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Improved machine learning-aided linear cryptanalysis: application to DES

CYBERSECURITY 2025年第1期8卷 1-16页

作者： Hou, Zezhou Ren, Jiongjiong Chen, Shaozhen Informat Engn Univ Zhengzhou 450000 Peoples R China

In CRYPTO 2019, Gohr built a bridge between machine learning and differential cryptanalysis, which show that machine learning-aided methods have advantages over classical differential cryptanalysis. Yet, for linear cryptanalysis, there is lack of effective works showing that machine learning-aided cryptanalysis can reach the benchmark of traditional counterparts and also lack of an effective universal framework using machine learning to assist linear cryptanalysis. In this paper, we mainly focus on machine learning-aided linear cryptanalysis and application to Des. First, we propose a machine learning-aided model to distinguish different Bernoulli distributions and demonstrate the validity of the model through experiments and theoretical analysis. Based on the model, we propose a new machine learning-aided linear cryptanalysis framework, which can be applied to one bit and multiple bits key-recovery attacks. As applications, we perform one bit attacks on 3-, 4-, 5-, 6-round Des and multiple bits attack on 8-round Des. Compared with the previous works about machine learning-aided linear cryptanalysis, the results improve the success rate and the complexity. Most importantly, more rounds are covered in our work. Besides, the work indicates that machine learning-aided cryptanalysis can achieve the same or marginally better performance than classical methods.

关键词： Machine learning linear cryptanalysis Neural distinguisher Key recovery Des

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linear cryptanalysis of reduced-round SPECK

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INFORMATION PROCESSING LETTERS 2016年第3期116卷 259-266页

作者： Liu, Yu Fu, Kai Wang, Wei Sun, Ling Wang, Meiqin Shandong Univ Key Lab Cryptol Technol & Informat Secur Minist Educ Jinan 250100 Peoples R China

SPECK is a family of lightweight block ciphers which was proposed by United States National Security Agency and designed for optimal performance in software. The paper gives the security of SPECK against linear cryptanalysis and introduces 9, 10, 12, 15 and 16 rounds linear approximations on SPECK for block sizes of 32, 48, 64, 96 and 128 bits, respectively. Partial linear mask table is used to speed up the search progress rather than the linear mask table. Using the structure of red-black tree to store the pLMT, we deduce the search time. Combining the Segment Searching with branch-and-bound method, the search time is further reduced. For 48-, 96- and 128-bit version the lengths of the linear approximations are 1, 9 and 10 rounds longer than the previous linear cryptanalytic. For SPECK64 the correlation of the linear approximation is twice as much as the previous linear cryptanalytic. As a result, we improve the previous linear cryptanalysis and gain more obvious advantage for block lengths of 96 and 128 bits. Especially, in aspect of SPECK96/144, SPECK128/192 and SPECK128/256 we can attack the same rounds as the best previous attacks. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Lightweight block cipher SPECK linear approximation linear cryptanalysis Cryptography

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linear cryptanalysis of PRESENT-like Ciphers with Secret Permutation

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COMPUTER JOURNAL 2016年第4期59卷 549-558页

作者： Liu, Guo-Qiang Jin, Chen-Hui Natl Univ Def Technol Coll Sci Dept Math & Syst Sci Changsha 410073 Hunan Peoples R China Informat Sci & Technol Inst Zhengzhou 450000 Henan Peoples R China

This paper investigates the linear cryptanalysis of PRESENT-like cipher with secret permutation. Our contributions are 3-fold. First, we construct a distinguisher with more advantages by combining with 240 distinguishing characteristics, and use it to determine 4-bit positions those are mapped as an input into the same S-box through the secret permutation with a low data complexity. Secondly, we propose a method of constructing the candidate permutations based on this distinguisher. Finally, we present a method with low time complexity to identify the correct permutation from equivalent ones based on the information coming from the secret permutation and its inverse. We test our attack in practice with various reduced round versions of a PRESENT-like cipher with secret permutations. The experiments show that the correct permutation of 12-round PRESENT-like cipher can be recovered with 2(30.8) known plaintexts/ciphertexts, 2(49.6) time complexity and 2(19.28) memory complexity at a success rate of 90%. Our attack is generic to PRESENT-like ciphers with secret bit permutation.

