Related-key Impossible Differential Analysis of Full Khudra

Khudra is a 18-round lightweight block cipher proposed by Souvik Kolay and Debdeep Mukhopadhyay in the SPACE 2014 conference which is applicable to Field Programmable Gate Arrays (FPGAs). In this paper, we obtain $2^{16}$ 14-round related-key impossible differentials of Khudra, and based on these related-key impossible differentials for 32 related keys, we launch an attack on the full Khudra with data complexity of $2^{63}$ related-key chosen-plaintexts, time complexity of about $2^{68.46}$ encryptions and memory complexity of $2^{64}$

A Guess-and-Determine Attack on Reduced-Round Khudra and Weak Keys of Full Cipher

Khudra is a lightweight block cipher designed for Field Programmable Gate Array (FPGA) based platforms. The cipher has an 18-round generalized type-2 Feistel structure with 64-bit block size. The key schedule takes 80-bit master key and produces 32-bit round keys performing very simple operations. In this work, we analyze the security of Khudra. We first show that the effective round key length is 16-bit. By the help of this observation, we improve the 14-round MITM attack proposed by Youssef et al. by reducing the memory complexity from $2^{64.8}$ to $2^{32.8}$. Also, we propose a new guess-and-determine type attack on 14 rounds where only 2 known plaintext-ciphertext pairs are required to mount the attack in a time complexity of $2^{64}$ encryption operations. To the best of our knowledge, this is the best attack in the single key model in terms of time, memory and data complexities where the data complexity is equal to the minimum theoretical data requirement. Moreover, we present two observations on differential probabilities of the round function and the symmetric structure of the cipher. We introduce $2^{40}$ weak keys for the full cipher by exploiting the symmetric structure of the cipher

An overview of memristive cryptography

Smaller, smarter and faster edge devices in the Internet of things era demands secure data analysis and transmission under resource constraints of hardware architecture. Lightweight cryptography on edge hardware is an emerging topic that is essential to ensure data security in near-sensor computing systems such as mobiles, drones, smart cameras, and wearables. In this article, the current state of memristive cryptography is placed in the context of lightweight hardware cryptography. The paper provides a brief overview of the traditional hardware lightweight cryptography and cryptanalysis approaches. The contrast for memristive cryptography with respect to traditional approaches is evident through this article, and need to develop a more concrete approach to developing memristive cryptanalysis to test memristive cryptographic approaches is highlighted.Comment: European Physical Journal: Special Topics, Special Issue on "Memristor-based systems: Nonlinearity, dynamics and applicatio

Cryptanalysis of Block Ciphers with New Design Strategies

Block ciphers are among the mostly widely used symmetric-key cryptographic primitives, which are fundamental building blocks in cryptographic/security systems. Most of the public-key primitives are based on hard mathematical problems such as the integer factorization in the RSA algorithm and discrete logarithm problem in the DiffieHellman. Therefore, their security are mathematically proven. In contrast, symmetric-key primitives are usually not constructed based on well-defined hard mathematical problems. Hence, in order to get some assurance in their claimed security properties, they must be studied against different types of cryptanalytic techniques. Our research is dedicated to the cryptanalysis of block ciphers. In particular, throughout this thesis, we investigate the security of some block ciphers constructed with new design strategies. These new strategies include (i) employing simple round function, and modest key schedule, (ii) using another input called tweak rather than the usual two inputs of the block ciphers, the plaintext and the key, to instantiate different permutations for the same key. This type of block ciphers is called a tweakable block cipher, (iii) employing linear and non-linear components that are energy efficient to provide low energy consumption block ciphers, (iv) employing optimal diffusion linear transformation layer while following the AES-based construction to provide faster diffusion rate, and (v) using rather weak but larger S-boxes in addition to simple linear transformation layers to provide provable security of ARX-based block ciphers against single characteristic differential and linear cryptanalysis. The results presented in this thesis can be summarized as follows: Initially, we analyze the security of two lightweight block ciphers, namely, Khudra and Piccolo against Meet-in-the-Middle (MitM) attack based on the Demirci and Selcuk approach exploiting the simple design of the key schedule and round function. Next, we investigate the security of two tweakable block ciphers, namely, Kiasu-BC and SKINNY. According to the designers, the best attack on Kiasu-BC covers 7 rounds. However, we exploited the tweak to present 8-round attack using MitM with efficient enumeration cryptanalysis. Then, we improve the previous results of the impossible differential cryptanalysis on SKINNY exploiting the tweakey schedule and linear transformation layer. Afterwards, we study the security of new low energy consumption block cipher, namely, Midori128 where we present the longest impossible differential distinguishers that cover complete 7 rounds. Then, we utilized 4 of these distinguishers to launch key recovery attack against 11 rounds of Midori128 to improve the previous results on this cipher using the impossible differential cryptanalysis. Then, using the truncated differential cryptanalysis, we are able to attack 13 rounds of Midori128 utilizing a 10-round differential distinguisher. We also analyze Kuznyechik, the standard Russian federation block cipher, against MitM with efficient enumeration cryptanalysis where we improve the previous results on Kuznyechik, using MitM attack with efficient enumeration, by presenting 6-round attack. Unlike the previous attack, our attack exploits the exact values of the coefficients of the MDS transformation that is used in the cipher. Finally, we present key recovery attacks using the multidimensional zero-correlation cryptanalysis against SPARX-128, which follows the long trail design strategy, to provide provable security of ARX-based block ciphers against single characteristic differential and linear cryptanalysis

