International Association
for Cryptologic Research

We present the first comprehensive approach for detecting and analyzing symmetric cryptographic primitives in gate-level descriptions of hardware. To capture both ASICs and FPGAs, we model the hardware as a directed graph, where gates become nodes and wires become edges. For modern chips, those graphs can easily consist of hundreds of thousands of nodes. More abstractly, we find subgraphs corresponding to cryptographic primitives in a potentially huge graph, the sea-of-gates, describing an entire chip. As we are particularly interested in unknown cryptographic algorithms, we cannot rely on searching for known parts such as S-boxes or round constants. Instead, we are looking for parts of the chip that perform highly local computations. A major result of our work is that many symmetric algorithms can be reliably located and sometimes even identified by our approach, which we call HAWKEYE. Our findings are verified by extensive experimental results, which involve SPN, ARX, Feistel, and LFSR-based ciphers implemented for both FPGAs and ASICs. We demonstrate the real-world applicability of HAWKEYE by evaluating it on OpenTitan's Earl Grey chip, an open-source secure micro-controller design. HAWKEYE locates all major cryptographic primitives present in the netlist comprising 424341 gates in 44.3 seconds.

We introduce a new approach between classical security proofs of modes of operation and dedicated security analysis for known crypt- analysis families: General Practical Cryptanalysis. This allows us to ana- lyze generically the security of the sum of two keyed permutations against known attacks. In many cases (of course, not all), we show that the se- curity of the sum is strongly linked to that of the composition of the two permutations. This enables the construction of beyond-birthday bound secure low-latency PRFs by cutting a known-to-be-secure block cipher into two equal parts. As a side result, our general analysis shows an in- evitable difficulty for the key recovery based on differential-type attacks against the sum, which leads to a correction of previously published at- tacks on the dedicated design Orthros

Recent constructions of (tweakable) block ciphers with an embedded cryptographic backdoor relied on the existence of probability-one differentials or perfect (non-)linear approximations over a reduced-round version of the primitive. In this work, we study how the existence of probability-one differentials or perfect linear approximations over two rounds of a substitution permutation network can be avoided by design. More precisely, we develop criteria on the s-box and the linear layer that guarantee the absence of probability-one differentials for all keys. We further present an algorithm that allows to efficiently exclude the existence of keys for which there exists a perfect linear approximation.

In this paper we, for the first time, study the question under which circumstances decomposing a round function of a Substitution-Permutation Network is possible uniquely. More precisely, we provide necessary and sufficient criteria for the non-linear layer on when a decomposition is unique. Our results in particular imply that, when cryptographically strong S-boxes are used, the decomposition is indeed unique. We then apply our findings to the notion of alignment, pointing out that the previous definition allows for primitives that are both aligned and unaligned simultaneously. As a second result, we present experimental data that shows that alignment might only have limited impact. For this, we compare aligned and unaligned versions of the cipher PRESENT.

In this paper we introduce the differential meet-in-the-middle framework, a new cryptanalysis technique for symmetric primitives. Our new cryptanalysis method combines techniques from both meet-in-the-middle and differential cryptanalysis. As such, the introduced technique can be seen as a way of extending meet-in-the-middle attacks and their variants but also as a new way to perform the key recovery part in differential attacks. We apply our approach to SKINNY-128-384 in the single key model and to AES-256 in the related-key model. Our attack on SKINNY-128-384 permits to break 25 out of the 56 rounds of this variant and improves by two rounds the previous best known attacks. For AES-256 we attack 12 rounds by considering two related keys, thus outperforming the previous best related-key attack on AES-256 with only two related keys by 2 rounds.

