International Association
for Cryptologic Research

The Nostradamus attack was originally proposed as a security vulnerability for a hash function by Kelsey and Kohno at EUROCRYPT 2006. It requires the attacker to commit to a hash value y of an iterated hash function H. Subsequently, upon being provided with a message prefix P, the adversary’s task is to identify a suffix S such that H(P∥S) equals y. Kelsey and Kohno demonstrated a herding attack requiring O(√n · 22n/3) evaluations of the compression function of H, where n represents the output and state size of the hash, placing this attack between preimage attacks and collision searches in terms of complexity. At ASIACRYPT 2022, Benedikt et al. transform Kelsey and Kohno’s attack into a quantum variant, decreasing the time complexity from O(√n · 22n/3) to O( 3√n · 23n/7). At ToSC 2023, Zhang et al. proposed the first dedicated Nostradamus attack on AES-like hashing in both classical and quantum settings. In this paper, we have made revisions to the multi-target technique incorporated into the meet-in-the-middle automatic search framework. This modification leads to a decrease in time complexity during the online linking phase, effectively reducing the overall attack time complexity in both classical and quantum scenarios. Specifically, we can achieve more rounds in the classical setting and reduce the time complexity for the same round in the quantum setting.

This paper proposes general meet-in-the-middle (MitM) attack frameworks for preimage and collision attacks on hash functions based on (generalized) sponge construction. As the first contribution, our MitM preimage attack framework covers a wide range of sponge-based hash functions, especially those with lower claimed security level for preimage compared to their output size. Those hash functions have been very widely standardized (e.g., {\tt Ascon-Hash}, {\tt PHOTON}, etc.), but are rarely studied against preimage attacks. Even the recent MitM attack framework on sponge construction by Qin et al. (EUROCRYPT 2023) cannot attack those hash functions. As the second contribution, our MitM collision attack framework shows a different tool for the collision cryptanalysis on sponge construction, while previous collision attacks on sponge construction are mainly based on differential attacks. Most of the results in this paper are the first third-party cryptanalysis results. If cryptanalysis previously existed, our new results significantly improve the previous results, such as improving the previous 2-round collision attack on {\tt Ascon-Hash} to the current 4 rounds, improving the previous 3.5-round quantum preimage attack on SPHINCS$^+$-{\tt Haraka} to our 4-round classical preimage attack, etc.

The machine learning problem of extracting neural network parameters has been proposed for nearly three decades. Functionally equivalent extraction is a crucial goal for research on this problem. When the adversary has access to the raw output of neural networks, various attacks, including those presented at CRYPTO 2020 and EUROCRYPT 2024, have successfully achieved this goal. However, this goal is not achieved when neural networks operate under a hard-label setting where the raw output is inaccessible. In this paper, we propose the first attack that theoretically achieves functionally equivalent extraction under the hard-label setting, which applies to ReLU neural networks. The effectiveness of our attack is validated through practical experiments on a wide range of ReLU neural networks, including neural networks trained on two real benchmarking datasets (MNIST, CIFAR10) widely used in computer vision. For a neural network consisting of $10^5$ parameters, our attack only requires several hours on a single core.

SHA-256 is a hash function standardized by NIST and has been widely deployed in real-world applications, e.g., Bitcoin. Recently, an improved collision attack on 31-step SHA-256 was proposed by Li- Liu-Wang at EUROCRYPT 2024, whose time and memory complexity are 2^{49.8} and 2^{48}, respectively. Such a result indicates that we are close to a practical collision attack on 31-step SHA-256, and that the current bottleneck is the memory complexity. To overcome such an obstacle, we develop a novel memory-efficient attack in this paper, which allows us to find the first practical colliding message pair for 31-step SHA-256 in only 1.2 hours with 64 threads and negligible memory. This technique is general and Li-Liu-Wang’s collision attack on 31-step SHA-512 can also be significantly improved, i.e., the time and memory complexity can be improved by a factor of 2^{20.9} and 2^{42.1}, respectively. Although we have set a new record in the practical collision attack on SHA-256, which improves the previous best practical attack published at EUROCRYPT 2013 by 3 steps, the attack is still far from threatening the security of SHA-256 since it has 64 steps in total. On the other hand, our new attack shows that nearly half of full SHA-256 can be practically cracked now, and it should be viewed as a major progress in the cryptanalysis of SHA-256 since 2013.

