Improved Meet-in-the-Middle Attacks on Reduced-Round Kalyna-128/256 and Kalyna-256/512

Kalyna is an SPN-based block cipher that was selected during Ukrainian National Public Cryptographic Competition (2007-2010) and its slight modification was approved as the new encryption standard of Ukraine. In this paper, we focus on the key-recovery attacks on reduced-round Kalyna-128/256 and Kalyna-256/512 with meet-in-the-middle method. The differential enumeration technique and key-dependent sieve technique which are popular to analyze AES are used to attack them. Using the key-dependent sieve technique to improve the complexity is not an easy task, we should build some tables to achieve this. Since the encryption procedure of Kalyna employs a pre- and post-whitening operations using addition modulo $2^{64}$ applied on the state columns independently, we carefully study the propagation of this operation and propose an addition plaintext structure to solve this. For Kalyna-128/256, we propose a 6-round distinguisher, and achieve a 9-round (out of total 14-round) attack. For Kalyna-256/512, we propose a 7-round distinguisher, then achieve an 11-round (out of total 18-round) attack. As far as we know, these are currently the best results on Kalyna-128/256 and Kalyna-256/512

Single Key Recovery Attacks on 9-round Kalyna-128/256 and Kalyna-256/512

The Kalyna block cipher has recently been established as the Ukranian encryption standard in June, 2015. It was selected in a Ukrainian National Public Cryptographic Competition running from 2007 to 2010. Kalyna supports block sizes and key lengths of 128, 256 and 512 bits. Denoting the variants of Kalyna as Kalyna-$b/k$, where $b$ denotes the block size and $k$ denotes the keylength, the design specifies $k \in \{b, 2b\}$. In this work, we re-evaluate the security bound of some reduced round Kalyna variants, specifically Kalyna-$128/256$ and Kalyna-$256/512$ against key recovery attacks in the single key model. We first construct new 6-round distinguishers and then use these distinguishers to demonstrate 9-round attacks on these Kalyna variants. These attacks improve the previous best 7-round attacks on the same.\\ Our 9-round attack on Kalyna-128/256 has data, time and memory complexity of $2^{105}$, $2^{245.83}$ and $2^{226.86}$ respectively. For our 9-round attack on Kalyna-256/512, the data/time/memory complexities are $2^{217}$, $2^{477.83}$ and $2^{443.45}$ respectively. The time and data complexities for Kalyna-256/512 reported in this work improve upon the previous best 7-round attack complexities on the same. The attacks presented in this work are currently the best on Kalyna. We apply multiset attack - a variant of meet-in-the-middle attack to achieve these results

A Meet-in-the-Middle Attack on Reduced-Round Kalyna-b/2b

Kalyna is an SPN-based block cipher that was selected during Ukrainian national public cryptographic competition (2007-2010), and its slight modification was approved as the new encryption standard of Ukraine (DSTU 7624:2014) in 2015. The cipher supports a block size and a key length of 128, 256 and 512 bits where the size of the key can be either double or equal to that of the block length. According to its designers, the cipher provides strength to several cryptanalytic methods after the fifth and sixth rounds of the 128-bit and 256-bit block versions, respectively. In this paper, we present a meet-in-the-middle attack on the 7-round reduced versions of Kalyna where the key size is double the block length. Our attack is based on the differential enumeration approach where we carefully deploy a four round distinguisher in the first four rounds to bypass the effect of the carry bits resulting from the pre-whitening modular key addition. We also exploit the linear relation between consecutive odd and even indexed round keys which enables us to attack seven rounds and recover all the round keys incrementally. The attack on Kalyna with 128-bit block has a data complexity of $2^{89}$ chosen plaintexts, time complexity of $2^{230.2}$ and a memory complexity of $2^{202.64}$. The data, time and memory complexities of our attack on Kalyna with 256-bit block are $2^{233}$, $2^{502.2}$ and $2^{170}$, respectively

