Practical Key-Recovery Attacks On Round-Reduced Ketje Jr, Xoodoo-AE And Xoodyak

2020 ◽  
Vol 63 (8) ◽  
pp. 1231-1246
Author(s):  
Haibo Zhou ◽  
Zheng Li ◽  
Xiaoyang Dong ◽  
Keting Jia ◽  
Willi Meier
Keyword(s):  
Time Complexity ◽  
Third Party ◽  
Lightweight Cryptography ◽  
Key Recovery ◽  
The Third ◽  
Cube Attack ◽  
Caesar Competition ◽  
Memory Cost ◽  
Key Recovery Attacks

Abstract A new conditional cube attack was proposed by Li et al. at ToSC 2019 for cryptanalysis of Keccak keyed modes. In this paper, we find a new property of Li et al.’s method. The conditional cube attack is modified and applied to cryptanalysis of 5-round Ketje Jr, 6-round Xoodoo-AE and Xoodyak, where Ketje Jr is among the third round CAESAR competition candidates and Xoodyak is a Round 2 submission of the ongoing NIST lightweight cryptography project. For the updated conditional cube attack, all our results are shown to be of practical time complexity with negligible memory cost, and test codes are provided. Notably, our results on Xoodyak represent the first third-party cryptanalysis for Xoodyak.

scholarly journals Misuse-Free Key-Recovery and Distinguishing Attacks on 7-Round Ascon

2021 ◽  
pp. 130-155
Author(s):  
Raghvendra Rohit ◽  
Kai Hu ◽  
Sumanta Sarkar ◽  
Siwei Sun
Keyword(s):  
Boolean Functions ◽  
Security Analysis ◽  
Third Party ◽  
Secret Key ◽  
Lightweight Cryptography ◽  
Key Recovery ◽  
Caesar Competition ◽  
Recovery Technique ◽  
Dimensional Cube ◽  
Key Recovery Attacks

Being one of the winning algorithms of the CAESAR competition and currently a second round candidate of the NIST lightweight cryptography standardization project, the authenticated encryption scheme Ascon (designed by Dobraunig, Eichlseder, Mendel, and Schläffer) has withstood extensive self and third-party cryptanalysis. The best known attack on Ascon could only penetrate up to 7 (out of 12) rounds due to Li et al. (ToSC Vol I, 2017). However, it violates the data limit of 264 blocks per key specified by the designers. Moreover, the best known distinguishers of Ascon in the AEAD context reach only 6 rounds. To fill these gaps, we revisit the security of 7-round Ascon in the nonce-respecting setting without violating the data limit as specified in the design. First, we introduce a new superpoly-recovery technique named as partial polynomial multiplication for which computations take place between the so-called degree-d homogeneous parts of the involved Boolean functions for a 2d-dimensional cube. We apply this method to 7-round Ascon and present several key recovery attacks. Our best attack can recover the 128-bit secret key with a time complexity of about 2123 7-round Ascon permutations and requires 264 data and 2101 bits memory. Also, based on division properties, we identify several 60 dimensional cubes whose superpolies are constant zero after 7 rounds. We further improve the cube distinguishers for 4, 5 and 6 rounds. Although our results are far from threatening the security of full 12-round Ascon, they provide new insights in the security analysis of Ascon.

scholarly journals Weak Keys in Reduced AEGIS and Tiaoxin

2021 ◽  
pp. 104-139
Author(s):  
Fukang Liu ◽  
Takanori Isobe ◽  
Willi Meier ◽  
Kosei Sakamoto
Keyword(s):  
Time Complexity ◽  
High Performance ◽  
Stream Cipher ◽  
Third Party ◽  
Key Recovery ◽  
Weak Keys ◽  
Internal States ◽  
Caesar Competition ◽  
Key Recovery Attack ◽  
Pass Through

