Abstract Boomerang attack serves as a potent cryptanalytic tool for assessing the security of block ciphers. Over the past few years, various automatic search models for boomerang distinguishers have been proposed for block ciphers with different structures. This paper presents improved Mixed-Integer Linear Programming (MILP)-based search models for both single-key and related-key boomerang distinguishers. In the single-key scenario, we propose a method for dynamic allocation of active S-boxes. Our search model for single-key boomerang distinguishers characterizes the distinguisher probability more accurately, addressing the suboptimality issue caused by non-fixed weight assignments in prior models. In the related-key scenario, a search model for related-key boomerang distinguisher is proposed for block ciphers with bit-level key schedule algorithms, where the probability of the boomerang switch is ensured to be 1. To validate the effectiveness of our models, we apply them to the lightweight block cipher LILLIPUT based on Extended Generalized Feistel Networks (EGFN), conducting a comprehensive security analysis against boomerang attacks. Using our models, we successfully derive single-key boomerang distinguishers for 8 to 13 rounds and a 15-round related-key boomerang distinguisher. Notably, the data complexity required for 13-round single-key distinguishing attack is reduced by $${2^{ 3.172}}$$ 2 3.172 , and the 15-round related-key boomerang distinguisher with a probability of $${2^{ - 58}}$$ 2 - 58 is currently the longest-round distinguisher among all known distinguishers for LILLIPUT. The application results fully demonstrate the capability of our models in evaluating the security of block ciphers. This research not only provides new insights and methods for the design and analysis of lightweight block ciphers, but also deepens the understanding of the security characteristics for LILLIPUT.

Differential and linear cryptanalysis are two important methods to evaluate the security of block ciphers. Building on these two methods, differential‐linear (DL) cryptanalysis was introduced by Langford and Hellman in 1994. This cryptanalytic method has been not only extensively researched but also proven to be effective. In this paper, a security evaluation framework for AND‐RX ciphers against DL cryptanalysis is proposed, which is denoted as . In addition to modeling the structure of all the possible differential trails and linear trails at the bit level, we introduce a method to calculate this structure round by round. Based on this approach, an automatic algorithm is proposed to construct the DL distinguisher. Unlike previous methods, uses a truncated differential and a linear hull instead of a differential characteristic and a linear approximation, which brings the bias of the DL distinguisher close to the experimental value. To validate the effectiveness of the framework, is applied to Simon and Simeck, which are two typical AND‐RX ciphers. With the automatic algorithm, we discover an 11‐round DL distinguisher of Simon32 with bias 2 −14.89 and a 12‐round DL distinguisher of Simeck32 with bias 2 −14.89 . Moreover, the 14‐round DL distinguisher of Simon48 with bias 2 −22.30 is longer than the longest DL distinguisher currently known. In addition, the framework shows advantages when analyzing ciphers with large block sizes. As far as we know, for Simon64/96/128 and Simeck48/64, the first DL distinguishers are obtained with our framework. The DL distinguishers are 16, 23, 32, 17, and 22 rounds of Simon64/96/128 and Simeck48/64 with bias 2 −24.31 , 2 −47.57 , 2 −60.75 , 2 −22.54 , and 2 −31.41 , respectively. To prove the correctness of distinguishers, experiments on Simon32 and Simeck32 have been performed. The experimental bias are 2 −13.76 and 2 −14.82 , respectively. Comparisons of the theoretical and experimental results show good agreement.

With the rapid development of the Internet of Things (IoT), many new lightweight block ciphers are designed in recent years to meet the security demand in IoT devices. Shadow is a lightweight block cipher designed for IoT Nodes (IEEE Internet of Things Journal, 2021). In this article, an efficient attack on full-round Shadow is proposed based on the idea of a related-key differential attack. First, a differential transfer property for AND operation is illustrated. This property demonstrates a link between the difference and the input value. If the difference of the input is not zero, to lead to a zero difference, there are some constraints on the input value. Furthermore, two properties for Shadow family ciphers are identified. According to these properties, some related keys on Shadow will lead to an internal collision for the subkey generator, which will eventually lead to a full-round distinguisher. Finally, with the idea of related-key differential attack, an efficient attack is applied to Shadow. For Shadow-32, with 4 related keys, 8 master key bits can be derived in about 0.044 seconds on average. For Shadow-64, with 4 related keys, 24 master key bits can be derived in about 3.9 hours on average. All our theoretical results are verified by experiments.

