A survey on machine learning applied to symmetric cryptanalysis

In this work we give a short review of the recent progresses of machine learning techniques applied to cryptanalysis of symmetric ciphers, with particular focus on artificial neural networks. We start with some terminology and basics of neural networks, to then classify the recent works in two categories: "black-box cryptanalysis", techniques that not require previous information about the cipher, and "neuro-aided cryptanalysis", techniques used to improve existing methods in cryptanalysis

Cryptanalysis of SKINNY in the Framework of the SKINNY 2018--2019 Cryptanalysis Competition

In April 2018, Beierle et al. launched the 3rd SKINNY cryptanalysis competition, a contest that aimed at motivating the analysis of their recent tweakable block cipher SKINNY . In contrary to the previous editions, the focus was made on practical attacks: contestants were asked to recover a 128-bit secret key from a given set of 2^20 plaintext blocks. The suggested SKINNY instances are 4- to 20-round reduced variants of SKINNY-64-128 and SKINNY-128-128. In this paper, we explain how to solve the challenges for 10-round SKINNY-128-128 and for 12-round SKINNY-64-128 in time equivalent to roughly 2^52 simple operations. Both techniques benefit from the highly biased sets of messages that are provided and that actually correspond to the encryption of various books in ECB mode

Quantum Distinguishing Attacks against Type-1 Generalized Feistel Ciphers

A generalized Feistel cipher is one of the methods to construct block ciphers, and it has several variants. Dong, Li, and Wang showed quantum distinguishing attacks against the $(2d-1)$-round Type-1 generalized Feistel cipher with quantum chosen-plaintext attacks, where $d\ge 3$, and they also showed key recovery attacks [Dong, Li, Wang. Sci China Inf Sci, 2019, 62(2): 022501]. In this paper, we show a polynomial time quantum distinguishing attack against the $(3d-3)$-round version, i.e., we improve the number of rounds by $(d-2)$. We also show a quantum distinguishing attack against the $(d^2-d+1)$-round version in the quantum chosen-ciphertext setting. We apply these quantum distinguishing attacks to obtain key recovery attacks against Type-1 generalized Feistel ciphers

More Rounds, Less Security?

This paper focuses on a surprising class of cryptanalysis results for symmetric-key primitives: when the number of rounds of the primitive is increased, the complexity of the cryptanalysis result decreases. Our primary target will be primitives that consist of identical round functions, such as PBKDF1, the Unix password hashing algorithm, and the Chaskey MAC function. However, some of our results also apply to constructions with non-identical rounds, such as the PRIDE block cipher. First, we construct distinguishers for which the data complexity decreases when the number of rounds is increased. They are based on two well-known observations: iterating a random permutation increases the expected number of fixed points, and iterating a random function decreases the expected number of image points. We explain that these effects also apply to components of cryptographic primitives, such as a round of a block cipher. Second, we introduce a class of key-recovery and preimage-finding techniques that correspond to exhaustive search, however on a smaller part (e.g. one round) of the primitive. As the time complexity of a cryptanalysis result is usually measured by the number of full-round evaluations of the primitive, increasing the number of rounds will lower the time complexity. None of the observations in this paper result in more than a small speed-up over exhaustive search. Therefore, for lightweight applications, implementation advantages may outweigh the presence of these observations

Cryptanalysis of Some AES-based Cryptographic Primitives

Current information security systems rely heavily on symmetric key cryptographic primitives as one of their basic building blocks. In order to boost the efficiency of the security systems, designers of the underlying primitives often tend to avoid the use of provably secure designs. In fact, they adopt ad hoc designs with claimed security assumptions in the hope that they resist known cryptanalytic attacks. Accordingly, the security evaluation of such primitives continually remains an open field. In this thesis, we analyze the security of two cryptographic hash functions and one block cipher. We primarily focus on the recent AES-based designs used in the new Russian Federation cryptographic hashing and encryption suite GOST because the majority of our work was carried out during the open research competition run by the Russian standardization body TC26 for the analysis of their new cryptographic hash function Streebog. Although, there exist security proofs for the resistance of AES- based primitives against standard differential and linear attacks, other cryptanalytic techniques such as integral, rebound, and meet-in-the-middle attacks have proven to be effective. The results presented in this thesis can be summarized as follows: Initially, we analyze various security aspects of the Russian cryptographic hash function GOST R 34.11-2012, also known as Streebog or Stribog. In particular, our work investigates five security aspects of Streebog. Firstly, we present a collision analysis of the compression function and its in- ternal cipher in the form of a series of modified rebound attacks. Secondly, we propose an integral distinguisher for the 7- and 8-round compression function. Thirdly, we investigate the one wayness of Streebog with respect to two approaches of the meet-in-the-middle attack, where we present a preimage analysis of the compression function and combine the results with a multicollision attack to generate a preimage of the hash function output. Fourthly, we investigate Streebog in the context of malicious hashing and by utilizing a carefully tailored differential path, we present a backdoored version of the hash function where collisions can be generated with practical complexity. Lastly, we propose a fault analysis attack which retrieves the inputs of the compression function and utilize it to recover the secret key when Streebog is used in the keyed simple prefix and secret-IV MACs, HMAC, or NMAC. All the presented results are on reduced round variants of the function except for our analysis of the malicious version of Streebog and our fault analysis attack where both attacks cover the full round hash function. Next, we examine the preimage resistance of the AES-based Maelstrom-0 hash function which is designed to be a lightweight alternative to the ISO standardized hash function Whirlpool. One of the distinguishing features of the Maelstrom-0 design is the proposal of a new chaining construction called 3CM which is based on the 3C/3C+ family. In our analysis, we employ a 4-stage approach that uses a modified technique to defeat the 3CM chaining construction and generates preimages of the 6-round reduced Maelstrom-0 hash function. Finally, we provide a key recovery attack on the new Russian encryption standard GOST R 34.12- 2015, also known as Kuznyechik. Although Kuznyechik adopts an AES-based design, it exhibits a faster diffusion rate as it employs an optimal diffusion transformation. In our analysis, we propose a meet-in-the-middle attack using the idea of efficient differential enumeration where we construct a three round distinguisher and consequently are able to recover 16-bytes of the master key of the reduced 5-round cipher. We also present partial sequence matching, by which we generate, store, and match parts of the compared parameters while maintaining negligible probability of matching error, thus the overall online time complexity of the attack is reduced

