Differential Analysis on Simeck and SIMON with Dynamic Key-guessing Techniques

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 evaluation of SIMON and Simeck like block ciphers regarding differential attacks. We use the differentials from Kölbl {\it et al.}\u27s work and also a differential with lower Hamming weight we find using Mixed Integer Linear Programming method to attack 22-round Simeck32, 28-round Simeck48 and 35-round Simeck64. Besides, we launch the same attack procedure on four members of SIMON family by use of newly proposed differentials in CRYPTO2015 and get new attack results on 22-round SIMON32/64, 24-round SIMON48/96, 28, 29-round SIMON64/96 and 29, 30-round SIMON64/128. As far as we are concerned, our results on SIMON64 are currently the best results

A Security Analysis of IoT Encryption: Side-channel Cube Attack on Simeck32/64

Simeck, a lightweight block cipher has been proposed to be one of the encryption that can be employed in the Internet of Things (IoT) applications. Therefore, this paper presents the security of the Simeck32/64 block cipher against side-channel cube attack. We exhibit our attack against Simeck32/64 using the Hamming weight leakage assumption to extract linearly independent equations in key bits. We have been able to find 32 linearly independent equations in 32 key variables by only considering the second bit from the LSB of the Hamming weight leakage of the internal state on the fourth round of the cipher. This enables our attack to improve previous attacks on Simeck32/64 within side-channel attack model with better time and data complexity of 2^35 and 2^11.29 respectively.Comment: 12 pages, 6 figures, 4 tables, International Journal of Computer Networks & Communication

Linear Hull Attack on Round-Reduced Simeck with Dynamic Key-guessing Techniques

Simeck is a new family of lightweight block ciphers proposed by Yang $et\ al.$ in CHES\u2715, which has efficient hardware implementation. In this paper, we find differentials with low hamming weight and high probability for Simeck using Kölbl\u27s 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. Our best results cover Simeck 32/64 reduced to 23 rounds, Simeck 48/96 reduced to 30 rounds, Simeck 64/128 reduced to 37 rounds. Our result is the best known so far for any variant of Simeck

Linear Cryptanalysis of Reduced-Round Simeck Using Super Rounds

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 state of the cipher depends on only 17 key bits (19 key bits for the larger variants of the cipher). Furthermore, due to the similarity between the design of Simon and Simeck, we were able to follow the same attack model and present improved linear attacks against all variants of Simeck. In this paper, we present attacks on 19-rounds of Simeck 32/64, 28-rounds of Simeck 48/96, and 33-rounds of Simeck 64/128, often with the direct recovery of the full master key without repeating the attack over multiple rounds. We also verified the results of linear cryptanalysis on 8, 10, and 12 rounds for Simeck 32/64

A brief comparison of Simon and Simeck

Abstract. Simeck is a new lightweight block cipher design based on combining 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 lower bounds for differential and linear characteristics with Simon. We also give a comparison of the effort of finding those bounds, which surprisingly is significant less for Simeck while covering a larger number of rounds. Furthermore, we provide new differentials for Simeck which can cover more rounds compared to previous results on Simon. Based on this we mount key recovery attacks on 19/26/33 rounds of Simeck32/48/64, which also give insights on the reduced key guessing effort due to the different set of rotation constants

Correlated Sequence Attack on Reduced-Round Simon-32/64 and Simeck-32/64

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 block ciphers, construct $(1, 8)$-correlated sequences and present the first 25-round attack on both ciphers. Next, we analyze the 8-th element of these sequences by considering the key scheduling algorithms and differential properties, and show that the attack can be improved by two rounds with the same complexities as of the 25-round attack. Overall, our technique is used to attack up to 27 rounds of both Simon-32/64 and Simeck-32/64 with a time complexity less than that of average exhaustive search and data complexity of 3. Our attack extends the number of previously attacked rounds by 4 and has a success probability 1. This reduces the security margin of both these ciphers to 16%. Up to our knowledge, this is currently the best attack on Simon-32/64 and Simeck-32/64

Clustering effect in Simon and Simeck

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 enumerating a set of good trails contributing to a differential or a linear approximation, we compute the probability distribution over this space, including all trails in the class. This results in stronger distinguishers than previously proposed, and we describe key recovery attacks against SIMON and SIMECK improving the previous results by u

Linear Cryptanalysis of Reduced-Round SIMECK Variants

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, covers 13 rounds we present a linear attack in this senario which covers 14 rounds of SIMECK32/64. Similarly, using algorithm 1 of Matsui, we present attacks on 19 and 22 rounds of SIMECK48/96 and SIMECK64/128 respectively, compare them with known attacks on 16 and 19 rounds SIMON48/96 and SIMON64/128 respectively. In addition, we use algorithm 2 of Matsui to attack 18, 23 and 27 rounds of SIMECK32/64, SIMECK48/96 and SIMECK64/128 respectively, compare them with known attacks on 18, 19 and 21 rounds SIMON32/64, SIMON48/96 and SIMON64/128 respectively

The Maiorana-McFarland structure based cryptanalysis of Simon

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 $\frac{1}{2^n}$ on the potential of the linear hull with the fixed input and output masks at arbitrary long rounds, under independent assumptions. We argue that for Simon2n the potential of the realistic linear hull of the Simon2n with the linear key-schedule should be bigger than $\frac{1}{2^{2n}}$.\\ On the other hand we prove that the expected differential probability (EDP) is at least $\frac{1}{2^n}$ under the independence assumptions. It is argued that the lower bound of EDP of Simon2n of realistic differential trails is bigger than $\frac{1}{2^{2n}}$. It seems that at least theoretically the Simon2n is insecure for the key-recovery attack based on our new constructed linear hulls and key-recovery attack based on our constructed differential trails.\

The Security of SIMON-like Ciphers Against Linear Cryptanalysis

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. We also extend this upper bound to SIMON-like ciphers. Meanwhile, an automatic search algorithm is proposed, which can find the optimal linear trails in SIMON-like ciphers under the Markov assumption. With the proposed algorithm, we find the provably optimal linear trails for $12$, $16$, $19$, $28$ and $37$ rounds of SIMON$32/48/64/96/128$. To the best of our knowledge, it is the first time that the provably optimal linear trails for SIMON$64$, SIMON$96$ and SIMON$128$ are reported. The provably optimal linear trails for $13$, $19$ and $25$ rounds of SIMECK$32/48/64$ are also found respectively. Besides the optimal linear trails, we also find the $23$, $31$ and $41$-round linear hulls for SIMON$64/96/128$, and $13$, $21$ and $27$-round linear hulls for SIMECK$32/48/64$. As far as we know, these are the best linear hull distinguishers for SIMON and SIMECK so far. Compared with the approach based on SAT/SMT solvers in \cite{KolblLT15}, our search algorithm is more efficient and practical to evaluate the security against linear cryptanalysis in the design of SIMON-like ciphers