AEGIS-128 and Tiaoxin-346 (Tiaoxin for short) are two AES-based primitives submitted to the CAESAR competition. Among them, AEGIS-128 has been selected in the final portfolio for high-performance applications, while Tiaoxin is a third-round candidate. Although both primitives adopt a stream cipher based design, they are quite different from the well-known bit-oriented stream ciphers like Trivium and the Grain family. Their common feature consists in the round update function, where the state is divided into several 128-bit words and each word has the option to pass through an AES round or not. During the 6-year CAESAR competition, it is surprising that for both primitives there is no third-party cryptanalysis of the initialization phase. Due to the similarities in both primitives, we are motivated to investigate whether there is a common way to evaluate the security of their initialization phases. Our technical contribution is to write the expressions of the internal states in terms of the nonce and the key by treating a 128-bit word as a unit and then carefully study how to simplify these expressions by adding proper conditions. As a result, we find that there are several groups of weak keys with 296 keys each in 5-round AEGIS-128 and 8-round Tiaoxin, which allows us to construct integral distinguishers with time complexity 232 and data complexity 232. Based on the distinguisher, the time complexity to recover the weak key is 272 for 5-round AEGIS-128. However, the weak key recovery attack on 8-round Tiaoxin will require the usage of a weak constant occurring with probability 2−32. All the attacks reach half of the total number of initialization rounds. We expect that this work can advance the understanding of the designs similar to AEGIS and Tiaoxin.

scholarly journals Conditional Cube Attack on Round-Reduced ASCON

2017 ◽  
pp. 175-202 ◽  
Author(s):  
Zheng Li ◽  
Xiaoyang Dong ◽  
Xiaoyun Wang
Keyword(s):  
Time Complexity ◽  
Authenticated Encryption ◽  
Key Recovery ◽  
Key Space ◽  
Cube Attack ◽  
Linear Layer ◽  
Non Linear ◽  
Caesar Competition ◽  
Key Recovery Attack ◽  
Total Time Complexity

This paper evaluates the secure level of authenticated encryption Ascon against cube-like method. Ascon submitted by Dobraunig et al. is one of 16 survivors of the 3rd round CAESAR competition. The cube-like method is first used by Dinur et al. to analyze Keccak keyed modes. At CT-RSA 2015, Dobraunig et al. applied this method to 5/6-round reduced Ascon, whose structure is similar to Keccak keyed modes. However, for Ascon the non-linear layer is more complex and state is much smaller, which make it hard for the attackers to select enough cube variables that do not multiply with each other after the first round. This seems to be the reason why the best previous key-recovery attack is on 6-round Ascon, while for Keccak keyed modes (Keccak-MAC and Keyak) the attacked round is no less than 7-round. In this paper, we generalize the conditional cube attack proposed by Huang et al., and find new cubes depending on some key bit conditions for 5/6-round reduced Ascon, and translate the previous theoretic 6-round attack with 266 time complexity to a practical one with 240 time complexity. Moreover, we propose the first 7-round key-recovery attack on Ascon. By introducing the cube-like key-subset technique, we divide the full key space into many subsets according to different key conditions. For each key subset, we launch the cube tester to determine if the key falls into it. Finally, we recover the full key space by testing all the key subsets. The total time complexity is about 2103.9. In addition, for a weak-key subset, whose size is 2117, the attack is more efficient and costs only 277 time complexity. Those attacks do not threaten the full round (12 rounds) Ascon.

scholarly journals New Conditional Cube Attack on Keccak Keyed Modes

2019 ◽  
pp. 94-124
Author(s):  
Zheng Li ◽  
Xiaoyang Dong ◽  
Wenquan Bi ◽  
Keting Jia ◽  
Xiaoyun Wang ◽  
...  
Keyword(s):  
Time Complexity ◽  
Degrees Of Freedom ◽  
Identity Transformation ◽  
Quadratic Term ◽  
Key Recovery ◽  
Cube Attack ◽  
Cube Attacks ◽  
First Time ◽  
Key Recovery Attacks