关键词： block cipher PRESENT-like linear cryptanalysis secret permutation

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linear cryptanalysis of NUSH block cipher

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Science in China(Series F) 2002年第1期45卷 59-67页

作者：吴文玲冯登国 StateKeyLaboratoryofInformationSecurity InstituteofSoftwareChineseAcademyofSciencesBeijing100080China/EngineeringResearchCenterforInformationSecurityTechnologyChineseAcademyofSciencesBeijing100080China EngineeringResearchCenterforInformationSecurityTechnology ChineseAcademyofSciencesBeijing100080China

NUSH is a block cipher as a candidate for NESSIE. NUSH is analyzed by linear crypt-analysis . The complexity δ = (ε , η) of the attack consists of data complexity ε and time complexity η. Three linear approximations are used to analyze NUSH with 64-bit block. When |K| = 128 bits, the complexities of three attacks are (258, 2124), (260, 278) and (262, 255) respectively. When |K| = 192 bits, the complexities of three attacks are (258, 2157) (260, 2%) and (262, 258) respectively. When |K| = 256 bits, the complexities of three attacks are (258, 2125), (260, 278) and (262, 253) respectively. Three linear approximations are used to analyze NUSH with 128-bit block. When |K|= 128 bits, the complexities of three attacks are (2122, 295), (2124, 257) and (2126, 252) respectively. When |K| = 192 bits, the complexities of three attacks are (2122, 2142), (2124, 275) and (2126, 258) respectively. When |K|= 256 bits, the complexities of three attacks are (2122, 2168), (2124, 281) and (2126, 264) respectively. Two linear approximations are used to analyze NUSH with 256-bit block. When |K|= 128 bits, the complexities of two attacks are (2252, 2122) and (2254, 2119) respectively. When |K|= 192 bits, the complexities of two attacks are (2252, 2181) and (2254, 2177) respectively. When |K|=256 bits, the complexities of two attacks are (2252, 2240) and (2254, 2219) respectively. These results show that NUSH is not immune to linear cryptanalysis, and longer key cannot enhance the security of NUSH.

关键词： block cipher linear cryptanalysis linear approximation.

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linear cryptanalysis of Baby Rijndael 4

Linear Cryptanalysis of Baby Rijndael

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2015 Forth International Conference on e-Technologies and Networks for Development

作者： Kokes, Josef Lorencz, Robert Czech Tech Univ Fac Informat Technol Thakurova 9 Prague 16000 6 Czech Republic

ISBN: (纸本)9781479984510

We present results of linear cryptanalysis of Baby Rijndael, a reduced-size model of Rijndael. The results were obtained using exhaustive search of all approximations and all keys and show some curious properties of both linear cryptanalysis and Baby Rijndael, particularly the existence of different classes of linear approximations with significantly different success rates of recovery of the cipher's key.

关键词： linear cryptanalysis linear approximations Baby Rijndael key recovery success rate

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linear cryptanalysis of the PP-1 and PP-2 Block Ciphers 15

Linear Cryptanalysis of the PP-1 and PP-2 Block Ciphers

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15th International Conference on Cryptology in India (INDOCRYPT)

作者： Colburn, Michael Keliher, Liam Mt Allison Univ AceCrypt Res Grp Sackville NB E0A 3C0 Canada

ISBN: (纸本)9783319130392;9783319130385

PP-1 and PP-2 are scalable SPN-based block ciphers introduced in 2008 and 2013, respectively. PP-2 was intended as an improvement to PP-1, which was broken in 2011 using differential cryptanalysis. The designers of PP-2 claim that it is comparable to the Advanced Encryption Standard (AES) in its resistance to linear and differential cryptanalysis. However, we demonstrate that both PP-1 and PP-2 with 64-bit and 128-bit block sizes are vulnerable to linear cryptanalysis. Specifically, we find high probability linear hulls that allow us to break each cipher faster than exhaustive search of the keyspace. This is the first use of linear cryptanalysis against PP-1, and the first successful attack of any kind against PP-2. We confirm our theoretical results by experimentally breaking a reduced-round version of PP-2.

关键词： PP-1 PP-2 Block cipher SPN linear cryptanalysis

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linear cryptanalysis of FF3-1 and FEA 41st

Linear Cryptanalysis of FF3-1 and FEA

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41st Annual International Cryptology Conference (CRYPTO)

作者： Beyne, Tim Katholieke Univ Leuven IMEC COSIC Leuven Belgium

ISBN: (纸本)9783030842420;9783030842413

Improved attacks on generic small-domain Feistel ciphers with alternating round tweaks are obtained using linear cryptanalysis. This results in practical distinguishing and message-recovery attacks on the United States format-preserving encryption standard FF3-1 and the South-Korean standards FEA-1 and FEA-2. The data complexity of the proposed attacks on FF3-1 and FEA-1 is (O) over tilde (Nr/2-1.5), where N-2 is the domain size and r is the number of rounds. For example, FF3-1 with N = 10(3) can be distinguished from an ideal tweakable block cipher with advantage >= 1/10 using 2(23 )encryption queries. Recovering the left half of a message with similar advantage requires 2(24) data. The analysis of FF3-1 serves as an interesting real-world application of (generalized) linear cryptanalysis over the group Z/NZ.