How to evaluate the security of Substitution-Permutation Network (SPN) block ciphers against impossible differential (ID) cryptanalysis is a valuable problem. In this paper, a series of methods for bounding the length of IDs of SPN block ciphers are proposed. Firstly, we propose the definitions of minimal representative set and partition table. Therefore, an improved partition-first implementation strategy for bounding the length of IDs is given. Secondly, we introduce a new definition of ladder and propose the ladder-first implementation strategy for bounding the length of IDs. In order to be able to apply ladder-first implementation strategy in practice, the methods for determining ladders and integrating a ladder into searching models are given. Thirdly, a heuristic algorithm called dynamic-ladder-partition implementation strategy is proposed. According to our experimental results, dynamic-ladder-partition implementation strategy is more suitable for SPN ciphers whose number of elements in partition tables is little. Fourthly, rotation-equivalence ID sets of ciphers are explored to reduce the number of models that need to be considered. As applications, we show that 9-round PRESENT, 5-round AES, 6-round Rijndael-160, 7-round Rijndael-192, 7-round Rijndael-224 and 7-round Rijndael-256 do not have any ID under the sole assumption that the round keys are uniformly random. What’s more, we obtain that 8-round GIFT-64, 12-round GIFT-128 and 14-round SKINNY-128 do not have any ID under the assumptions that GIFT and SKINNY are Markov ciphers and the round keys are uniformly random. Our methods fill crucial gaps on bounding the length of IDs with the differential properties of S-boxes considered. They enhance our confidence in the security and are valuable, especially for designers.

In this paper, a security evaluation framework for AND-RX ciphers against impossible differential cryptanalysis is proposed. This framework is constructed based on three different methods towards finding the theoretical upper boundary, theoretical lower boundary, and practical boundary of impossible differential distinguishers (short for ID) respectively. The provable security boundary (upper boundary) can be calculated with two round-function-related matrices through a few matrix multiplications, this calculation is beyond actual input and output differences. For searching longer IDs (lower boundary), an automatic method is proposed. With this method, given the input and output difference, all the possible direct and indirect contradictions are detected. For the practical boundary, a method of approximating all the potential longest IDs with concrete differential trails is introduced. The three boundaries validate the correctness from each other. According to our result, on the one hand, the boundaries derived with well-designed ID-construction methods can already reach the practical boundary for some block ciphers and it is unlikely to be improved based on known construction methods or future unknown construction methods. On the other hand, for those ciphers whose current best result does not reach our boundary, longer IDs can be discovered with this framework. The correctness is validated by a series of applications. For the provable security boundary, four family ciphers-SIMON, Simeck, Friet-PC and SAND are investigated. For SIMON and Simeck, the lengths of current longest IDs have reached their provable security boundaries. For Friet-PC and SAND, there is a gap between the provable security boundary and current best results. With the automatic searching method, some longer IDs on Friet-PC and SAND are discovered. For Friet-PC, 128 11-round IDs are discovered, while the previous best differential distinguisher is 9-round. For SAND64, 256 11-round IDs are proposed. For SAND128, 456 14-round IDs are presented. Both results extend previous longest IDs by one round and all these newly proposed distinguishers reached corresponding provable security boundaries. For Simeck, the length of longest IDs has not been improved. However, more distinguishers of the same length are discovered. For Simeck64, the increased ratio for the quantity can reach 300%. Besides, the practical boundary of SIMON is investigated, the results indicate that for SIMON, the practical boundary is identical with the provable security boundary or the boundary derived with the automatic searching method.

In 2013, a lightweight block cipher SIMON is proposed by NSA. This paper tries to investigate this design criterion in terms of resisting against impossible differential cryptanalysis. On one hand, starting from all the possible rotation constants, this paper sieves those “bad parameters” step by step, for each step, the regular patterns for those “bad parameters” are deduced. Accordingly, basic rules for selecting rotation constants on SIMON-type ciphers to construct shorter longest impossible differentials are proposed. On the other hand, the authors categorize the optimal parameters proposed in CRYPTO 2015, according to these results, some “good parameters” in terms of differential cryptanalysis may be rather “bad parameters” while considering impossible differential cryptanalysis. Finally, a concrete attack on 26-round SIMON(13,0,10) is proposed, which is a suggested SIMON variant in CRYPTO 2015 against differential cryptanalysis and linear cryptanalysis. The result in this paper indicates that it is very important to choose appropriate rotation constants when designing a new block cipher.