The conditional cube attack on round-reduced Keccak keyed modes was proposed by Huang et al. at EUROCRYPT 2017. In their attack, a conditional cube variable was introduced, whose diffusion was significantly reduced by certain key bit conditions. The attack requires a set of cube variables which are not multiplied in the first round while the conditional cube variable is not multiplied with other cube variables (called ordinary cube variables) in the first two rounds. This has an impact on the degree of the output of Keccak and hence gives a distinguisher. Later, the MILP method was applied to find ordinary cube variables. However, for some Keccak based versions with few degrees of freedom, one could not find enough ordinary cube variables, which weakens or even invalidates the conditional cube attack.In this paper, a new conditional cube attack on Keccak is proposed. We remove the limitation that no cube variables multiply with each other in the first round. As a result, some quadratic terms may appear in the first round. We make use of some new bit conditions to prevent the quadratic terms from multiplying with other cube variables in the second round, so that there will be no cubic terms in the first two rounds. Furthermore, we introduce the kernel quadratic term and construct a 6-2-2 pattern to reduce the diffusion of quadratic terms significantly, where the Θ operation even in the second round becomes an identity transformation (CP-kernel property) for the kernel quadratic term. Previous conditional cube attacks on Keccak only explored the CP-kernel property of Θ operation in the first round. Therefore, more degrees of freedom are available for ordinary cube variables and fewer bit conditions are used to remove the cubic terms in the second round, which plays a key role in the conditional cube attack on versions with very few degrees of freedom. We also use the MILP method in the search of cube variables and give key-recovery attacks on round-reduced Keccak keyed modes.As a result, we reduce the time complexity of key-recovery attacks on 7-round Keccak-MAC-512 and 7-round Ketje Sr v2 from 2111, 299 to 272, 277, respectively. Additionally, we have reduced the time complexity of attacks on 9-round KMAC256 and 7-round Ketje Sr v1. Besides, practical attacks on 6-round Ketje Sr v1 and v2 are also given in this paper for the first time.

scholarly journals Multidimensional linear cryptanalysis with key difference invariant bias for block ciphers

Cybersecurity ◽  
2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Wenqin Cao ◽  
Wentao Zhang
Keyword(s):  
Time Complexity ◽  
Block Ciphers ◽  
Linear Cryptanalysis ◽  
Compression Technique ◽  
Key Recovery ◽  
Linear Approximations ◽  
Theoretical Advantage ◽  
Multidimensional Linear ◽  
Multidimensional Linear Cryptanalysis ◽  
Key Recovery Attacks

AbstractFor block ciphers, Bogdanov et al. found that there are some linear approximations satisfying that their biases are deterministically invariant under key difference. This property is called key difference invariant bias. Based on this property, Bogdanov et al. proposed a related-key statistical distinguisher and turned it into key-recovery attacks on LBlock and TWINE-128. In this paper, we propose a new related-key model by combining multidimensional linear cryptanalysis with key difference invariant bias. The main theoretical advantage is that our new model does not depend on statistical independence of linear approximations. We demonstrate our cryptanalysis technique by performing key recovery attacks on LBlock and TWINE-128. By using the relations of the involved round keys to reduce the number of guessed subkey bits. Moreover, the partial-compression technique is used to reduce the time complexity. We can recover the master key of LBlock up to 25 rounds with about 260.4 distinct known plaintexts, 278.85 time complexity and 261 bytes of memory requirements. Our attack can recover the master key of TWINE-128 up to 28 rounds with about 261.5 distinct known plaintexts, 2126.15 time complexity and 261 bytes of memory requirements. The results are the currently best ones on cryptanalysis of LBlock and TWINE-128.

scholarly journals Efficient Side-Channel Secure Message Authentication with Better Bounds

2020 ◽  
pp. 23-53
Author(s):  
Chun Guo ◽  
François-Xavier Standaert ◽  
Weijia Wang ◽  
Yu Yu
Keyword(s):  
Time Complexity ◽  
Side Channel ◽  
Message Authentication ◽  
Security Threat ◽  
Cryptographic Primitives ◽  
Key Recovery ◽  
Leakage Resilience ◽  
Authentication Schemes ◽  
Key Recovery Attacks ◽  
Provably Secure