HALFLOOP is a family of tweakable block ciphers that are used for encrypting automatic link establishment (ALE) messages in high frequency radio, a technology commonly used by the military, other government agencies and industries which require high robustness in long-distance communications. Recently, it was shown in [DDLS22] that the smallest version of the cipher, HALFLOOP-24, can be attacked within a practical time and memory complexity. However, in the real-word ALE setting, it turns out that this attack require to wait more than 500 years to collect the necessary amount of plaintext-tweak-ciphertext pairs fulfilling the conditions of the attack.In this paper, we present real-world practical attacks against HALFLOOP-24 which are based on a probability-one differential distinguisher. In our attacks, we significantly reduce the data complexity to three differential pairs in the chosen-plaintext (CPA) setting which is optimal in the sense that even a brute force attack needs at least six plaintext-tweak-ciphertext pairs to uniquely identify the correct key. Considering the same ALE setting as [DDLS22], this translates to a reduction from 541 years to 2 hours worth of intercepted traffic.Besides, we provide the first, non generic, public cryptanalysis of HALFLOOP-48 and HALFLOOP-96. More precisely, we present Demirci-Selçuk meet-in-the-middle attacks against full-round HALFLOOP-48 and round-reduced HALFLOOP-96 to recover the complete master key in a CPA setting. However, unlike the attacks on HALFLOOP-24, our attacks on the larger versions are only theoretical. Moreover for HALFLOOP-96 the known generic time-memory trade-off attack, based on a flawed tweak handling, remains the strongest attack vector.In conclusion, we iterate what was already stated in [DDLS22]: HALFLOOP does not provide adequate protection and should not be used.

About 20 years ago, Wagner showed that most of the (then) known techniques used in the cryptanalysis of block ciphers were particular cases of what he called commutative diagram cryptanalysis. However, to the best of our knowledge, this general framework has not yet been leveraged to find concrete attacks.In this paper, we focus on a particular case of this framework and develop commutative cryptanalysis, whereby an attacker targeting a primitive E constructs affine permutations A and B such that E ○ A = B ○ E with a high probability, possibly for some weak keys. We develop the tools needed for the practical use of this technique: first, we generalize differential uniformity into “A-uniformity” and differential trails into “commutative trails”, and second we investigate the commutative behaviour of S-box layers, matrix multiplications, and key additions.Equipped with these new techniques, we find probability-one distinguishers using only two chosen plaintexts for large classes of weak keys in both a modified Midori and in Scream. For the same weak keys, we deduce high probability truncated differentials that can cover an arbitrary number of rounds, but which do not correspond to any high probability differential trails. Similarly, we show the existence of a trade-off in our variant of Midori whereby the probability of the commutative trail can be decreased in order to increase the weak key density. We also show some statistical patterns in the AES super S-box that have a much higher probability than the best differentials, and which hold for a class of weak keys of density about 2−4.5.

We present several improvements to the framework of differential-linear attacks with a special focus on ARX ciphers. As a demonstration of their impact, we apply them to Chaskey and ChaCha and we are able to significantly improve upon the best attacks published so far.

CRAFT is a lightweight tweakable Substitution-Permutation-Network (SPN) block cipher optimized for efficient protection of its implementations against Differential Fault Analysis (DFA) attacks. In this paper, we present an equivalent description of CRAFT up to a simple mapping on the plaintext, ciphertext and round tweakeys. We show that the new representation, for a sub-class of keys, leads to a new structure which is a Feistel network, with non-linear operation and key addition only on half the state. Consequently, it reveals a class of weak keys for which CRAFT is less resistant against differential and linear cryptanalyses. As a result, we present one weak-key single-tweak differential attack on 23 rounds (with time complexity of 294 encryptions and data complexity of 274 chosen plaintext/tweak/ciphertext tuples and works for 2112 weak keys) and one weak-key related-tweak attack on 26 rounds of the cipher (with time complexity of 2105 encryptions and data complexity 273 chosen plaintext/tweak/ciphertext tuples and works for 2108 weak keys). Note that these attacks do not break the security claim of the CRAFT block cipher.

In this paper we deepen our understanding of how to apply Simon's algorithm to break symmetric cryptographic primitives. On the one hand, we automate the search for new attacks. Using this approach we automatically find the first efficient key-recovery attacks against constructions like 5-round MISTY L-FK or 5-round Feistel-FK (with internal permutation) using Simon's algorithm. On the other hand, we study generalizations of Simon's algorithm using non-standard Hadamard matrices, with the aim to expand the quantum symmetric cryptanalysis toolkit with properties other than the periods. Our main conclusion here is that none of these generalizations can accomplish that, and we conclude that exploiting non-standard Hadamard matrices with quantum computers to break symmetric primitives will require fundamentally new attacks.