Application of Fault Analysis to Some Cryptographic Standards

Cryptanalysis methods can be classified as pure mathematical attacks, such as linear and differential cryptanalysis, and implementation dependent attacks such as power analysis and fault analysis. Pure mathematical attacks exploit the mathematical structure of the cipher to reveal the secret key inside the cipher. On the other hand, implementation dependent attacks assume that the attacker has access to the cryptographic device to launch the attack. Fault analysis is an example of a side channel attack in which the attacker is assumed to be able to induce faults in the cryptographic device and observe the faulty output. Then, the attacker tries to recover the secret key by combining the information obtained from the faulty and the correct outputs. Even though fault analysis attacks may require access to some specialized equipment to be able to insert faults at specific locations or at specific times during the computation, the resulting attacks usually have time and memory complexities which are far more practical as compared to pure mathematical attacks. Recently, several AES-based primitives were approved as new cryptographic standards throughout the world. For example, Kuznyechik was approved as the standard block cipher in Russian Federation, and Kalyna and Kupyna were approved as the standard block cipher and the hash function, respectively, in Ukraine. Given the importance of these three new primitives, in this thesis, we analyze their resistance against fault analysis attacks. Firstly, we modified a differential fault analysis (DFA) attack that was applied on AES and applied it on Kuzneychik. Application of DFA on Kuznyechik was not a trivial task because of the linear transformation layer used in the last round of Kuznyechik. In order to bypass the effect of this linear transformation operation, we had to use an equivalent representation of the last round which allowed us to recover the last two round keys using a total of four faults and break the cipher. Secondly, we modified the attack we applied on Kuzneychik and applied it on Kalyna. Kalyna has a complicated key scheduling and it uses modulo 264 addition operation for applying the first and last round keys. This makes Kalyna more resistant to DFA as com- pared to AES and Kuznyechik but it is still practically breakable because the number of key candidates that can be recovered by DFA can be brute-forced in a reasonable time. We also considered the case where the SBox entries of Kalyna are not known and showed how to recover a set of candidates for the SBox entries. Lastly, we applied two fault analysis attacks on Kupyna hash function. In the first case, we assumed that the SBoxes and all the other function parameters are known, and in the second case we assumed that the SBoxes were kept secret and attacked the hash function accordingly. Kupyna can be used as the underlying hash function for the construction of MAC schemes such as secret IV, secret prefix, HMAC or NMAC. In our analysis, we showed that secret inputs of Kupyna can be recovered using fault analysis. To conclude, we analyzed two newly accepted standard ciphers (Kuznyechik, Kalyna) and one newly approved standard hash function (Kupyna) for their resistance against fault attacks. We also analyzed Kalyna and Kupyna with the assumption that these ciphers can be deployed with secret user defined SBoxes in order to increase their security

Оцінка кількості вентилів для реалізації шифру Калина в квантовій моделі обчислень

Кваліфікаційна робота містить: 94 сторінок, 12 рисунків, 22 таблиці, 31 джерело,1 додаток. Мета роботи: Визначення кількості необхідних ресурсів, таких як квантові вентилі, на реалізацію шифру Калина. Об’єкт дослідження: Інформаційні процеси в системах криптографічного захисту в квантовій моделі обчислень. Предмет дослідження: Складність реалізації шифру Калина в квантовій моделі обчислень. У результаті цієї роботи було отримано оцінку кількості вентилів Тоффолі, необхідних для реалізації шифру Калина в квантовій моделі обчислень. Спочатку було оцінено кількості вентилів, необхідних для виконання підстановок, операції AddRoundKey та раундів шифру. Отримано, що для одного виконання операції AddRoundKey необхідно близько 12.737 вентилів Тоффолі, а для одного раунду шифрування – близько 17.832 вентилів Тоффолі. Для реалізації підстановок шифру Калина нуобхідно 1278, 1273, 1252 та 1262 вентилів Тоффолі, для π0, π1, π2 та π3 відповідно. А для повної реалізації шифру Калина-k/k необхідно близько 202.600, 273.510 та 344.420 вентилів Тоффолі, для k = 128, 256, 512 відповідно.The work contains 94 pages, 12 illustrations, 22 tables, 1 appendices, 31 sources of literature. The aim of work: Estimation of the amount of necessary resources, such as quantum gates, for the implementation of the Kalyna cipher. Object of research: Information processes in cryptographic protection systems in a quantum computing model. Subject of research: The complexity of the implementation of the Kalyna cipher in the quantum model of computing. As a result of this work, an estimate was obtained of the number of Toffoli gates needed to implement the Kalyna cipher in the quantum computing model. First, the number of gates needed to perform the substitutions, the AddRoundKey operation, and the cipher rounds was estimated. It was found that for one execution of the AddRoundKey operation, 12.737 Toffoli gates are needed, and for one round of encryption, about 17.832 Toffoli gates. To implement Kalyna cipher permutations, needed 1278, 1273,1252 та 1262 Toffoli gates, for π0, π1, π2 and π3 And for the full implementation of the Kalyna-k/k cipher about 202.600, 273.510 and 344.420 Toffoli gates are needed, for k = 128, 256, 512