We investigate constructing message authentication schemes from symmetric cryptographic primitives, with the goal of achieving security when most intermediate values during tag computation and verification are leaked (i.e., mode-level leakage-resilience). Existing efficient proposals typically follow the plain Hash-then-MAC paradigm T = TGenK(H(M)). When the domain of the MAC function TGenK is {0, 1}128, e.g., when instantiated with the AES, forgery is possible within time 264 and data complexity 1. To dismiss such cheap attacks, we propose two modes: LRW1-based Hash-then-MAC (LRWHM) that is built upon the LRW1 tweakable blockcipher of Liskov, Rivest, and Wagner, and Rekeying Hash-then-MAC (RHM) that employs internal rekeying. Built upon secure AES implementations, LRWHM is provably secure up to (beyond-birthday) 278.3 time complexity, while RHM is provably secure up to 2121 time. Thus in practice, their main security threat is expected to be side-channel key recovery attacks against the AES implementations. Finally, we benchmark the performance of instances of our modes based on the AES and SHA3 and confirm their efficiency.

scholarly journals Boomeyong: Embedding Yoyo within Boomerang and its Applications to Key Recovery Attacks on AES and Pholkos

2021 ◽  
pp. 137-169
Author(s):  
Mostafizar Rahman ◽  
Dhiman Saha ◽  
Goutam Paul
Keyword(s):  
Time Complexity ◽  
Block Cipher ◽  
New Technique ◽  
Small Scale ◽  
Key Recovery ◽  
Boomerang Attack ◽  
Tweakable Block Cipher ◽  
Key Recovery Attack ◽  
Key Recovery Attacks

This work investigates a generic way of combining two very effective and well-studied cryptanalytic tools, proposed almost 18 years apart, namely the boomerang attack introduced by Wagner in FSE 1999 and the yoyo attack by Ronjom et al. in Asiacrypt 2017. In doing so, the s-box switch and ladder switch techniques are leveraged to embed a yoyo trail inside a boomerang trail. As an immediate application, a 6-round key recovery attack on AES-128 is mounted with time complexity of 278. A 10-round key recovery attack on recently introduced AES-based tweakable block cipher Pholkos is also furnished to demonstrate the applicability of the new technique on AES-like constructions. The results on AES are experimentally verified by applying and implementing them on a small scale variant of AES. We provide arguments that draw a relation between the proposed strategy with the retracing boomerang attack devised in Eurocrypt 2020. To the best of our knowledge, this is the first attempt to merge the yoyo and boomerang techniques to analyze SPN ciphers and warrants further attention as it has the potential of becoming an important cryptanalysis tool.

scholarly journals Improved Conditional Differential Analysis on NLFSR-Based Block Cipher KATAN32 with MILP

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Zhaohui Xing ◽  
Wenying Zhang ◽  
Guoyong Han
Keyword(s):  
Mixed Integer Linear Programming ◽  
Time Complexity ◽  
Block Cipher ◽  
Mixed Integer ◽  
Differential Analysis ◽  
Nonlinear Feedback ◽  
Key Recovery ◽  
Nonlinear Feedback Shift Register ◽  
Feedback Shift Register ◽  
Key Recovery Attacks

In this paper, a new method for constructing a Mixed Integer Linear Programming (MILP) model on conditional differential cryptanalysis of the nonlinear feedback shift register- (NLFSR-) based block ciphers is proposed, and an approach to detecting the bit with a strongly biased difference is provided. The model is successfully applied to the block cipher KATAN32 in the single-key scenario, resulting in practical key-recovery attacks covering more rounds than the previous. In particular, we present two distinguishers for 79 and 81 out of 254 rounds of KATAN32. Based on the 81-round distinguisher, we recover 11 equivalent key bits of 98-round KATAN32 and 13 equivalent key bits of 99-round KATAN32. The time complexity is less than 2 31 encryptions of 98-round KATAN32 and less than 2 33 encryptions of 99-round KATAN32, respectively. Thus far, our results are the best known practical key-recovery attacks for the round-reduced variants of KATAN32 regarding the number of rounds and the time complexity. All the results are verified experimentally.