Deliberately weakened ciphers are of great interest in political discussion on law enforcement, as in the constantly recurring crypto wars, and have been put in the spotlight of academics by recent progress. A paper at Eurocrypt 2021 showed a strong indication that the security of the widely-deployed stream cipher GEA-1 was deliberately and secretly weakened to 40 bits in order to fulfill European export restrictions that have been in place in the late 1990s. However, no explanation of how this could have been constructed was given. On the other hand, we have seen the MALICIOUS design framework, published at CRYPTO 2020, that allows to construct tweakable block ciphers with a backdoor, where the difficulty of recovering the backdoor relies on well-understood cryptographic assumptions. The constructed tweakable block cipher however is rather unusual and very different from, say, general-purpose ciphers like the AES. In this paper, we pick up both topics. For GEA-1 we thoroughly explain how the weakness was constructed, solving the main open question of the work mentioned above. By generalizing MALICIOUS we - for the first time - construct backdoored tweakable block ciphers that follow modern design principles for general-purpose block ciphers, i.e., more natural-looking deliberately weakened tweakable block ciphers.

HALFLOOP-24 is a tweakable block cipher that is used to protect automatic link establishment messages in high frequency radio, a technology commonly used by government agencies and industries that need highly robust long-distance communications. We present the first public cryptanalysis of HALFLOOP-24 and show that HALFLOOP-24, despite its key size of 128 bits, is far from providing 128 bit security. More precisely, we give attacks for ciphertext-only, known-plaintext, chosen-plaintext and chosen-ciphertext scenarios. In terms of their complexities, most of them can be considered practical. However, in the real world, the amount of available data is too low for our attacks to work. Our strongest attack, a boomerang key-recovery, finds the first round key with less than 210 encryption and decryption queries. In conclusion, we strongly advise against using HALFLOOP-24.

There are many recent results on reverse-engineering (potentially hidden) structure in cryptographic S-boxes. The problem of recovering structure in the other main building block of symmetric cryptographic primitives, namely, the linear layer, has not been paid that much attention so far. To fill this gap, in this work, we develop a systematic approach to decomposing structure in the linear layer of a substitutionpermutation network (SPN), covering the case in which the specification of the linear layer is obfuscated by applying secret linear transformations to the S-boxes. We first present algorithms to decide whether an ms x ms matrix with entries in a prime field Fp can be represented as an m x m matrix over the extension field Fps . We then study the case of recovering structure in MDS matrices by investigating whether a given MDS matrix follows a Cauchy construction. As an application, for the first time, we show that the 8 x 8 MDS matrix over F28 used in the hash function Streebog is a Cauchy matrix.

Integral attacks belong to the classical attack vectors against any given block ciphers. However, providing arguments that a given cipher is resistant against those attacks is notoriously difficult. In this paper, based solely on the assumption of independent round keys, we develop significantly stronger arguments than what was possible before: our main result is that we show how to argue that the sum of ciphertexts over any possible subset of plaintext is key-dependent, i.e., the non existence of integral distinguishers.

We propose a general technique to improve the key-guessing step of several attacks on block ciphers. This is achieved by defining and studying some new properties of the associated S-boxes and by representing them as a special type of decision trees that are crucial for finding fine-grained guessing strategies for various attack vectors. We have proposed and implemented the algorithm that efficiently finds such trees, and use it for providing several applications of this approach, which include the best known attacks on NOKEON, GIFT, and RECTANGLE.

In order to lower costs, the fabrication of Integrated Circuits (ICs) is increasingly delegated to offshore contract foundries, making them exposed to malicious modifications, known as hardware Trojans. Recent works have demonstrated that a strong form of Trojan-resilience can be obtained from untrusted chips by exploiting secret sharing and Multi-Party Computation (MPC), yet with significant cost overheads. In this paper, we study the possibility of building a symmetric cipher enabling similar guarantees in a more efficient manner. To reach this goal, we exploit a simple round structure mixing a modular multiplication and a multiplication with a binary matrix. Besides being motivated as a new block cipher design for Trojan resilience, our research also exposes the cryptographic properties of the modular multiplication, which is of independent interest.

