Improved Integral Cryptanalysis of FOX Block Cipher

FOX is a new family of block ciphers presented recently, which is based upon some results on proven security and has high performances on various platforms. In this paper, we construct some distinguishers between 3-round FOX and a random permutation of the blocks space. By using integral attack and collision-searching techniques, the distinguishers are used to attack on 4, 5, 6 and 7-round of FOX64, 4 and 5-round FOX128. The attack is more efficient than previous integral attack on FOX. The complexity of improved integral attack is $2^{77.6}$ on 4-round FOX128, $2^{205.6}$ against 5-round FOX128 respectively. For FOX64, the complexity of improved integral attack is $2^{45.4}$ on 4-round FOX64, $2^{109.4}$ against 5-round FOX64, $2^{173.4}$ against 6-round FOX64, $2^{237.4}$ against 7-round FOX64 respectively. Therefore, 4-round FOX64/64, 5-round FOX64/128, 6-round FOX64/192, 7-round FOX64/256 and 5-round FOX128/256 are not immune to the attack in this paper

Impossible Differential Cryptanalysis of FOX

Block ciphers are the very foundation of computer and information security. FOX, also known as IDEA NXT, is a family of block ciphers published in 2004 and is famous for its provable security to cryptanalysis. In this paper, we apply impossible differential cryptanalysis on FOX cipher. We find a 4-round impossible difference, by using which adversaries can attack 5, 6 and 7-round FOX64 with $2^{71}$, $2^{135}$ and $2^{199}$ one-round encryptions respectively. Compared to the previous best attack with $2^{109.4}$, $2^{173.4}$ and $2^{237.4}$ full-round encryptions to 5, 6 and 7-round FOX64, the method in this paper is the best attack to FOX cipher. This attack can also be applied to 5-round FOX128 with $2^{135}$ one-round encryptions

Statistical cryptanalysis of block ciphers

Since the development of cryptology in the industrial and academic worlds in the seventies, public knowledge and expertise have grown in a tremendous way, notably because of the increasing, nowadays almost ubiquitous, presence of electronic communication means in our lives. Block ciphers are inevitable building blocks of the security of various electronic systems. Recently, many advances have been published in the field of public-key cryptography, being in the understanding of involved security models or in the mathematical security proofs applied to precise cryptosystems. Unfortunately, this is still not the case in the world of symmetric-key cryptography and the current state of knowledge is far from reaching such a goal. However, block and stream ciphers tend to counterbalance this lack of "provable security" by other advantages, like high data throughput and ease of implementation. In the first part of this thesis, we would like to add a (small) stone to the wall of provable security of block ciphers with the (theoretical and experimental) statistical analysis of the mechanisms behind Matsui's linear cryptanalysis as well as more abstract models of attacks. For this purpose, we consider the underlying problem as a statistical hypothesis testing problem and we make a heavy use of the Neyman-Pearson paradigm. Then, we generalize the concept of linear distinguisher and we discuss the power of such a generalization. Furthermore, we introduce the concept of sequential distinguisher, based on sequential sampling, and of aggregate distinguishers, which allows to build sub-optimal but efficient distinguishers. Finally, we propose new attacks against reduced-round version of the block cipher IDEA. In the second part, we propose the design of a new family of block ciphers named FOX. First, we study the efficiency of optimal diffusive components when implemented on low-cost architectures, and we present several new constructions of MDS matrices; then, we precisely describe FOX and we discuss its security regarding linear and differential cryptanalysis, integral attacks, and algebraic attacks. Finally, various implementation issues are considered

Improved All-Subkeys Recovery Attacks on FOX, KATAN and SHACAL-2 Block Ciphers

The all-subkeys recovery (ASR) attack is an extension of the meet-in-the-middle attack, which allows evaluating the security of a block cipher without analyzing its key scheduling function. Combining the ASR attack with some advanced techniques such as the function reduction and the repetitive ASR attack, we show the improved ASR attacks on the 7-round reduced FOX64 and FOX128. Moreover, the improved ASR attacks on the 119-, 105- and 99-round reduced KATAN32, KATAN48 and KATAN64, and the 42-round reduced SHACAL-2 are also presented, respectively. As far as we know, all of those attacks are the best single-key attacks with respect to the number of attacked rounds in literature

