Authenticated-Encryption with Associated-Data (AEAD) plays an important role in guaranteeing confidentiality, integrity, and authenticity in network communications. To meet the requirements of high-performance applications, several AEADs make use of AES New Instructions (AES-NI), which can conduct operations of AES encryption and decryption dramatically fast by hardware accelerations. At SAC 2013, Wu and Preneel proposed an AES-based AEAD scheme called AEGIS-128/128L/256, to achieve high-speed software implementation. At FSE 2016, Jean and Nikolić generalized the construction of AEGIS and proposed more efficient round functions. At ToSC 2021, Sakamoto et al. further improved the constructions of Jean and Nikolić, and proposed an AEAD scheme called Rocca for beyond 5G. In this study, we first evaluate the security of the initialization phases of Rocca and AEGIS family against differential and integral attacks using MILP (Mixed Integer Linear Programming) tools. Specifically, according to the evaluation based on the lower bounds for the number of active S-boxes, the initialization phases of AEGIS-128/128L/256 are secure against differential attacks after 4/3/6 rounds, respectively. Regarding integral attacks, we present the integral distinguisher on 6 rounds and 6/5/7 rounds in the initialization phases of Rocca and AEGIS-128/128L/256, respectively. Besides, we evaluate the round function of Rocca and those of Jean and Nikolić as cryptographic permutations against differential, impossible differential, and integral attacks. Our results indicate that, for differential attacks, the growth rate of increasing the number of active S-boxes in Rocca is faster than those of Jean and Nikolić. For impossible differential and integral attacks, we show that the round function of Rocca achieves the sufficient level of the security against these attacks in smaller number of rounds than those of Jean and Nikolić.

This paper investigates the security of KCipher-2 against differential attacks. We utilize an MILP-based method to evaluate the minimum number of active S-boxes in each round. We try to construct an accurate model to describe the 8-bit truncated difference propagation through the modular addition operation and the linear transformation of KCipher-2, respectively, which were omitted or simplified in the previous evaluation by Preneel et al. In our constructed model, the difference characteristics neglected in Preneel et al.'s evaluation can be taken into account and all valid differential characteristics can be covered. As a result, we reveal that the minimal number of active S-boxes is 25 over 15 rounds in the related IV setting and it is 17 over 24 rounds in the related IV-key setting. Therefore, this paper shows for the first time that KCipher-2 is secure against the related IV differential attack.

SPARX-128/256 is one of the two versions of the SPARX-128 block cipher family. It has 128-bit block size and 256-bit key size. SPARX has been developed using ARX-based S-boxes with the aim of achieving provable security against single-trail differential and linear cryptanalysis. In this letter, we propose 20-round impossible differential distinguishers for SPARX-128. Then, we utilize these distinguishers to attack 24 rounds (out of 40 rounds) of SPARX-128/256. Our attack has time complexity of 2232 memory accesses, memory complexity of 2160.81 128-bit blocks, and data complexity of 2104 chosen plaintexts.

SIMON is a lightweight block cipher designed by NSA in 2013. NSA presented the specification and the implementation efficiency, but they did not provide detailed security analysis nor the design rationale. The original SIMON has rotation constants of (1,8,2), and Kölbl et al. regarded the constants as a parameter (a,b,c), and analyzed the security of SIMON block cipher variants against differential and linear attacks for all the choices of (a,b,c). This paper complements the result of Kölbl et al. by considering integral and impossible differential attacks. First, we search the number of rounds of integral distinguishers by using a supercomputer. Our search algorithm follows the previous approach by Wang et al., however, we introduce a new choice of the set of plaintexts satisfying the integral property. We show that the new choice indeed extends the number of rounds for several parameters. We also search the number of rounds of impossible differential characteristics based on the miss-in-the-middle approach. Finally, we make a comparison of all parameters from our results and the observations by Kölbl et al. Interesting observations are obtained, for instance we find that the optimal parameters with respect to the resistance against differential attacks are not stronger than the original parameter with respect to integral and impossible differential attacks. Furthermore, we consider the security against differential attacks by considering differentials. From the result, we obtain a parameter that is potential to be better than the original parameter with respect to security against these four attacks.