We introduce SPEEDY, a family of ultra low-latency block ciphers. We mix engineering expertise into each step of the cipher’s design process in order to create a secure encryption primitive with an extremely low latency in CMOS hardware. The centerpiece of our constructions is a high-speed 6-bit substitution box whose coordinate functions are realized as two-level NAND trees. In contrast to other low-latency block ciphers such as PRINCE, PRINCEv2, MANTIS and QARMA, we neither constrain ourselves by demanding decryption at low overhead, nor by requiring a super low area or energy. This freedom together with our gate- and transistor-level considerations allows us to create an ultra low-latency cipher which outperforms all known solutions in single-cycle encryption speed. Our main result, SPEEDY-6-192, is a 6-round 192-bit block and 192-bit key cipher which can be executed faster in hardware than any other known encryption primitive (including Gimli in Even-Mansour scheme and the Orthros pseudorandom function) and offers 128-bit security. One round more, i.e., SPEEDY-7-192, provides full 192-bit security. SPEEDY primarily targets hardware security solutions embedded in high-end CPUs, where area and energy restrictions are secondary while high performance is the number one priority.

A division property is a generic tool to search for integral distinguishers, and automatic tools such as MILP or SAT/SMT allow us to evaluate the propagation efficiently. In the application to stream ciphers, it enables us to estimate the security of cube attacks theoretically, and it leads to the best key-recovery attacks against well-known stream ciphers. However, it was reported that some of the key-recovery attacks based on the division property degenerate to distinguishing attacks due to the inaccuracy of the division property. Three-subset division property (without unknown subset) is a promising method to solve this inaccuracy problem, and a new algorithm using automatic tools for the three-subset division property was recently proposed at Asiacrypt2019. In this paper, we first show that this state-of-the-art algorithm is not always efficient and we cannot improve the existing key-recovery attacks. Then, we focus on the three-subset division property without unknown subset and propose another new efficient algorithm using automatic tools. Our algorithm is more efficient than existing algorithms, and it can improve existing key-recovery attacks. In the application to Trivium , we show a 842-round key-recovery attack. We also show that a 855-round key-recovery attack, which was proposed at CRYPTO2018, has a critical flaw and does not work. As a result, our 842-round attack becomes the best key-recovery attack. In the application to Grain-128AEAD, we show that the known 184-round key-recovery attack degenerates to a distinguishing attack. Then, the distinguishing attacks are improved up to 189 rounds, and we also show the best key-recovery attack against 190 rounds. In the application to ACORN , we prove that the 772-round key-recovery attack at ISC2019 is in fact a constant-sum distinguisher. We then give new key-recovery attacks mounting to 773-, 774- and 775-round ACORN . We verify the current best key-recovery attack on 892-round Kreyvium and recover the exact superpoly. We further propose a new attack mounting to 893 rounds.

We present several improvements to the framework of differential-linear attacks with a special focus on ARX ciphers. As a demonstration of their impact, we apply them to Chaskey and ChaCha and we are able to significantly improve upon the best attacks published so far.

Only the method to estimate the upper bound of the algebraic degree on block ciphers is known so far, but it is not useful for the designer to guarantee the security. In this paper we provide meaningful lower bounds on the algebraic degree of modern block ciphers.

A division property is a generic tool to search for integral distinguishers, and automatic tools such as MILP or SAT/SMT allow us to evaluate the propagation efficiently. In the application to stream ciphers, it enables us to estimate the security of cube attacks theoretically, and it leads to the best key-recovery attacks against well-known stream ciphers. However, it was reported that some of the key-recovery attacks based on the division property degenerate to distinguishing attacks due to the inaccuracy of the division property. Three-subset division property (without unknown subset) is a promising method to solve this inaccuracy problem, and a new algorithm using automatic tools for the three-subset division property was recently proposed at Asiacrypt2019. In this paper, we first show that this state-of-the-art algorithm is not always efficient and we cannot improve the existing key-recovery attacks. Then, we focus on the feature of the three-subset division property without unknown subset and propose another new efficient algorithm using automatic tools. Our algorithm is more efficient than existing algorithms, and it can improve existing key-recovery attacks. In the application to Trivium, we show a 841-round key-recovery attack. We also show that a 855-round key-recovery attack, which was proposed at CRYPTO2018, has a critical flaw and does not work. As a result, our 841-round attack becomes the best key-recovery attack. In the application to Grain-128AEAD, we show that the known 184-round key-recovery attack degenerates to distinguishing attacks. Then, the distinguishing attacks are improved up to 189 rounds, and we also show the best key-recovery attack against 190 rounds.