Improved quantum attack on Type-1 Generalized Feistel Schemes and Its application to CAST-256

Generalized Feistel Schemes (GFS) are important components of symmetric ciphers, which have been extensively researched in classical setting. However, the security evaluations of GFS in quantum setting are rather scanty. In this paper, we give more improved polynomial-time quantum distinguishers on Type-1 GFS in quantum chosen-plaintext attack (qCPA) setting and quantum chosen-ciphertext attack (qCCA) setting. In qCPA setting, we give new quantum polynomial-time distinguishers on $(3d-3)$-round Type-1 GFS with branches $d\geq3$, which gain $d-2$ more rounds than the previous distinguishers. Hence, we could get better key-recovery attacks, whose time complexities gain a factor of $2^{\frac{(d-2)n}{2}}$. In qCCA setting, we get $(3d-3)$-round quantum distinguishers on Type-1 GFS, which gain $d-1$ more rounds than the previous distinguishers. In addition, we give some quantum attacks on CAST-256 block cipher. We find 12-round and 13-round polynomial-time quantum distinguishers in qCPA and qCCA settings, respectively, while the best previous one is only 7 rounds. Hence, we could derive quantum key-recovery attack on 19-round CAST-256. While the best previous quantum key-recovery attack is on 16 rounds. When comparing our quantum attacks with classical attacks, our result also reaches 16 rounds on CAST-256 with 128-bit key under a competitive complexity

Differential-ML Distinguisher: Machine Learning based Generic Extension for Differential Cryptanalysis

Differential cryptanalysis is an important technique to evaluate the security of block ciphers. There exists several generalisations of differential cryptanalysis and it is also used in combination with other cryptanalysis techniques to improve the attack complexity. In 2019, usefulness of machine learning in differential cryptanalysis is introduced by Gohr to attack the lightweight block cipher SPECK. In this paper, we present a framework to extend the classical differential distinguisher using machine learning (ML) based differential distinguisher. We propose a novel technique to construct differential-ML distinguisher for Feistel, SPN and ARX structure based block ciphers. We demonstrate our technique on lightweight block ciphers SPECK, SIMON & GIFT64 and construct differential-ML distinguishers for these ciphers. Data complexity for 9-round SPECK, 12-round SIMON & 8-round GIFT64 is reduced from 2^31 to 2^21, 2^34 to 2^22 and 2^28 to 2^22 respectively. The 12-round differential-ML distinguisher for SIMON is first distinguisher with data complexity less than 2^32

Linear and Differential Cryptanalysis of Reduced SMS4 Block Cipher

SMS4 is a 128-bit block cipher with a 128-bit user key and 32 rounds, which is used in WAPI, the Chinese WLAN national standard. In this paper, we present a linear attack and a differential attack on a 22-round reduced SMS4; our 22-round linear attack has a data complexity of 2^{117} known plaintexts, a memory complexity of 2^{109} bytes and a time complexity of 2^{109.86} 22-round SMS4 encryptions and 2^{120.39} arithmetic operations, while our 22-round differential attack requires 2^{118} chosen plaintexts, 2^{123} memory bytes and 2^{125.71} 22-round SMS4 encryptions. Both of our attacks are better than any previously known cryptanalytic results on SMS4 in terms of the number of attacked rounds. Furthermore, we present a boomerang and a rectangle attacks on a 18-round reduced SMS4. These results are better than previously known rectangle attacks on reduced SMS4. The methods presented to attack SMS4 can be applied to other unbalanced Feistel ciphers with incomplete diffusion

Improved Meet-in-the-Middle Attacks on Round-Reduced Crypton-256

The meet-in-the-middle (MITM) attack has prove to be efficient in analyzing the AES block cipher. Its efficiency has been increasing with the introduction of various techniques such as differential enumeration, key-dependent sieve, super-box etc. The recent MITM attack given by Li and Jin has successfully mounted to 10-round AES-256. Crypton is an AES-like block cipher. In this paper, we apply the MITM method to the cryptanalysis of Crypton-256. Following Li and Jin\u27s idea, we give the first 6-round distinguisher for Crypton. Based on the distinguisher as well as the properties of Crypton\u27s simple key schedule, we successfully launch MITM attacks on Crypton-256 reduced to 9 and 10 rounds. For 9-round Crypton-256, our MITM attack can recover the 256-bit key with a time complexity $2^{173.05}$, a memory complexity $2^{241.17}$. For the 10-round version, we give two MITM attacks. The basic attack requires a time complexity $2^{240.01}$ and memory complexity $2^{241.59}$. The time/memory complexity of the advanced MITM attack on 10-round Crypton is $2^{245.05}/2^{209.59}$. Our MITM attacks share the same data complexity $2^{113}$ and their error rates are negligible

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