Piccolo is a lightweight block cipher proposed by Sony Corporation in 2011. The designers showed two key modes, Piccolo-80 and Piccolo-128, which use an 80-bit secret key and a 128-bit one, respectively. Isobe and Shibutani estimated the security of Piccolo-80, and they showed that 14-round (reduced) Piccolo-80 w/o whitening keys is vulnerable against the Meet-in-the-Middle attack. The time complexity of their attack is about 273, but unfortunately it requires 264 texts, namely, the full code book. In this paper, we propose a new impossible differential attack against 14-round Piccolo-80 w/o whitening keys, and it can recover the secret key without relying on the full code book. The time complexity is 268 and it uses 262.2 distinct know plaintexts.

Counting the number of differentially active S-boxes is of great importance in evaluating the security of a block cipher against differential attack. Mouha et al. proposed a technique based on Mixed-Integer Linear Programming (MILP) to automatically calculate a lower bound of the number of differentially active S-boxes for word-oriented block ciphers, and applied it to symmetric ciphers AES and Enocoro-128v2. Later Sun et al. extended the method by introducing bit-level representations for S-boxes and new constraints in the MILP problem, and applied the extended method to PRESENT-80 and LBlock. This kind of methods greatly depends on the constraints in the MILP problem describing the differential propagation of the block cipher. A more accurate description of the differential propagation leads to a tighter bound on the number of differentially active S-boxes. In this paper, we refine the constraints in the MILP problem describing XOR operations, and apply the refined MILP modeling to determine a lower bound of the number of active S-boxes for the Lai-Massey type block cipher FOX in the model of single-key differential attack, and obtain a tighter bound in FOX64 than existing results. Experimental results show that 6, instead of currently known 8, rounds of FOX64 is strong enough to resist against basic single-key differential attack since the differential characteristic probability is upper bounded by 2-64, and thus the maximum differential characteristic probability of 12-round FOX64 is upper bounded by 2-128, where 128 is the key-length of FOX64. We also get the lower bound of the number of differentially active S-boxes for 5-round FOX128, and proved the security of the full-round FOX128 with respect to single-key differential attack.

CLEFIA is a 128-bit block cipher proposed by Shirai et al. at FSE2007. It has been reported that CLEFIA has a 9-round saturation characteristic, in which 32bits of the output of 9-th round 112-th order differential equals to zero. By using this characteristic, a 14-round CLEFIA with 256-bit secret key is attacked with 2113 blocks of chosen plaintext and 2244.5 times of data encryption. In this paper, we focused on a higher order differential of CLEFIA. This paper introduces two new concepts for higher order differential which are control transform for the input and observation transform for the output. With these concepts, we found a new 6-round saturation characteristic, in which 24bits of the output of 6-th round 9-th order differential equals to zero. We also show a new 9-round saturation characteristic using 105-th order differential which is a 3-round extension of the 6-round one. If we use it, instead of 112-th order differential, using the meet-in-the-middle attack technique for higher order differential table, the data and computational complexity for the attack to 14-round CLEFIA can be reduced to around 2-5, 2-34 of the conventional attack, respectively.

MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it is recommended for Japanese e-Government ciphers by the CRYPTREC project. In this paper, we report on 12th order differentials in 3-round MISTY1 with FL functions and 44th order differentials in 4-round MISTY1 with FL functions both previously unknown. We also report that both data complexity and computational complexity of higher order differential attacks on 6-round MISTY1 with FL functions and 7-round MISTY1 with FL functions using the 46th order differential can be reduced to as much as 1/22 of the previous values by using multiple 44th order differentials simultaneously.

Impossible differential attack (IDA) uses impossible differential characteristics extracted from enough plaintext pairs to retrieve subkeys of the first and the last several rounds of AES. In this paper, a general IDA on 7-round AES is proposed. Such attack takes the number of all-zero columns of the 7th and the 6th round as parameters (α,β). And a trade-off relation between the number of plaintexts and times of encryptions in the process of the attack is derived, which makes only some values of (α,β) allowed in the attack for different key length.

MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper shows that higher order differential attacks can be successful against 7-round versions of MISTY1 with FL functions. The attack on 7-round MISTY1 can recover a partial subkey with a data complexity of 254.1 and a computational complexity of 2120.8, which signifies the first successful attack on 7-round MISTY1 with no limitation such as a weak key. This paper also evaluates the complexity of this higher order differential attack on MISTY1 in which the key schedule is replaced by a pseudorandom function. It is shown that resistance to the higher order differential attack is not substantially improved even in 7-round MISTY1 in which the key schedule is replaced by a pseudorandom function.

MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper reports a previously unknown higher order differential characteristic of 4-round MISTY1 with the FL functions. It also shows that a higher order differential attack that utilizes this newly discovered characteristic is successful against 6-round MISTY1 with the FL functions. This attack can recover a partial subkey with a data complexity of 253.7 and a computational complexity of 264.4, which is better than any previous cryptanalysis of MISTY1.

This paper proposes novel calculuses of linearizing attack that can be applied to higher order differential attack. Higher order differential attack is a powerful and versatile attack on block ciphers. It can be roughly summarized as follows: (1) Derive an attack equation to estimate the key by using the higher order differential properties of the target cipher, (2) Determine the key by solving an attack equation. Linearizing attack is an effective method of solving attack equations. It linearizes an attack equation and determines the key by solving a system of linearized equations using approaches such as the Gauss-Jordan method. We enhance the derivation algorithm of the coefficient matrix for linearizing attack to reduce computational cost (fast calculus 1). Furthermore, we eliminate most of the unknown variables in the linearized equations by making the coefficient column vectors 0 (fast calculus 2). We apply these algorithms to an attack of the five-round variant of KASUMI and show that the attack complexity is equivalent to 228.9 chosen plaintexts and 231.2 KASUMI encryptions.

In this paper, we describe a technique for optimizing the algebraic method that is applied to higher order differential attack. The higher order differential attack is a well-known attack on block ciphers, in which we derive an attack equation to determine a round key from a property of a higher order differential of a target block cipher. The algebraic method is a linearization of the attack equation and determines the true key by a method such as Gaussian elimination. Our technique is based on linear dependency and can reduce the complexity of that method. We also describe a technique that allows the algebraic method to be used as an attack equation that holds probabilistically. We demonstrate this method by attacking a five-round MISTY1 and show that it needs 221.6 chosen plaintexts and 228.0 encryption times. The computer simulation took about two minutes to complete.

The encryption algorithm Camellia is a 128 bit block cipher proposed by NTT and Mitsubishi, Japan. Since the algebraic degree of the outputs after 3 rounds is greater than 128, designers estimate that it is impossible to attack Camellia by higher order differential. In this paper, we show a new higher order differential attack which controls the value of differential using proper fixed value of plaintext. As the result, we found that 6-round F-function can be attacked using 8th order differentials. The attack requires 217 chosen plaintexts and 222 F-function operations. Our computer simulation took about 2 seconds for the attack. If we take 2-R elimination algorithm, 7-round F-function will be attacked using 8th order differentials. This attack requires 219 chosen plaintexts and 264 F-function operations, which is less than exhaustive search for 128 bit key.

Interpolation attack was presented by Jakobsen and Knudsen at FSE'97. Interpolation attack is effective against ciphers that have a certain algebraic structure like the PURE cipher which is a prototype cipher, but it is difficult to apply the attack to real-world ciphers. This difficulty is due to the difficulty of deriving a low degree polynomial relation between ciphertexts and plaintexts. In other words, it is difficult to evaluate the security against interpolation attack. This paper generalizes the interpolation attack. The generalization makes easier to evaluate the security against interpolation attack. We call the generalized interpolation attack linear sum attack. We present an algorithm that evaluates the security of byte-oriented ciphers against linear sum attack. Moreover, we show the relationship between linear sum attack and higher order differential attack. In addition, we show the security of CRYPTON, E2, and RIJNDAEL against linear sum attack using the algorithm.

Since the proposal of differential cryptanalysis and linear cryptanalysis in 1991 and 1993, respectively, the resistance to these cryptanalysis has been studied. In FSE2, Knudsen proposed a method of attacking block ciphers that used the higher order differential, and in FSE4, Jakobsen and Knudsen applied it to a cipher proposed by Nyberg and Knudsen. Their approach, however, requires large complexity of running time. In this paper, we improve this attack and show that our improved algorithm requires much fewer chosen texts and much less complexity than those of previous works.

We propose a new randomized version of DES in which a key-dependent swapping is used to strengthen DES and DES-like cryptosystems against differential cryptanalysis. This new scheme, called RDES, decreases the probability of success in differential attack by decreasing the characteristic probability. The characteristic is the effect of particular differences in plaintext pairs on the differences in the resultant ciphertext pairs. The characteristic probability for the n-round RDES is 2-n+1 times that for the n-round DES. As for the differential cryptanalysis based on characteristics, the 16-round RDES is as strong as the about 20-round DES. Encryption/decryption speed of n-round RDES is almost the same as that of the n-round DES.