The security and performance of many integrity proof systems like SNARKs, STARKs and Bulletproofs highly depend on the underlying hash function. For this reason several new proposals have recently been developed. These primitives obviously require an in-depth security evaluation, especially since their implementation constraints have led to less standard design approaches. This work compares the security levels offered by two recent families of such primitives, namely GMiMC and HadesMiMC. We exhibit low-complexity distinguishers against the GMiMC and HadesMiMC permutations for most parameters proposed in recently launched public challenges for STARK-friendly hash functions. In the more concrete setting of the sponge construction corresponding to the practical use in the ZK-STARK protocol, we present a practical collision attack on a round-reduced version of GMiMC and a preimage attack on some instances of HadesMiMC. To achieve those results, we adapt and generalize several cryptographic techniques to fields of odd characteristic.

We present the family of authenticated encryption schemes SKINNY-AEAD and the family of hashing schemes SKINNY-Hash. All of the schemes employ a member of the SKINNY family of tweakable block ciphers, which was presented at CRYPTO 2016, as the underlying primitive. In particular, for authenticated encryption, we show how to instantiate members of SKINNY in the Deoxys-I-like ΘCB3 framework to fulfill the submission requirements of the NIST lightweight cryptography standardization process. For hashing, we use SKINNY to build a function with larger internal state and employ it in a sponge construction. To highlight the extensive amount of third-party analysis that SKINNY obtained since its publication, we briefly survey the existing cryptanalysis results for SKINNY-128-256 and SKINNY-128-384 as of February 2020. In the last part of the paper, we provide a variety of ASIC implementations of our schemes and propose new simple SKINNY-AEAD and SKINNY-Hash variants with a reduced number of rounds while maintaining a very comfortable security margin. https://csrc.nist.gov/Projects/Lightweight-Cryptography

This paper defines Spook: a sponge-based authenticated encryption with associated data algorithm. It is primarily designed to provide security against side-channel attacks at a low energy cost. For this purpose, Spook is mixing a leakageresistant mode of operation with bitslice ciphers enabling efficient and low latency implementations. The leakage-resistant mode of operation leverages a re-keying function to prevent differential side-channel analysis, a duplex sponge construction to efficiently process the data, and a tag verification based on a Tweakable Block Cipher (TBC) providing strong data integrity guarantees in the presence of leakages. The underlying bitslice ciphers are optimized for the masking countermeasures against side-channel attacks. Spook is an efficient single-pass algorithm. It ensures state-of-the-art black box security with several prominent features: (i) nonce misuse-resilience, (ii) beyond-birthday security with respect to the TBC block size, and (iii) multiuser security at minimum cost with a public tweak. Besides the specifications and design rationale, we provide first software and hardware implementation results of (unprotected) Spook which confirm the limited overheads that the use of two primitives sharing internal components imply. We also show that the integrity of Spook with leakage, so far analyzed with unbounded leakages for the duplex sponge and a strongly protected TBC modeled as leak-free, can be proven with a much weaker unpredictability assumption for the TBC. We finally discuss external cryptanalysis results and tweaks to improve both the security margins and efficiency of Spook.

Progress in the areas of multi-party computation (MPC) and fully homomorphic encryption (FHE) caused the demand of new design strategies, that minimize the number of multiplications in symmetric primitives. Rasta is an approach for a family of stream ciphers with an exceptional low AND depth, which equals the number of ANDs per encrypted bit. This is achieved in particular by randomizing parts of the computation with the help of a PRNG, implying that the security arguments rely on the provided randomness and the encryption/ decryption is potentially slowed down by this generation.In this paper we propose a variant of Rasta that achieves the same performance with respect to the AND depth and the number of ANDs per encrypted bit, but does not rely on a PRNG, i.e. is based on fixed linear layers.