Криптографические протоколы и примитивы в сетях интернета вещей

В статье рассмотрены криптографические протоколы и примитивы, которые могут быть использованы в сетях интернета вещей. Интернет вещей предполагает объединение в информационную сеть многих аспектов частной жизни человека и поэтому требует особой защиты. В данной работе рассматривается вопрос применимости атрибутно-основанного шифрования и легковесных криптографических примитивов в системах интернета вещей

Autoguess: A Tool for Finding Guess-and-Determine Attacks and Key Bridges

The guess-and-determine technique is one of the most widely used techniques in cryptanalysis to recover unknown variables in a given system of relations. In such attacks, a subset of the unknown variables is guessed such that the remaining unknowns can be deduced using the information from the guessed variables and the given relations. This idea can be applied in various areas of cryptanalysis such as finding the internal state of stream ciphers when a sufficient amount of output data is available, or recovering the internal state and the secret key of a block cipher from very few known plaintexts. Another important application is the key-bridging technique in key-recovery attacks on block ciphers, where the attacker aims to find the minimum number of required sub-key guesses to deduce all involved sub-keys via the key schedule. Since the complexity of the guess-and-determine technique directly depends on the number of guessed variables, it is essential to find the smallest possible guess basis, i.e., the subset of guessed variables from which the remaining variables can be deduced. In this paper, we present Autoguess, an easy-to-use general tool to search for a minimal guess basis. We propose several new modeling techniques to harness SAT/SMT, MILP, and Gröbner basis solvers. We demonstrate their usefulness in guess-and-determine attacks on stream ciphers and block ciphers, as well as finding key-bridges in key recovery attacks on block ciphers. Moreover, integrating our CP models for the key-bridging technique into the previous CP-based frameworks to search for distinguishers, we propose a unified and general CP model to search for key recovery friendly distinguishers which supports both linear and nonlinear key schedules

Revisiting the Boomerang Attack from a Perspective of 3-differential

In this paper, inspired by the work of Beyne and Rijmen at CRYPTO 2022, we explore the accurate probability of $d$-differential in the fixed-key model. The theoretical foundations of our method are based on a special matrix $-$ quasi-$d$-differential transition matrix, which is a natural extension of the quasidifferential transition matrix. The role of quasi-$d$-differential transition matrices in polytopic cryptananlysis is analogous to that of correlation matrices in linear cryptanalysis. Therefore, the fixed-key probability of a $d$-differential can be exactly expressed as the sum of the correlations of its quasi-$d$-differential trails. Then we revisit the boomerang attack from a perspective of 3-differential. Different from previous works, the probability of a boomerang distinguisher can be exactly expressed as the sum of the correlations of its quasi-$3$-differential trails without any assumptions in our work. In order to illustrate our theory, we apply it to the lightweight block cipher GIFT. It is interesting to find the probability of every optimal 3-differential characteristic of an existing 2-round boomerang is zero, which can be seen as an evidence that the security of block ciphers adopting half-round key XOR might be overestimated previously to some extent in differential-like attacks

Improving the Rectangle Attack on GIFT-64

GIFT is a family of lightweight block ciphers based on SPN structure and composed of two versions named GIFT-64 and GIFT-128. In this paper, we reevaluate the security of GIFT-64 against the rectangle attack under the related-key setting. Investigating the previous rectangle key recovery attack on GIFT-64, we obtain the core idea of improving the attack——trading off the time complexity of each attack phase. We flexibly guess part of the involved subkey bits to balance the time cost of each phase so that the overall time complexity of the attack is reduced. Moreover, the reused subkey bits are identified according to the linear key schedule of GIFT-64 and bring additional advantages for our attacks. Furthermore, we incorporate the above ideas and propose a dedicated MILP model for finding the best rectangle key recovery attack on GIFT-64. As a result, we get the improved rectangle attacks on 26-round GIFT-64, which are the best attacks on it in terms of time complexity so far