MILP-aided Cryptanalysis of Some Block Ciphers

Symmetric-key cryptographic primitives, such as block ciphers, play a pivotal role in achieving confidentiality, integrity, and authentication – which are the core services of information security. Since symmetric-key primitives do not rely on well-defined hard mathematical problems, unlike public-key primitives, there are no formal mathematical proofs for the security of symmetric-key primitives. Consequently, their security is guaranteed only by measuring their immunity against a set of predefined cryptanalysis techniques, e.g., differential, linear, impossible differential, and integral cryptanalysis. The attacks based on cryptanalysis techniques usually include searching in an exponential space of patterns, and for a long time, cryptanalysts have performed this task manually. As a result, it has been hard, time-consuming, and an error-prone task. Indeed, the need for automatic tools becomes more pressing. This thesis is dedicated to investigating the security of symmetric-key cryptographic primitives, precisely block ciphers. One of our main goals is to utilize Mixed Integer Linear Programming (MILP) to automate the evaluation and the validation of block cipher security against a wide range of cryptanalysis techniques. Our contributions can be summarized as follows. First, we investigate the security of two recently proposed block ciphers, CRAFT and SPARX-128/256 against two variants of differential cryptanalysis. We utilize the simple key schedule of CRAFT to construct several repeatable 2-round related-key differential characteristics with the maximum differential probability. Consequently, we are able to mount a practical key recovery attack on full-round CRAFT in the related-key setting. In addition, we use impossible differential cryptanalysis to assess SPARX-128/256 that is provable secure against single-trail differential and linear cryptanalysis. As a result, we can attack 24 rounds similar to the internal attack presented by the designers. However, our attack is better than the integral attack regarding the time and memory complexities. Next, we tackle the limitation of the current Mixed Integer Linear Programming (MILP) model to automate the search for differential distinguishers through modular additions. The current model assumes that the inputs to the modular addition and the consecutive rounds are independent. However, we show that this assumption does not necessarily hold and the current model might lead to invalid attacks. Accordingly, we propose a more accurate MILP model that takes into account the dependency between consecutive modular additions. As a proof of the validity and efficiency of our model, we use it to analyze the security of Bel-T cipher—the standard of the Republic of Belarus. Afterwards, we shift focus to another equally important cryptanalysis technique, i.e., integral cryptanalysis using the bit-based division property (BDP). We present MILP models to automate the search for the BDP through modular additions with a constant and modular subtractions. Consequently, we assess the security of Bel-T block cipher against the integral attacks. Next, we analyze the security of the tweakable block cipher T-TWINE. We present key recovery attacks on 27 and 28 rounds of T-TWINE-80 and T-TWINE-128, respectively. Finally, we address the limitation of the current MILP model for the propagation of the bit-based division property through large non-bit-permutation linear layers. The current models are either inaccurate, which might lead to missing some balanced bits, or inefficient in terms of the number of constraints. As a proof of the effectiveness of our approach, we improve the previous 3- and 4-round integral distinguishers of the Russian encryption standard—Kuznyechik, and the 4-round one of PHOTON’s internal permutation (P288). We also report a 4-round integral distinguisher for the Ukrainian standard Kalyna and a 5-round integral distinguisher for PHOTON’s internal permutation (P288)