We give the first practical instance – bison – of the Whitened Swap-Or-Not construction. After clarifying inherent limitations of the construction, we point out that this way of building block ciphers allows easy and very strong arguments against differential 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.

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.

Grassi et al. [Gra+16] introduced subspace trail cryptanalysis as a generalization of invariant subspaces and used it to give the first five round distinguisher for Aes. While it is a generic method, up to now it was only applied to the Aes and Prince. One problem for a broad adoption of the attack is a missing generic analysis algorithm. In this work we provide efficient and generic algorithms that allow to compute the provably best subspace trails for any substitution permutation cipher.

Recent developments in multi party computation (MPC) and fully homomorphic encryption (FHE) promoted the design and analysis of symmetric cryptographic schemes that minimize multiplications in one way or another. In this paper, we propose with Rastaa design strategy for symmetric encryption that has ANDdepth d and at the same time only needs d ANDs per encrypted bit. Even for very low values of d between 2 and 6 we can give strong evidence that attacks may not exist. This contributes to a better understanding of the limits of what concrete symmetric-key constructions can theoretically achieve with respect to AND-related metrics, and is to the best of our knowledge the first attempt that minimizes both metrics simultaneously. Furthermore, we can give evidence that for choices of d between 4 and 6 the resulting implementation properties may well be competitive by testing our construction in the use-case of removing the large ciphertext-expansion when using the BGV scheme.

We study possible alternatives for ShiftRows to be used as cell permutations in AES-like ciphers. As observed during the design process of the block cipher Midori, when using a matrix with a non-optimal branch number for the MixColumns operation, the choice of the cell permutation, i.e., an alternative for ShiftRows, can actually improve the security of the primitive. In contrast, when using an MDS matrix it is known that one cannot increase the minimum number of active S-boxes by deviating from the ShiftRows-type permutation. However, finding the optimal choice for the cell permutation for a given, non-optimal, MixColumns operation is a highly non-trivial problem. In this work, we propose techniques to speed up the search for the optimal cell permutations significantly. As case studies, we apply those techniques to Midori and Skinny and provide possible alternatives for their cell permutations. We finally state an easy-to-verify sufficient condition on a cell permutation, to be used as an alternative in Midori, that attains a high number of active S-boxes and thus provides good resistance against differential and linear attacks.

This work studies deterministic and non-deterministic nonlinear approximations for cryptanalysis of block ciphers and cryptographic permutations and embeds it into the well-understood framework of linear cryptanalysis. For a deterministic (i.e., with correlation ±1) nonlinear approximation we show that in many cases, such a nonlinear approximation implies the existence of a highly-biased linear approximation. For non-deterministic nonlinear approximations, by transforming the cipher under consideration by conjugating each keyed instance with a fixed permutation, we are able to transfer many methods from linear cryptanalysis to the nonlinear case. Using this framework we in particular show that there exist ciphers for which some transformed versions are significantly weaker with regard to linear cryptanalysis than their original counterparts.

This paper serves as a systematization of knowledge of linear cryptanalysis and provides novel insights in the areas of key schedule design and tweakable block ciphers. We examine in a step by step manner the linear hull theorem in a general and consistent setting. Based on this, we study the influence of the choice of the key scheduling on linear cryptanalysis, a – notoriously difficult – but important subject. Moreover, we investigate how tweakable block ciphers can be analyzed with respect to linear cryptanalysis, a topic that surprisingly has not been scrutinized until now.

Recently a lot of attention is paid to the search for efficiently implementable MDS matrices for lightweight symmetric primitives. Most previous work concentrated on locally optimizing the multiplication with single matrix elements. Separate from this line of work, several heuristics were developed to find shortest linear straightline programs. Solving this problem actually corresponds to globally optimizing multiplications by matrices. In this work we combine those, so far largely independent lines of work. As a result, we achieve implementations of known, locally optimized, and new MDS matrices that significantly outperform all implementations from the literature. Interestingly, almost all previous locally optimized constructions behave very similar with respect to the globally optimized implementation. As a side effect, our work reveals the so far best implementation of the Aes Mix- Columns operation with respect to the number of XOR operations needed.