In this paper, a security evaluation framework for AND-RX ciphers against rotational-XOR differential cryptanalysis is proposed. This framework first models the structure of all the possible rotational-XOR differential (abbreviated to “RXD”) trails and introduces a method to calculate this structure round by round. Based on this approach, an automatic method is proposed for searching RXD trails. In this method, four strategies are proposed to derive better result and improve the efficiency. Unlike previous automations, the time complexity for this framework can be pre-computed, which is bounded by${\mathcal{ O}}\left ({{c\cdot n\cdot R^{2}\cdot C_{n}^{n_{1}}} }\right)$(where$n$is the block size,$n_{1}$is the number of active bits for the starting point of automatic method,$R$is the length of the targeted rounds and$c$is a fixed constant). Under the given strategies and searching subspaces, the derived RXD trails are guaranteed to be optimal. To prove the correctness and efficiency, this framework is applied to all the ten variants for SIMON and three variants for Simeck. When compared with previous RXD trails, the best improvement is up to three rounds. To validate the correctness of the derived rotational-XOR differential trails, a concrete experiment on Simeck32 is conducted and the experimental result complies with the theoretical analysis. As far as we know, for all the variants of Simeck, current longest distinguishers over all the cryptanalytic methods are obtained in this paper.

Since proposed by the National Security Agency in June 2013, two lightweight block ciphers‐SIMON and SPECK have attracted the attention of cryptographers from all over the world. At CHES 2015, Simeck, a new block cipher inspired from both SIMON and SPECK is proposed, which is more compact and efficient. However, the security evaluation on Simeck against zero‐correlation linear cryptanalysis seems missing from the specification. The main focus of this study is to fill this gap and evaluate the security level of Simeck against zero‐correlation linear cryptanalysis. According to the authors' study, 11‐, 13‐ and 15‐round zero‐correlation linear distinguishers on Simeck32/48/64 are proposed, respectively, then zero‐correlation linear cryptanalysis on 21‐, 24‐, 28‐round Simeck32/48/64 are first proposed. As far as they know, for Simeck32, their result is the best result up to date.

Abstract In lightweight cryptographic primitives, round functions with simple operations XOR, modular addition, and shift (or rotation) are widely used nowadays. Among these ciphers, TEA and XTEA are two famous lightweight block ciphers. At AFRICACRYPT 2012, Jiazhe Chen, Meiqin Wang, and Bart Preneel proposed a method to establish impossible differential distinguishers for TEA and XTEA. At FSE 2012, with similar approach, Andrey Bogdanov and Meiqin Wang identified zero correlation linear distinguishers for TEA and XTEA. We find similarities in these two kinds of distinguishers and then probe into the deeper relationship between them. In this paper, we extend the TEA and XTEA to a more general TEA family‐type ciphers and study the impossible differential distinguishers and zero correlation linear distinguishers for this kind of ciphers. More specifically, with the methods proposed in these two references earlier, firstly, we prove the longest lengths for impossible differential distinguishers and zero correlation linear distinguishers on TEA family‐type ciphers. Secondly, the number of longest impossible differential distinguishers and zero correlation linear distinguishers are calculated respectively. Then, the specific forms of their input and output differences (or linear masks) are given. Thirdly, a dual property is proposed to demonstrate the deeper relationship between these two kinds of distinguishers. Finally, we give some suggestions for algorithm designers on how to shorten these two kinds of distinguishers for TEA family‐type ciphers. Copyright © 2017 John Wiley & Sons, Ltd.

Abstract In lightweight cryptographic primitives, non‐linear feedback shift registers (NFSR) are widely used nowadays. At ASIACRYPT 2010, conditional differential cryptanalysis was proposed to analyze NFSR‐based cryptosystems. To get better result, we propose an improved version of this attack. We apply this new method to analyze the security of lightweight hash functions QUARK family of ciphers, including the recently proposed C‐QUARK. Using the new method, for an advantage of 0.68, our results for U‐QUARK, D‐QUARK, S‐QUARK, and subsequently C‐QUARK are, respectively, 121(22)/131(213)/153(218),143(22)/154(212)/159(222),216 (22)/236(218)/248(224),421(22)/436(214)/445(220), whereas a(b) means that with data complexity b, we can attack a rounds of the cipher. All these results are first cryptanalytic results known thus far for QUARK family of ciphers and have been achieved by experiment in practical time. Copyright © 2014 John Wiley & Sons, Ltd.