Pholkos -- Efficient Large-state Tweakable Block Ciphers from the AES Round Function

With the dawn of quantum computers, higher security than $128$ bits has become desirable for primitives and modes. During the past decade, highly secure hash functions, MACs, and encryption schemes have been built primarily on top of keyless permutations, which simplified their analyses and implementation due to the absence of a key schedule. However, the security of these modes is most often limited to the birthday bound of the state size, and their analysis may require a different security model than the easier-to-handle secret-permutation setting. Yet, larger state and key sizes are desirable not only for permutations but also for other primitives such as block ciphers. Using the additional public input of tweakable block ciphers for domain separation allows for exceptionally high security or performance as recently proposed modes have shown. Therefore, it appears natural to ask for such designs. While security is fundamental for cryptographic primitives, performance is of similar relevance. Since 2009, processor-integrated instructions have allowed high throughput for the AES round function, which already motivated various constructions based on it. Moreover, the four-fold vectorization of the AES instruction sets in Intel\u27s Ice Lake architecture is yet another leap in terms of performance and gives rise to exploit the AES round function for even more efficient designs. This work tries to combine all aspects above into a primitive and to build upon years of existing analysis on its components. We propose Pholkos, a family of (1) highly efficient, (2) highly secure, and (3) tweakable block ciphers. Pholkos is no novel round-function design, but utilizes the AES round function, following design ideas of Haraka and AESQ to profit from earlier analysis results. It extends them to build a family of primitives with state and key sizes of $256$ and $512$ bits for flexible applications, providing high security at high performance. Moreover, we propose its usage with a $128$-bit tweak to instantiate high-security encryption and authentication schemes such as SCT, ThetaCB3, or ZAE. We study its resistance against the common attack vectors, including differential, linear, and integral distinguishers using a MILP-based approach and show an isomorphism from the AES to Pholkos-$512$ for bounding impossible-differential, or exchange distinguishers from the AES. Our proposals encrypt at around $1$--$2$ cycles per byte on Skylake processors, while supporting a much more general application range and considerably higher security guarantees than comparable primitives and modes such as PAEQ/AESQ, AEGIS, Tiaoxin346, or Simpira

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

Cryptanalysis, Reverse-Engineering and Design of Symmetric Cryptographic Algorithms

In this thesis, I present the research I did with my co-authors on several aspects of symmetric cryptography from May 2013 to December 2016, that is, when I was a PhD student at the university of Luxembourg under the supervision of Alex Biryukov. My research has spanned three different areas of symmetric cryptography. In Part I of this thesis, I present my work on lightweight cryptography. This field of study investigates the cryptographic algorithms that are suitable for very constrained devices with little computing power such as RFID tags and small embedded processors such as those used in sensor networks. Many such algorithms have been proposed recently, as evidenced by the survey I co-authored on this topic. I present this survey along with attacks against three of those algorithms, namely GLUON, PRINCE and TWINE. I also introduce a new lightweight block cipher called SPARX which was designed using a new method to justify its security: the Long Trail Strategy. Part II is devoted to S-Box reverse-engineering, a field of study investigating the methods recovering the hidden structure or the design criteria used to build an S-Box. I co-invented several such methods: a statistical analysis of the differential and linear properties which was applied successfully to the S-Box of the NSA block cipher Skipjack, a structural attack against Feistel networks called the yoyo game and the TU-decomposition. This last technique allowed us to decompose the S-Box of the last Russian standard block cipher and hash function as well as the only known solution to the APN problem, a long-standing open question in mathematics. Finally, Part III presents a unifying view of several fields of symmetric cryptography by interpreting them as purposefully hard. Indeed, several cryptographic algorithms are designed so as to maximize the code size, RAM consumption or time taken by their implementations. By providing a unique framework describing all such design goals, we could design modes of operations for building any symmetric primitive with any form of hardness by combining secure cryptographic building blocks with simple functions with the desired form of hardness called plugs. Alex Biryukov and I also showed that it is possible to build plugs with an asymmetric hardness whereby the knowledge of a secret key allows the privileged user to bypass the hardness of the primitive

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