The impossible differential (ID) attack is one of the most important cryptanalytic techniques for block ciphers. There are two phases to finding an ID attack: searching for the distinguisher and building a key recovery upon it. Previous works only focused on automated distinguisher discovery, leaving key recovery as a manual post-processing task, which may lead to a suboptimal final complexity. At EUROCRYPT~2023, Hadipour et al. introduced a unified constraint programming (CP) approach based...

In 1994, Langford and Hellman introduced differential-linear (DL) cryptanalysis, with the idea of decomposing the block cipher E into two parts, EU and EL, such that EU exhibits a high-probability differential trail, while EL has a high-correlation linear trail.Combining these trails forms a distinguisher for E, assuming independence between EU and EL. The dependency between the two parts of DL distinguishers remained unaddressed until EUROCRYPT 2019, where Bar-On et al. introduced the DLCT...

Machine Learning (ML) is almost ubiquitously used in multiple disciplines nowadays. Recently, we have seen its usage in the realm of differential distinguishers for symmetric key ciphers. In this work, we explore the possibility of a number of ciphers with respect to various ML-based distinguishers. We show new distinguishers on the unkeyed and round reduced version of SPECK-32, SPECK-128, ASCON, SIMECK-32, SIMECK-64 and SKINNY-128. We explore multiple avenues in the process. In summary,...

In this paper, we propose a rectangle-like method called \textit{rotational-XOR differential rectangle} attack to search for better distinguishers. It is a combination of the rotational-XOR cryptanalysis and differential cryptanalysis in the rectangle-based way. In particular, we put a rotational-XOR characteristic before a differential characteristic to construct a rectangle structure. By choosing some appropriate rotational-XOR and differential characteristics as well as considering...

The Simeck family of lightweight block ciphers was proposed by Yang et al. in 2015, which combines the design features of the NSA-designed block ciphers Simon and Speck. Linear cryptanalysis using super-rounds was proposed by Almukhlifi and Vora to increase the efficiency of implementing Matsui’s second algorithm and achieved good results on all variants of Simon. The improved linear attacks result from the observation that, after four rounds of encryption, one bit of the left half of the...

Rotational-XOR (RX) cryptanalysis is a cryptanalytic method aimed at finding distinguishable statistical properties in ARX-C ciphers, i.e., ciphers that can be described only by using modular addition, cyclic rotation, XOR, and the injection of constants. In this paper we extend RX-cryptanalysis to AND-RX ciphers, a similar design paradigm where the modular addition is replaced by vectorial bitwise AND; such ciphers include the block cipher families Simon and Simeck. We analyze the...

In CRYPTO 2019, Gohr made a pioneering attempt and successfully applied deep learning to the differential cryptanalysis against NSA block cipher Speck32/64, achieving higher accuracy than the pure differential distinguishers. By its very nature, mining effective features in data plays a crucial role in data-driven deep learning. In this paper, in addition to considering the integrity of the information from the training data of the ciphertext pair, domain knowledge about the structure of...

In this paper we propose the linear hull construction for block ciphers with quadratic Maiorana-McFarland structure round functions. The search for linear trails with high squared correlations from our Maiorana-McFarland structure based constructive linear cryptanalysis is linear algebraic. Hence from this linear algebraic essence, the space of all linear trails has the structure such that good linear hulls can be constructed. Then for the Simon2n and its variants, we prove the lower bound...

Simon and Simeck are two lightweight block ciphers with a simple round function using only word rotations and a bit-wise AND operation. Previous work has shown a strong clustering effect for differential and linear cryptanalysis, due to the existence of many trails with the same inputs and outputs. In this paper, we explore this clustering effect by exhibiting a class of high probability differential and linear trails where the active bits stay in a fixed window of $w$ bits. Instead of...

In this work we investigate how the choice of the key-expansion algorithm and its interaction with the round function affect the resistance of Simon-like ciphers against rotational-XOR (RX) cryptanalysis. We observe that among the key-expansion algorithms we consider, Simon is most resistant, while Simeck is much less so. Implications on lightweight ciphers design are discussed and open questions are proposed.

The advances of the Internet of Things (IoT) have had a fundamental impact and influence in sharping our rich living experiences. However, since IoT devices are usually resource-constrained, lightweight block ciphers have played a major role in serving as a building block for secure IoT protocols. In CHES 2015, SIMECK, a family of block ciphers, was designed for resource-constrained IoT devices. Since its publication, there have been many analyses on its security. In this paper, under the...

Search for the right pairs of inputs in difference-based distinguishers is an important task for the experimental verification of the distinguishers in symmetric-key ciphers. In this paper, we develop an MILP-based approach to verify the possibility of difference-based distinguishers and extract the right pairs. We apply the proposed method to some presented difference-based trails (Related-Key Differentials (RKD), Rotational-XOR (RX)) of block ciphers \texttt{SIMECK}, and \texttt{SPECK}. ...

Rotational-XOR cryptanalysis is a cryptanalytic method aimed at finding distinguishable statistical properties in ARX-C ciphers, i.e., ciphers that can be described only using modular addition, cyclic rotation, XOR, and the injection of constants. In this paper we extend RX-cryptanalysis to AND-RX ciphers, a similar design paradigm where the modular addition is replaced by vectorial bitwise AND; such ciphers include the block cipher families Simon and Simeck. We analyse the propagation of...

Division property is a generalized integral property proposed by Todo at EUROCRYPT 2015, and then conventional bit-based division property (CBDP) and bit-based division property using three subsets (BDPT) were proposed by Todo and Morii at FSE 2016. The huge time and memory complexity that once restricted the applications of CBDP have been solved by Xiang et al. at ASIACRYPT 2016. They extended Mixed Integer Linear Programming (MILP) method to search integral distinguishers based on CBDP....

