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

Tweaks and Keys for Block Ciphers: the TWEAKEY Framework

We propose the TWEAKEY framework with goal to unify the design of tweakable block ciphers and of block ciphers resistant to related-key attacks. Our framework is simple, extends the key-alternating construction, and allows to build a primitive with arbitrary tweak and key sizes, given the public round permutation (for instance, the AES round). Increasing the sizes renders the security analysis very difficult and thus we identify a subclass of TWEAKEY, that we name STK, which solves the size issue by the use of finite field multiplications on low hamming weight constants. We give very efficient instances of STK, in particular, a 128-bit tweak/key/state block cipher Deoxys-BC that is the first AES-based ad-hoc tweakable block cipher. At the same time, Deoxys-BC could be seen as a secure alternative to AES-256, which is known to be insecure in the related-key model. As another member of the TWEAKEY framework, we describe Kiasu-BC, which is a very simple and even more efficient tweakable variation of AES-128 when the tweak size is limited to 64 bits. In addition to being efficient, our proposals, compared to the previous schemes that use AES as a black box, offer security beyond the birthday bound. Deoxys-BC and Kiasu-BC represent interesting pluggable primitives for authenticated encryption schemes, for instance, OCB instantiated with Kiasu-BC runs at about 0.75 c/B on Intel Haswell. Our work can also be seen as advances on the topic of secure key schedule design for AES-like ciphers, describing several proposals in this direction

Automatic Search Model for Related-Tweakey Impossible Differential Cryptanalysis

The design and analysis of dedicated tweakable block ciphers constitute a dynamic and relatively recent research field in symmetric cryptanalysis. The assessment of security in the related-tweakey model is of utmost importance owing to the existence of a public tweak. This paper proposes an automatic search model for identifying related-tweakey impossible differentials based on the propagation of states under specific constraints, which is inspired by the research of Hu et al. in ASIACRYPT 2020. Our model is universally applicable to block ciphers, but its search efficiency may be limited in some cases. To address this issue, we introduce the Locality Constraint Analysis (LCA) technique to impossible differential cryptanalysis and propose a generalized automatic search model. Technically, we transform our models into Satisfiability Modulo Theories (SMT) problems and solve them using the STP solver. We have applied our tools to several tweakable block ciphers, such as Joltik-BC, SKINNY, QARMA, and CRAFT, to evaluate their effectiveness and practicality. Specifically, we have discovered 7-round related-tweakey impossible differentials for Joltik-BC-192, and 12-round related-tweak impossible differentials, as well as 15-round related-tweakey impossible differentials for CRAFT for the first time. Based on the search results, we demonstrate that the LCA technique can be effectively performed when searching and determining the contradictory positions for the distinguisher with long trails or ciphers with large sizes in impossible differential cryptanalysis

General Classification of the Authenticated Encryption Schemes for the CAESAR Competition

An Authenticated encryption scheme is a scheme which provides privacy and integrity by using a secret key. In 2013, CAESAR (the ``Competition for Authenticated Encryption: Security, Applicability, and Robustness\u27\u27) was co-founded by NIST and Dan Bernstein with the aim of finding authenticated encryption schemes that offer advantages over AES-GCM and are suitable for widespread adoption. The first round started with 57 candidates in March 2014; and nine of these first-round candidates where broken and withdrawn from the competition. The remaining 48 candidates went through an intense process of review, analysis and comparison. While the cryptographic community benefits greatly from the manifold different submission designs, their sheer number implies a challenging amount of study. This paper provides an easy-to-grasp overview over functional aspects, security parameters, and robustness offerings by the CAESAR candidates, clustered by their underlying designs (block-cipher-, stream-cipher-, permutation-/sponge-, compression-function-based, dedicated). After intensive review and analysis of all 48 candidates by the community, the CAESAR committee selected only 30 candidates for the second round. The announcement for the third round candidates was made on 15th August 2016 and 15 candidates were chosen for the third round

Impossible-Differential and Boomerang Cryptanalysis of Round-Reduced Kiasu-BC

Kiasu-BC is a tweakable block cipher proposed by Jean et al. at ASIACRYPT 2014 alongside their TWEAKEY framework. The cipher is almost identical to the AES-128 except for the tweak, which renders it an attractive primitive for various modes of operation and applications requiring tweakable block ciphers. Therefore, studying how the additional tweak input affects security compared to that of the AES is highly valuable to gain trust in future instantiations. This work proposes impossible-differential and boomerang attacks on eight rounds of Kiasu-BC in the single-key model, using the core idea that the tweak input allows to construct local collisions. While our results do not threat the security of the full-round version, they help concretize the security of Kiasu-BC in the single-key model

Square Attack on 7-Round Kiasu-BC

Kiasu-BC is a tweakable block cipher presented within the TWEAKEY framework at AsiaCrypt 2014. Kiasu-BC is almost identical to AES-128, the only difference to AES-128 is the tweak addition, where the 64-bit tweak is xored to the first two rows of every round-key. The security analysis of the designers focuses primarily on related-key related-tweak differential characteristics and meet-in-the-middle attacks. For other attacks, they conclude that the security level of Kiasu-BC is similar to AES-128. In this work, we provide the first third-party analysis of Kiasu-BC. We show that we can mount Square attacks on up to 7-round Kiasu-BC with a complexity of about $2^{48.5}$ encryptions, which improves upon the best published 7-round attacks for AES-128. Furthermore, we show that such attacks are applicable to the round-reduced OCB3-like mode of the CAESAR candidate Kiasu. To be specific, we show a key-recovery attack on 7-round Kiasu$\neq$ with a complexity of about $2^{82}$ encryptions

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

State of the Art in Lightweight Symmetric Cryptography

Lightweight cryptography has been one of the hot topics in symmetric cryptography in the recent years. A huge number of lightweight algorithms have been published, standardized and/or used in commercial products. In this paper, we discuss the different implementation constraints that a lightweight algorithm is usually designed to satisfy in both the software and the hardware case. We also present an extensive survey of all lightweight symmetric primitives we are aware of. It covers designs from the academic community, from government agencies and proprietary algorithms which were reverse-engineered or leaked. Relevant national (NIST...) and international (ISO/IEC...) standards are listed. We identified several trends in the design of lightweight algorithms, such as the designers\u27 preference for ARX-based and bitsliced-S-Box-based designs or simpler key schedules. We also discuss more general trade-offs facing the authors of such algorithms and suggest a clearer distinction between two subsets of lightweight cryptography. The first, ultra-lightweight cryptography, deals with primitives fulfilling a unique purpose while satisfying specific and narrow constraints. The second is ubiquitous cryptography and it encompasses more versatile algorithms both in terms of functionality and in terms of implementation trade-offs

Generalized Related-Key Rectangle Attacks on Block Ciphers with Linear Key Schedule: Applications to SKINNY and GIFT

This paper gives a new generalized key-recovery model of related-key rectangle attacks on block ciphers with linear key schedules. The model is quite optimized and applicable to various block ciphers with linear key schedule. As a proof of work, we apply the new model to two very important block ciphers, i.e. SKINNY and GIFT, which are basic modules of many candidates of the Lightweight Cryptography (LWC) standardization project by NIST. For SKINNY, we reduce the complexity of the best previous 27-round related-tweakey rectangle attack on SKINNY-128-384 from $2^{331}$ to $2^{294}$. In addition, the first 28-round related-tweakey rectangle attack on SKINNY-128-384 is given, which gains one more round than before. For the case of GIFT-64, we give the first 24-round related-key rectangle attack with a time complexity $2^{91.58}$, while the best previous attack on GIFT-64 only reaches 23 rounds at most