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

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

MILP-Aided Related-Tweak/Key Impossible Differential Attack and Its applications to QARMA, Joltik-BC

In this paper, we study the relation of single-key impossible differentials with the related-tweakey/key ones and propose an interesting algorithm that can efficiently derive longer related-tweakey/key impossible differentials from single-key ones. With application of the MILP technique, the algorithm can be converted an automatic tool for searching related-tweakey/key impossible differentials. We use this automatic tool to analyze QARMA-64 and give a 11-round key recovery attack, which attacks one more round than the best previous result. Moreover, we also analyze Joltik-BC-128, a internal tweakable block cipher of an authenticated encryption candidate of the CAESAR competition Joltik and our result can attack two more rounds than the result given by the cipher designers

Related-Tweakey Impossible Differential Attack on Reduced-Round Deoxys-BC-256

Deoxys-BC is the internal tweakable block cipher of Deoxys, a third-round authenticated encryption candidate at the CAESAR competition. In this study, by adequately studying the tweakey schedule, we seek a six-round related-tweakey impossible distinguisher of Deoxys-BC-256, which is transformed from a 3.5-round single-key impossible distinguisher of AES, by application of the mixed integer linear programming (MILP) method. We present a detailed description of this interesting transformation method and the MILP-modeling process. Based on this distinguisher, we mount a key-recovery attack on 10 (out of 14) rounds of Deoxys-BC-256. Compared to previous results that are valid only when the key size $>204$ and the tweak size $<52$, our method can attack 10-round Deoxys-BC-256 as long as the key size $\geq174$ and the tweak size $\leq82$. For the popular setting in which the key size is 192 bits, we can attack one round more than previous works. This version gives the distinguisher and the attack differential which follows the description of the $h$ permutation in the Deoxys document, instead of that in the Deoxys reference implementation in the SUPERCOP package, which is wrong confirmed by the designers. Note that this work only gives a more accurate security evaluation and does not threaten the security of full-round Deoxys-BC-256

Generating graphs packed with paths: Estimation of linear approximations and differentials:Estimation of linear approximations and differentials

When designing a new symmetric-key primitive, the designer must show resistance to known attacks. Perhaps most prominent amongst these are linear and differential cryptanalysis. However, it is notoriously difficult to accurately demonstrate e.g. a block cipher’s resistance to these attacks, and thus most designers resort to deriving bounds on the linear correlations and differential probabilities of their design. On the other side of the spectrum, the cryptanalyst is interested in accurately assessing the strength of a linear or differential attack. While several tools have been developed to search for optimal linear and differential trails, e.g. MILP and SAT based methods, only few approaches specifically try to find as many trails of a single approximation or differential as possible. This can result in an overestimate of a cipher’s resistance to linear and differential attacks, as was for example the case for PRESENT. In this work, we present a new algorithm for linear and differential trail search. The algorithm represents the problem of estimating approximations and differentials as the problem of finding many long paths through a multistage graph. We demonstrate that this approach allows us to find a very large number of good trails for each approximation or differential. Moreover, we show how the algorithm can be used to efficiently estimate the key dependent correlation distribution of a linear approximation, facilitating advanced linear attacks. We apply the algorithm to 17 different ciphers, and present new and improved results on several of these

Lightweight cryptography methods

While our conventional cryptography methods, such for AES (encryption), SHA-256 (hashing) and RSA/Elliptic Curve (signing), work well on systems which have reasonable processing power and memory capabilities, these do not scale well into a world with embedded systems and sensor networks. Thus lightweight cryptography methods are proposed to overcome many of the problems of conventional cryptography. This includes constraints related to physical size, processing requirements, memory limitation and energy drain. This paper outlines many of the techniques that are defined as replacements for conventional cryptography within an Internet of Things (IoT) space and discuss some trends in the design of lightweight algorithms

CRAFT: Lightweight Tweakable Block Cipher with Efficient Protection Against DFA Attacks

Traditionally, countermeasures against physical attacks are integrated into the implementation of cryptographic primitives after the algorithms have been designed for achieving a certain level of cryptanalytic security. This picture has been changed by the introduction of PICARO, ZORRO, and FIDES, where efficient protection against Side-Channel Analysis (SCA) attacks has been considered in their design. In this work we present the tweakable block cipher CRAFT: the efficient protection of its implementations against Differential Fault Analysis (DFA) attacks has been one of the main design criteria, while we provide strong bounds for its security in the related-tweak model. Considering the area footprint of round-based hardware implementations, CRAFT outperforms the other lightweight ciphers with the same state and key size. This holds not only for unprotected implementations but also when fault-detection facilities, side-channel protection, and their combination are integrated into the implementation. In addition to supporting a 64-bit tweak, CRAFT has the additional property that the circuit realizing the encryption can support the decryption functionality as well with very little area overhead

Generating Graphs Packed with Paths

When designing a new symmetric-key primitive, the designer must show resistance to known attacks. Perhaps most prominent amongst these are linear and differential cryptanalysis. However, it is notoriously difficult to accurately demonstrate e.g. a block cipher\u27s resistance to these attacks, and thus most designers resort to deriving bounds on the linear correlations and differential probabilities of their design. On the other side of the spectrum, the cryptanalyst is interested in accurately assessing the strength of a linear or differential attack. While several tools have been developed to search for optimal linear and differential trails, e.g. MILP and SAT based methods, only few approaches specifically try to find as many trails of a single approximation or differential as possible. This can result in an overestimate of a cipher\u27s resistance to linear and differential attacks, as was for example the case for PRESENT. In this work, we present a new algorithm for linear and differential trail search. The algorithm represents the problem of estimating approximations and differentials as the problem of finding many long paths through a multistage graph. We demonstrate that this approach allows us to find a very large number of good trails for each approximation or differential. Moreover, we show how the algorithm can be used to efficiently estimate the key dependent correlation distribution of a linear approximation, facilitating advanced linear attacks. We apply the algorithm to 17 different ciphers, and present new and improved results on several of these

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

Design of Efficient Symmetric-Key Cryptographic Algorithms

兵庫県立大学大学院202