduce the QARMAv2 family of tweakable block ciphers. It is a redesign of QARMA (from FSE 2017) to improve its security bounds and allow for longer tweaks, while keeping similar latency and area. The wider tweak input caters to both specific use cases and the design of modes of operation with higher security bounds. This is achieved through new key and tweak schedules, revised S-Box and linear layer choices, and a more comprehensive security analysis. QARMAv2 offers competitive latency and area in fully unrolled hardware implementations. Some of our results may be of independent interest. These include: new MILP models of certain classes of diffusion matrices; the comparative analysis of a full reflection cipher against an iterative half-cipher; our boomerang attack framework; and an improved approach to doubling the width of a block cipher