• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.1
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• pp.435-451
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• 2019

Impossible differential cryptanalysis is an essential cryptanalytic technique and its key point is whether there is an impossible differential path. The main factor of influencing impossible differential cryptanalysis is the length of the rounds of the impossible differential trail because the attack will be more close to the real encryption algorithm with the number becoming longer. We provide the upper bound of the longest impossible differential trails of several important block ciphers. We first analyse the national standard of the Russian Federation in 2015, Kuznyechik, which utilizes the 16-byte LFSR to achieve the linear transformation. We conclude that there is no any 3-round impossible differential trail of the Kuznyechik without the consideration of the specific S-boxes. Then we ascertain the longest impossible differential paths of several other important block ciphers by using the matrix method which can be extended to many other block ciphers. As a result, we show that, unless considering the details of the S-boxes, there is no any more than or equal to 5-round, 7-round and 9-round impossible differential paths for KLEIN, Midori64 and MIBS respectively.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.11
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• pp.5773-5784
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• 2019

ARIA is an involutory SPN block cipher. Its block size is 128-bit and the master key sizes are 128/192/256-bit, respectively. Accordingly, they are called ARIA-128/192/256. As we all know, ARIA is a Korean Standard block cipher nowadays. This paper focuses on the security of ARIA against impossible differential attack. We firstly construct a new 4-round impossible differential of ARIA. Furthermore, based on this impossible differential, a new 7-round impossible differential attack on ARIA-256 is proposed in our paper. This attack needs 2¹¹⁸ chosen plaintexts and 2²¹⁰ 7-round encryptions. Comparing with the previous best result, we improve both the data complexity and time complexity. To our knowledge, it is the best impossible differential attack on ARIA-256 so far.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.3
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• pp.972-985
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• 2022

In the year 2020, a new lightweight block cipher µ² is proposed. It has both good software and hardware performance, and it is especially suitable for constrained resource environment. However, the security evaluation on µ² against impossible differential cryptanalysis seems missing from the specification. To fill this gap, an impossible differential cryptanalysis on µ² is proposed. In this paper, firstly, some cryptographic properties on µ² are proposed. Then several longest 7-round impossible differential distinguishers are constructed. Finally, an impossible differential cryptanalysis on µ² reduced to 10 rounds is proposed based on the constructed distinguishers. The time complexity for the attack is about 2^69.63 10-round µ² encryptions, the data complexity is O(2⁴⁸), and the memory complexity is 2^63.57 Bytes. The reported result indicates that µ² reduced to 10 rounds can't resist against impossible differential cryptanalysis.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.27 no.3
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• pp.427-437
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• 2017

Impossible differential characteristics distinguish the corresponding block cipher from random substitution and can also be used for key recovery attack. Recently Cui et al. proposed an automatic method for searching impossible differential characteristics of several ARX - based block ciphers using Mixed Integer Linear Programming(MILP). By optimizing the method proposed by Cui et al., It was possible to find new impossible differential characteristics which could not be founded by the method by using less linear constraint expression than the existing method. It was applied to the SPECK family and LEA using the modified method. We found 7-rounds for SPECK32, SPECK48, SPECK64, SPECK96 and 8-rounds impossible differential characteristics of SPECK128. These impossible differential characteristics are all newly found. We also found existing 10-rounds of impossible differential characteristic and new 10-rounds of impossible differential characteristics of LEA.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.10
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• pp.3815-3833
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• 2021

MILP-based automatic search is the most common method in analyzing the security of cryptographic algorithms. However, this method brings many issues such as low efficiency due to the large size of the model, and the difficulty in finding the contradiction of the impossible differential distinguisher. To analyze the security of ESF algorithm, this paper introduces a simplified MILP-based search model of the differential distinguisher by reducing constrains of XOR and S-box operations, and variables by combining cyclic shift with its adjacent operations. Also, a new method to find contradictions of the impossible differential distinguisher is proposed by introducing temporary variables, which can avoid wrong and miss selection of contradictions. Based on a 9-round impossible differential distinguisher, 15-round attack of ESF can be achieved by extending forward and backward 3-round in single-key setting. Compared with existing results, the exact lower bound of differential active S-boxes in single-key setting for 10-round ESF are improved. Also, 2108 9-round impossible differential distinguishers in single-key setting and 14 12-round impossible differential distinguishers in related-key setting are obtained. Especially, the round of the discovered impossible differential distinguisher in related-key setting is the highest, and compared with the previous results, this attack achieves the highest round number in single-key setting.