Cryptanalysis of Some Block Cipher Constructions

When the public-key cryptography was introduced in the 1970s, symmetric-key cryptography was believed to soon become outdated. Nevertheless, we still heavily rely on symmetric-key primitives as they give high-speed performance. They are used to secure mobile communication, e-commerce transactions, communication through virtual private networks and sending electronic tax returns, among many other everyday activities. However, the security of symmetric-key primitives does not depend on a well-known hard mathematical problem such as the factoring problem, which is the basis of the RSA public-key cryptosystem. Instead, the security of symmetric-key primitives is evaluated against known cryptanalytic techniques. Accordingly, the topic of furthering the state-of-the-art of cryptanalysis of symmetric-key primitives is an ever-evolving topic. Therefore, this thesis is dedicated to the cryptanalysis of symmetric-key cryptographic primitives. Our focus is on block ciphers as well as hash functions that are built using block ciphers. Our contributions can be summarized as follows: First, we tackle the limitation of the current Mixed Integer Linear Programming (MILP) approaches to represent the differential propagation through large S-boxes. Indeed, we present a novel approach that can efficiently model the Difference Distribution Table (DDT) of large S-boxes, i.e., 8-bit S-boxes. As a proof of the validity and efficiency of our approach, we apply it on two out of the seven AES-round based constructions that were recently proposed in FSE 2016. Using our approach, we improve the lower bound on the number of active S-boxes of one construction and the upper bound on the best differential characteristic of the other. Then, we propose meet-in-the-middle attacks using the idea of efficient differential enumeration against two Japanese block ciphers, i.e., Hierocrypt-L1 and Hierocrypt-3. Both block ciphers were submitted to the New European Schemes for Signatures, Integrity, and Encryption (NESSIE) project, selected as one of the Japanese e-Government recommended ciphers in 2003 and reselected in the candidate recommended ciphers list in 2013. We construct five S-box layer distinguishers that we use to recover the master keys of reduced 8 S-box layer versions of both block ciphers. In addition, we present another meet-in-the-middle attack on Hierocrypt-3 with slightly higher time and memory complexities but with much less data complexity. Afterwards, we shift focus to another equally important cryptanalytic attack, i.e., impossible differential attack. SPARX-64/128 is selected among the SPARX family that was recently proposed to provide ARX based block cipher whose security against differential and linear cryptanalysis can be proven. We assess the security of SPARX-64/128 against impossible differential attack and show that it can reach the same number of rounds the division-based integral attack, proposed by the designers, can reach. Then, we pick Kiasu-BC as an example of a tweakable block cipher and prove that, on contrary to its designers’ claim, the freedom in choosing the publicly known tweak decreases its security margin. Lastly, we study the impossible differential properties of the underlying block cipher of the Russian hash standard Streebog and point out the potential risk in using it as a MAC scheme in the secret-IV mode

Electromagnetic Side-Channel Resilience against Lightweight Cryptography

Side-channel attacks are an unpredictable risk factor in cryptography. Therefore, observations of leakages through physical parameters, i.e., power and electromagnetic (EM) radiation, etc., of digital devices are essential to minimise vulnerabilities associated with cryptographic functions. Compared to costs in the past, performing side-channel attacks using inexpensive test equipment is becoming a reality. Internet-of-Things (IoT) devices are resource-constrained, and lightweight cryptography is a novel approach in progress towards IoT security. Thus, it would provide sufficient data and privacy protection in such a constrained ecosystem. Therefore, cryptanalysis of physical leakages regarding these emerging ciphers is crucial. EM side-channel attacks seem to cause a significant impact on digital forensics nowadays. Within existing literature, power analysis seems to have considerable attention in research whereas other phenomena, such as EM, should continue to be appropriately evaluated in playing a role in forensic analysis.The emphasis of this thesis is on lightweight cryptanalysis. The preliminary investigations showed no Correlation EManalysis (CEMA) of PRESENT lightweight algorithm. The PRESENT is a block cipher that promises to be adequate for IoT devices, and is expected to be used commercially in the future. In an effort to fill in this research gap, this work examines the capabilities of a correlation EM side-channel attack against the PRESENT. For that, Substitution box (S-box) of the PRESENT was targeted for its 1st round with the use of a minimum number of EM waveforms compared to other work in literature, which was 256. The attack indicates the possibility of retrieving 8 bytes of the secret key out of 10 bytes. The experimental process started from a Simple EMA (SEMA) and gradually enhanced up to a CEMA. The thesis presents the methodology of the attack modelling and the observations followed by a critical analysis. Also, a technical review of the IoT technology and a comprehensive literature review on lightweight cryptology are included