In this paper, we propose a novel cryptanalytic technique called correlated sequence attack on block ciphers. Our attack exploits the properties of given key dependent sequences of length $t$ to obtain other keyed sequences of same length with $\sigma$ ($0\le \sigma < t$) computations of the non-linear function. We call these sequences $(\sigma,t)$-correlated sequences, and utilize them in a meet-in-the-middle attack for $2t$ rounds. We apply this technique on Simon-32/64 and Simeck-32/64...

Satisfiability modulo theories or SMT can be stated as a generalization of Boolean satisfiability problem or SAT. The core idea behind the introduction of SMT solvers is to reduce the complexity through providing more information about the problem environment. In this paper, we take advantage of a similar idea and feed the SMT solver itself, by extra information provided through middle state Cube characteristics, to introduce a new method which we call SMT-based Cube Attack, and apply it to...

The purpose of the work is to estimate the resistance of lightweight block ciphers Speck, Simon, Simeck, HIGHT, LEA to a distinguishing attack. (This attack is a form of cryptanalysis on data encrypted by a cipher that allows an attacker to distinguish the encrypted data from random data.) Modern lightweight block ciphers must be designed to be immune to such an attack. It turned out that Speck, Simon, HIGHT and LEA showed a sufficient resistance to the distinguishing attack, but Simeck...

In this paper, we propose a family of lightweight cryptographic permutations called sLiSCP, with the sole aim to provide a realistic minimal design}that suits a variety of lightweight device applications. More precisely, we argue that for such devices the chip area dedicated for security purposes should, not only be consumed by an encryption or hashing algorithm, but also provide as many cryptographic functionalities as possible. Our main contribution is the design of a lightweight...

In the present paper, we analyze the security of SIMON-like ciphers against linear cryptanalysis. First, an upper bound is derived on the squared correlation of SIMON-like round function. It is shown that the upper bound on the squared correlation of SIMON-like round function decreases with the Hamming weight of output mask increasing. Based on this, we derive an upper bound on the squared correlation of linear trails for SIMON and SIMECK, which is $2^{-2R+2}$ for any $R$-round linear trail....

In the present paper, we propose an automatic search algorithm for optimal differential trails in SIMON-like ciphers. First, we give a more accurate upper bound on the differential probability of SIMON-like round function. It is shown that when the Hamming weight of the input difference $\alpha$, which is denoted by $wt(\alpha)$, is less than one half of the input size, the corresponding maximum differential probability of SIMON-like round function is less than or equal to...

Division property is a generalized integral property proposed by Todo at EUROCRYPT 2015, and very recently, Todo et al. proposed bit-based division property and applied to SIMON32 at FSE 2016. However, this technique can only be applied to block ciphers with block size no larger than 32 due to its high time and memory complexity. In this paper, we extend Mixed Integer Linear Programming (MILP) method, which is used to search differential characteristics and linear trails of block ciphers, to...

In this work, we analyze the resistance of SIMON-like ciphers against differential attacks without using computer-aided methods. In this context, we first define the notion of a SIMON-like cipher as a generalization of the SIMON design. For certain instances, we present a method for proving the resistance against differential attacks by upper bounding the probability of a differential characteristic by $2^{-2T+2}$ where $T$ denotes the number of rounds. Interestingly, if $2n$ denotes the...

Simeck is a new family of lightweight block ciphers proposed by Yang $et\ al.$ in CHES'15, which has efficient hardware implementation. In this paper, we find differentials with low hamming weight and high probability for Simeck using Kölbl's tool, then we consider the links between the differential and linear characteristic to construct linear hulls for Simeck. We give improved linear hull attack with dynamic key-guessing techniques on Simeck according to the property of the AND operation....

SIMON and SPECK family ciphers have attracted the attention of cryptographers all over the world since proposed by NSA in June, 2013. 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 paper is to fill this gap and evaluate the security level on Simeck against zero...

The Simeck family of lightweight block ciphers was proposed in CHES 2015 which combines the good design components from NSA designed ciphers SIMON and SPECK. Dynamic key-guessing techniques were proposed by Wang {\it et al.} to greatly reduce the key space guessed in differential cryptanalysis and work well on SIMON. In this paper, we implement the dynamic key-guessing techniques in a program to automatically give out the data in dynamic key-guessing procedure and thus simplify the security...

SIMECK is a family of 3 lightweight block ciphers designed by Yang et al. They follow the framework used by Beaulieu et al. from the United States National Security Agency (NSA) to design SIMON and SPECK. A cipher in this family with K-bit key and N-bit block is called SIMECKN=K.We show that the security of this block cipher against linear cryptanalysis is not as good as its predecessors SIMON. More precisely, while the best known linear attack for SIMON32/64, using algorithm 1 of Matsui,...

Simeck is a new lightweight block cipher design based on combining the design principles of the Simon and Speck block cipher. While the design allows a smaller and more efficient hardware implementation, its security margins are not well understood. The lack of design rationals of its predecessors further leaves some uncertainty on the security of Simeck. In this work we give a short analysis of the impact of the design changes by comparing the upper bounds on the probability of...

Two lightweight block cipher families, SIMON and SPECK, have been proposed by researchers from the NSA recently. In this paper, we introduce Simeck, a new family of lightweight block ciphers that combines the good design components from both SIMON and SPECK, in order to devise even more compact and efficient block ciphers. For Simeck32/64, we can achieve 505 GEs (before the Place and Route phase) and 549 GEs (after the Place and Route phase), with the power consumption of 0.417 $\mu W$ in...