• ETRI Journal
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• v.36 no.6
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• pp.1032-1040
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• 2014

The Lai-Massey scheme, proposed by Vaudenay, is a modified structure in the International Data Encryption Algorithm cipher. A family of block ciphers, named FOX, were built on the Lai-Massey scheme. Impossible differential cryptanalysis is a powerful technique used to recover the secret key of block ciphers. This paper studies the impossible differential cryptanalysis of the Lai-Massey scheme with affine orthomorphism for the first time. Firstly, we prove that there always exist 4-round impossible differentials of a Lai-Massey cipher having a bijective F-function. Such 4-round impossible differentials can be used to help find 4-round impossible differentials of FOX64 and FOX128. Moreover, we give some sufficient conditions to characterize the existence of 5-, 6-, and 7-round impossible differentials of Lai-Massey ciphers having a substitution-permutation (SP) F-function, and we observe that if Lai-Massey ciphers having an SP F-function use the same diffusion layer and orthomorphism as a FOX64, then there are indeed 5- and 6-round impossible differentials. These results indicate that both the diffusion layer and orthomorphism should be chosen carefully so as to make the Lai-Massey cipher secure against impossible differential cryptanalysis.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.3
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• pp.119-127
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• 2003

Impossible differential cryptanalysis(IDC) introduced by Biham et. ${al}^{[4]}$ uses impossible differential characteristics. There-fore, a security of a block cipher against IDC is measured by impossible differential characteristics. In this paper, we pro-vide a wildly applicable method to find various impossible differential characteristics of block cipher structures not using the specified form of a round function. Using this method, we can find various impossible differential characteristics for Nyberg's generalized Feistel network and a generalized RC6-like structure. Throughout the paper, we assume round functions used in block cipher structures are bijective.ctive.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.4
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• pp.77-85
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• 2002

We present the impossible differential cryptanalysis of the block cipher XTEA[7] and TEA[6]. The core of the design principle of these block ciphers is an easy implementation and a simplicity. But this simplicity dose not offer a large diffusion property. Our impossible differential cryptanalysis of reduced-round versions of XTEA and TEA is based on this fact. We will show how to construct a 12-round impossible characteristic of XTEA. We can then derive 128-bit user key of the 14-round XTEA with $2^{62.5}$ chosen plaintexts and $2^{85}$ encryption times using the 12-round impossible characteristic. In addition, we will show how to construct a 10-round impossible characteristic or TEA. Then we can derive 128-bit user key or the 11-round TEA with $2^{52.5}$ chosen plaintexts and $2^{84}$ encryption times using the 10-round impossible characteristic.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.3
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• pp.103-107
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• 2005

Impossible differential attacks on AES have been proposed up to 6-round which requires $2^{91.5}$ chosen plaintexts and $2^{122}$ 6-round AES encryptions. In this paper, we introduce various 4-round impossible differentials and using them, we propose improved impossible differential attacks on 6-round AES. The current attacks require $2^{83.4}$ chosen plaintexts and $2^{105.4}$ 6-round AES encryptions to retrieve 11 bytes of the first and the last round keys.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.1
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• pp.13-24
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• 2009

CLEFIA is a 128-bit block cipher which is proposed by SONY corporation and ARIA is a 128-bit block cipher which is selected as a standard cryptographic primitive. In this paper, we introduce new multiple impossible differential cryptanalysis and apply it to CLEFIA using 9-round impossible differentials proposed in [7], and apply it to ARIA using 4-round impossible differentials proposed in [11]. Our cryptanalytic results on CLEFIA and ARIA are better than previous impossible differential attacks.