• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권3호
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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.

• ETRI Journal
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• 제36권6호
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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.

• 정보보호학회논문지
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• 제12권4호
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• pp.77-85
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• 2002

본 논문에서는 TEA[7]와 TEA[6]의 축소된 라운드에 대한 불능 차분 공격 (Impossible Differential Cryptanalysis)에 관하여 알아본다. 이 두 블록 암호의 주요 설계원리는 단순성과 효율성의 추구이다. 그러나 단순성 추구가 큰 확산 (diffusion) 효과를 주지 못하여, XTEA와 TEA의 축소된 라운드에 대한 불능 차분 공격을 가능하게 한다. 구체적으로 말하면 12라운드 불능 차분 특성을 이용하여 14라운드 XTEA에 대하여 $2^{62.5}$개의 선택평문들과 $2^{85}$번의 암호화 과정을 통하여 128비트 마스터키를 찾아낼 수 있다. 또한, TEA의 경우 10라운드 불능 차분 특성을 이용하여 11라운드 마스터키를 $2^{52.5}$개의 선택평문들과 약 $2^{84}$번의 암호화 과정을 통하여 찾아낸다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권1호
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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.

• 정보보호학회논문지
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• 제19권1호
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• pp.13-24
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• 2009

CLEFIA는 SONY사에서 제안한 128-비트 블록 암호이다. 그리고 ARIA는 국내 표준으로 선정된 128-비트 블록 암호이다. 본 논문에서는 다중 불능 차분 공격을 소개하고, [7]에서 제시한 9-라운드 불능 차분을 이용하여 다중 불능 차분 공격을 CLEFIA에 적용한다. 또한 [11]에서 제시한 4-라운드 불능 차분을 이용하여 다중 불능 차분 공격을 ARIA에 적용한다. 본 논문의 CLEFIA 및 ARIA에 대한 다중 불능 차분 공격은 지금까지 제안된 불능 차분 공격보다 더 좋은 결과를 보여준다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권11호
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• pp.5717-5730
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• 2019

LBlock-s is the core block cipher of authentication encryption algorithm LAC, which uses the same structure of LBlock and an improved key schedule algorithm with better diffusion property. Using the differential properties of the key schedule algorithm and the cryptanalytic technique which combines impossible boomerang attacks with related-key attacks, a 15-round related-key impossible boomerang distinguisher is constructed for the first time. Based on the distinguisher, an attack on 22-round LBlock-s is proposed by adding 4 rounds on the top and 3 rounds at the bottom. The time complexity is about only 2^68.76 22-round encryptions and the data complexity is about 2⁵⁸ chosen plaintexts. Compared with published cryptanalysis results on LBlock-s, there has been a sharp decrease in time complexity and an ideal data complexity.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권4호
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• pp.1944-1956
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• 2016

The Digital Video Broadcasting-Common Scrambling Algorithm is an ETSI-designated algorithm designed for protecting MPEG-2 signal streams, and it is universally used. Its structure is a typical hybrid symmetric cipher which contains stream part and block part within a symmetric cipher, although the entropy is 64 bits, there haven't any effective cryptanalytic results up to now. This paper studies the security level of CSA against impossible differential cryptanalysis, a 20-round impossible differential for the block cipher part is proposed and a flaw in the cipher structure is revealed. When we attack the block cipher part alone, to recover 16 bits of the initial key, the data complexity of the attack is O(2^44.5), computational complexity is O(2^22.7) and memory complexity is O(2^10.5) when we attack CSA-BC reduced to 21 rounds. According to the structure flaw, an attack on CSA with block cipher part reduced to 21 rounds is proposed, the computational complexity is O(2^21.7), data complexity is O(2^43.5) and memory complexity is O(2^10.5), we can recover 8 bits of the key accordingly. Taking both the block cipher part and stream cipher part of CSA into consideration, it is currently the best result on CSA which is accessible as far as we know.

• 정보보호학회논문지
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• 제13권3호
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• pp.119-127
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• 2003

Biha $m^{［4］}$등에 의해 소개된 불능 차분 공격은 불능 차분 특성을 이용하는 공격법이다 그러므로 블록 암호의 불능차분 공격에 대한 안전성은 불능 차분 특성에 의해 측정된다. 본 논문에서는 라운드 함수의 구체적인 형태를 고려하지 아니한 블록 암호 구조로부터 발생할 수 있는 여러 가지 불능 차분 특성을 찾는 널리 활용 가능한 방법을 제시한다. 이 방법을 이용하여 Nyber $g^{［12］}$ 가 제시한 일반화된 Feistel network와 일반화된 RC6 유사 구조에 대한 여러 가지 불능 차분 특성을 찾을 수 있다. 본 논문에서 다루는 모든 라운드 함수는 전단사 함수이다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제7권3호
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• pp.509-521
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• 2013

Impossible Differential Cryptanalysis (IDC) uses impossible differentials to discard wrong subkeys for the first or the last several rounds of block ciphers. Thus, the security of a block cipher against IDC can be evaluated by impossible differentials. This paper studies impossible differentials for Rijndael-like and 3D-like ciphers, we introduce methods to find 4-round impossible differentials of Rijndael-like ciphers and 6-round impossible differentials of 3D-like ciphers. Using our methods, various new impossible differentials of Rijndael and 3D could be searched out.

• 정보보호학회논문지
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• 제27권3호
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• pp.427-437
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• 2017

불능 차분 특성은 해당 블록 암호를 랜덤 치환과 구별을 해주며, 키 복구 공격에도 사용될 수 있다. 최근 Cui 등이 ARX 기반 블록 암호에 대해 Mixed-Integer Linear Programming(MILP)를 이용해서 자동화된 불능 차분 특성 탐색 방법을 제안하였다. Cui 등이 제안한 방법을 개선하면 기존에 방법에 비해 더 적은 선형 제약식을 이용하여 기존 방식으로 찾지 못하는 불능 차분 특성까지 추가 되어 더 많은 불능 차분 특성을 찾아 낼 수 있다. 수정한 방법을 이용하여 SPECK family와 LEA에 적용하였다. SPECK32, SPECK48, SPECK64, SPECK96에 대해 7-라운드, SPECK128에 대해 8-라운드 불능 차분 특성을 찾아내었다. 이 불능 차분 특성은 모두 새롭게 발견된 것이다. LEA에 대해서는 기존의 10-라운드인 불능 차분 특성을 포함한 새로운 10-라운드 불능 차분 특성을 찾아내었다.