关键词： linear cryptanalysis FF3-1 FEA-1 FEA-2 Format-preserving encryption

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linear cryptanalysis of Reduced-Round Speck with a Heuristic Approach: Automatic Search for linear Trails 21st

Linear Cryptanalysis of Reduced-Round Speck with a Heuristic...

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21st International Information Security Conference (ISC)

作者： Bodden, Daniel Katholieke Univ Leuven IMEC COSIC Leuven Belgium

ISBN: (纸本)9783319991368;9783319991351

Previous research on linear cryptanalysis with Speck has proved that good linear trails and a meaningful distinguisher for variants of Speck can be found. In this paper we use two different linear approximations of modular addition to search for even better linear trails. Also, we have added a heuristic to search for large bias approximations for the state conversion approach. We will explain how the automatic search works and discuss its performance. Finally we illustrate that linear approximations with large bias exist in variants of Speck.

关键词： Speck Lightweight ciphers Heuristic Automatic search linear cryptanalysis

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linear cryptanalysis and Its Variants with Fast Fourier Transformation Technique on MPC/FHE/ZK-Friendly Fp-Based Ciphers 28th

Linear Cryptanalysis and Its Variants with Fast Fourier Tran...

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28th Australasian Conference on Information Security and Privacy (ACISP)

作者： Xu, Zeyu Chen, Shiyao Wang, Meiqin Wei, Puwen Shandong Univ Key Lab Cryptol Technol & Informat Secur Minist Educ Jinan Peoples R China Shandong Univ Sch Cyber Sci & Technol Qingdao Peoples R China Nanyang Technol Univ Strateg Ctr Res Privacy Preserving Technol & Syst Singapore Singapore Quan Cheng Shandong Lab Jinan Peoples R China

ISBN: (纸本)9783031354854;9783031354861

The emergence of advanced cryptographic protocols has promoted the developments of many applications, such as secure multiparty computation (MPC). For this reason, new symmetric-key primitives have been designed to natively support the finite field F-p with odd characteristic for better efficiencies. However, some well-studied symmetric cryptanalytic methods and techniques over F-2(n) cannot be applied to these new primitives over F-p directly. Considering less standard design approaches adopted in these novel MPC-friendly ciphers, these proposals are in urgent need of full investigations;generalizations of the traditional cryptanalytic tools and techniques to F-p will also contribute to better understand the security of these new designs. In this paper, we first show that the Fast Fourier Transform (FFT) technique for the estimations of correlation, introduced by Collard et al. at ICISC 2007, can be applied to F-p and significantly improves the complexity of Matsui's Algorithm 2 over F-p. Then, we formalize the differential-linear (DL) cryptanalysis to F-p. Inspired by the differential-linear connectivity table (DLCT) introduced by Bar-On et al. at EUROCRYPT 2019, we also include the DLCT into the consideration, and find the relation between DLCT and differential distribution table (DDT) over F-p. Finally, we mount key recovery attacks on a version of HADESMiMC, which is a SHARK-like MPC-friendly block cipher proposed by Grassi et al. at EUROCRYPT 2020. We denote this version as HADESMiMC-128 in this paper. For linear cryptanalysis with the FFT technique, we can attack 7 rounds of HADESMiMC-128. For DL cryptanalysis, a 7-round key recovery attack of HADESMiMC-128 is also mounted but with better time and data complexity. It should be noted that the attacks are still far from threatening the security of the full 14-round HADESMiMC-128.

关键词： MPC-Friendly Block Ciphers linear cryptanalysis Differential-linear cryptanalysis Fast Fourier Transformation HADES

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linear cryptanalysis Reduced Round of Piccolo-80 1

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3rd International Symposium on Cyber Security Cryptography and Machine Learning (CSCML)

作者： Ashur, Tomer Dunkelman, Orr Masalha, Nael Katholieke Univ Leuven Dept Elect Engn ESAT COSIC Leuven Belgium IMinds Leuven Belgium Univ Haifa Dept Comp Sci Haifa Israel

ISBN: (数字)9783030209513

ISBN: (纸本)9783030209513;9783030209506

Piccolo is a 64-bit lightweight block cipher suitable for constrained environments such as wireless sensor networks. In this paper we evaluate the security of Piccolo-80 against linear cryptanalysis, we present a 6-round linear approximation of Piccolo-80 with probability 1/2 + 2(-29.04). We use this approximation to attack 7-round Piccolo-80 (with whitening keys) with data complexity of 2(61) known plaintexts and time complexity of 2(61). Its extension to an 8-round attack merely increases the time complexity to 2(70). This is the best linear attack against Piccolo-80 and it is also applicable to Piccolo-128 as the difference between the two variates is only the number of rounds and the key schedule algorithm. Moreover, we show that the bias in the approximation of the F-function, in some cases, is related to the MSB of the input. We utilize this relation to efficiently extract the MSBs of the whitening keys in the first round.

关键词： Piccolo linear cryptanalysis

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