scholarly journals Automatic Search of Cubes for Attacking Stream Ciphers

2021 ◽  
pp. 100-123
Author(s):  
Yao Sun
Keyword(s):  
Heuristic Method ◽  
Stream Ciphers ◽  
Divide And Conquer ◽  
Key Recovery ◽  
Cube Attack ◽  
Automatic Search ◽  
The Common ◽  
Key Recovery Attack ◽  
First Time ◽  
Key Recovery Attacks

Cube attack was proposed by Dinur and Shamir, and it has become an important tool for analyzing stream ciphers. As the problem that how to recover the superpolys accurately was resolved by Hao et al. in EUROCRYPT 2020, another important problem is how to find “good” superpolys, which is equivalent to finding “good” cubes. However, there are two difficulties in finding “good” cubes. Firstly, the number of candidate cubes is enormous and most of the cubes are not “good”. Secondly, it is costly to evaluate whether a cube is “good”.In this paper, we present a new algorithm to search for a kind of “good” cubes, called valuable cubes. A cube is called valuable, if its superpoly has (at least) a balanced secret variable. A valuable cube is “good”, because its superpoly brings in 1 bit of information about the key. More importantly, the superpolys of valuable cubes could be used in both theoretical and practical analyses. To search for valuable cubes, instead of testing a set of cubes one by one, the new algorithm deals with the set of cubes together, such that the common computations can be done only once for all candidate cubes and duplicated computations are avoided. Besides, the new algorithm uses a heuristic method to reject useless cubes efficiently. This heuristic method is based on the divide-and-conquer strategy as well as an observation.For verifications of this new algorithm, we applied it to Trivium and Kreyvium, and obtained three improvements. Firstly, we found two valuable cubes for 843-round Trivium, such that we proposed, as far as we know, the first theoretical key-recovery attack against 843-round Trivium, while the previous highest round of Trivium that can be attacked was 842, given by Hao et al. in EUROCRYPT 2020. Secondly, by finding many small valuable cubes, we presented practical attacks against 806- and 808-round Trivium for the first time, while the previous highest round of Trivium that can be attacked practically was 805. Thirdly, based on the cube used to attack 892-round Kreyvium in EUROCRYPT 2020, we found more valuable cubes and mounted the key-recovery attacks against Kreyvium to 893-round.

scholarly journals Cryptanalysis of NORX v2.0

2017 ◽  
pp. 156-174 ◽  
Author(s):  
Colin Chaigneau ◽  
Thomas Fuhr ◽  
Henri Gilbert ◽  
Jérémy Jean ◽  
Jean-René Reinhard
Keyword(s):  
Authenticated Encryption ◽  
Forgery Attack ◽  
Key Recovery ◽  
Design Decisions ◽  
The Third ◽  
Caesar Competition ◽  
Internal Operations ◽  
Key Recovery Attack ◽  
Associated Data ◽  
Main Change

NORX is an authenticated encryption scheme with associated data being publicly scrutinized as part of the ongoing CAESAR competition, where 14 other primitives are also competing. It is based on the sponge construction and relies on a simple permutation that allows efficient and versatile implementations. Thanks to research on the security of the sponge construction, the design of NORX, whose permutation is inspired from the permutations used in BLAKE and ChaCha, has evolved throughout three main versions (v1.0, v2.0 and v3.0). In this paper, we investigate the security of the full NORX v2.0 primitive that has been accepted as third-round candidate in the CAESAR competition. We show that some non-conservative design decisions probably motivated by implementation efficiency considerations result in at least one strong structural distinguisher of the underlying sponge permutation that can be turned into an attack on the full primitive. This attack yields a ciphertext-only forgery with time and data complexity 266 (resp. 2130) for the variant of NORX v2.0 using 128-bit (resp. 256-bit) keys and breaks the designers’ claim of a 128-bit, resp. 256-bit security. Furthermore, we show that this forgery attack can be extended to a key-recovery attack on the full NORX v2.0 with the same time and data complexities. We have implemented and experimentally verified the correctness of the attacks on a toy version of NORX. We emphasize that the scheme has recently been tweaked to NORX v3.0 at the beginning of the third round of the CAESAR competition: the main change introduces some key-dependent internal operations, which make NORX v3.0 immune to our attacks. However, the structural distinguisher of the permutation persists.

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