Automated Dynamic Cube Attack on Block Ciphers: Cryptanalysis of SIMON and KATAN

A few work has ever been performed in cryptanalysis of block ciphers using cube attacks. This paper presents a new framework for an efficient key recovery attack on block ciphers based on cube technique. In this method, a cube tester is positioned at the middle of the cipher which is extended in two directions over the maximum possible upper and lower rounds, given that some subkey bits are guessed. It is shown that an automated algorithm for this dynamic cube attack on block ciphers can be realized. Furthermore, we show its effectiveness on two lightweight block ciphers KATAN and SIMON. Our results shows that this method can break 117 and 152 out of 254 rounds of KATAN-32 in non-full-codebook and full-codebook attack scenarios, respectively. In the case of SIMON32/64, we succeed to cryptanalyse 16 and 18 out of 32 rounds, by the same scenarios. Both results show that although this method does not outperform all the existing attacks on these two ciphers, it can absolutely compete with the well-established and mature methods of cryptanalysis of block ciphers, such as linear, differential and meet in the middle attack families

A Salad of Block Ciphers

This book is a survey on the state of the art in block cipher design and analysis. It is work in progress, and it has been for the good part of the last three years -- sadly, for various reasons no significant change has been made during the last twelve months. However, it is also in a self-contained, useable, and relatively polished state, and for this reason I have decided to release this \textit{snapshot} onto the public as a service to the cryptographic community, both in order to obtain feedback, and also as a means to give something back to the community from which I have learned much. At some point I will produce a final version -- whatever being a ``final version\u27\u27 means in the constantly evolving field of block cipher design -- and I will publish it. In the meantime I hope the material contained here will be useful to other people

Quantum Attacks on Lai-Massey Structure

Aaram Yun et al. considered that Lai-Massey structure has the same security as Feistel structure. However, Luo et al. showed that 3-round Lai-Massey structure can resist quantum attacks of Simon\u27s algorithm, which is different from Feistel structure. We give quantum attacks against a typical Lai-Massey structure. The result shows that there exists a quantum CPA distinguisher against 3-round Lai-Massey structure and a quantum CCA distinguisher against 4-round Lai-Massey Structure, which is the same as Feistel structure. We extend the attack on Lai-Massey structure to quasi-Feistel structure. We show that if the combiner of quasi-Feistel structure is linear, there exists a quantum CPA distinguisher against 3-round balanced quasi-Feistel structure and a quantum CCA distinguisher against 4-round balanced quasi-Feistel Structure

Related-Key Differential Attack on Round Reduced RECTANGLE-80

RECTANGLE is a newly proposed lightweight block cipher which allows fast implementations for multiple platforms by using bit-slice techniques. It is an iterative 25-round SPN block cipher with a 64-bit block size and a 80-bit or 128-bit key size. Until now, the results on analyzing the cipher are not too much, which includes an attack on the 18-round reduced version proposed by the designers themselves. In this paper, we find all 15-round differential characteristics with 26--30 active S-boxes for given input, output and round subkey differences, which have a total probability $2^{-60.5}$. Based on these differential characteristics, we extend the corresponding distinguisher to 2 rounds backward and forward respectively, and propose an attack on the 19-round reduced RECTANGLE-80 with data complexity of $2^{62}$ plaintexts, time complexity of about $2^{67.42}$ encryptions and memory complexity of $2^{72}$. TThese data and time complexities are much lower than that of the designers for the 18-round reduced RECTANGLE-80

Multi-algorithmic Cryptography using Deterministic Chaos with Applications to Mobile Communications

In this extended paper, we present an overview of the principal issues associated with cryptography, providing historically significant examples for illustrative purposes as part of a short tutorial for readers that are not familiar with the subject matter. This is used to introduce the role that nonlinear dynamics and chaos play in the design of encryption engines which utilize different types of Iteration Function Systems (IFS). The design of such encryption engines requires that they conform to the principles associated with diffusion and confusion for generating ciphers that are of a maximum entropy type. For this reason, the role of confusion and diffusion in cryptography is discussed giving a design guide to the construction of ciphers that are based on the use of IFS. We then present the background and operating framework associated with a new product - CrypsticTM - which is based on the application of multi-algorithmic IFS to design encryption engines mounted on a USB memory stick using both disinformation and obfuscation to ‘hide’ a forensically inert application. The protocols and procedures associated with the use of this product are also briefly discussed