The Meet-in-the-Middle (MitM) attack has been widely applied to preimage attacks on Merkle-Damgård (MD) hashing. In this paper, we introduce a generic framework of the MitM attack on sponge-based hashing. We find certain bit conditions can significantly reduce the diffusion of the unknown bits and lead to longer MITM characteristics. To find good or optimal configurations of MitM attacks, e.g., the bit conditions, the neutral sets, and the matching points, we introduce the bit-level MILP-based automatic tools on Keccak, Ascon and Xoodyak. To reduce the scale of bit-level models and make them solvable in reasonable time, a series of properties of the targeted hashing are considered in the modelling, such as the linear structure and CP-kernel for Keccak, the Boolean expression of Sbox for Ascon. Finally, we give an improved 4-round preimage attack on Keccak-512/SHA3, and break a nearly 10 years’ cryptanalysis record. We also give the first preimage attacks on 3-/4-round Ascon-XOF and 3-round Xoodyak-XOF.

Fault analysis is a powerful technique to retrieve secret keys by exploiting side-channel information. Differential fault analysis (DFA) is one of the most powerful threats utilizing differential information between correct and faulty ciphertexts and can recover keys for symmetric-key cryptosystems efficiently. Since DFA usually targets the first or last few rounds of the block ciphers, some countermeasures against DFA only protect the first and last few rounds for efficiency. Therefore, to explore how many rounds DFA can affect is very important to make sure how many rounds to protect in practice. At CHES 2011, Derbez et al. proposed an improved DFA on AES based on MitM approach, which covers one more round than previous DFAs. To perform good (or optimal) MitM DFA on block ciphers, the good (or optimal) attack configurations should be identified, such as the location where the faults inject, the matching point with differential relationship, and the two independent computation paths where two independent subsets of the key are involved. In this paper, we formulate the essential ideas of the construction of the attack, and translate the problem of searching for the best MitM DFA into optimization problems under constraints in Mixed-Integer-Linear-Programming (MILP) models. With the models, we achieve more powerful and practical DFA attacks on SKINNY, CRAFT, QARMA, PRINCE, PRINCEv2, and MIDORI with faults injected in 1 to 9 earlier rounds than the best previous DFAs.

At ASIACRYPT 2022, Benedikt, Fischlin, and Huppert proposed the quantum herding attacks on iterative hash functions for the first time. Their attack needs exponential quantum random access memory (qRAM), more precisely {$2^{0.43n}$} quantum accessible classical memory (QRACM). As the existence of large qRAM is questionable, Benedikt et al. leave an open question on building low-qRAM quantum herding attacks. In this paper, we answer this open question by building a quantum herding attack, where the time complexity is slightly increased from Benedikt et al.'s $2^{0.43n}$ to ours $2^{0.46n}$, but {it does not need qRAM anymore (abbreviated as no-qRAM)}. Besides, we also introduce various low-qRAM {or no-qRAM} quantum attacks on hash concatenation combiner, hash XOR combiner, Hash-Twice, and Zipper hash functions.

Feistel network and its generalizations (GFN) are another important building blocks for constructing hash functions, e.g., Simpiravb, Areion, and the ISO standard Lesamnta-lw. The Meet-in-the-Middle (MitM) is a general paradigm to build preimage and collision attacks on hash functions, which has been automated in several papers. However, those automatic tools mostly focus on hash function with Substitution–Permutation network (SPN) as building blocks, and only one for Feistel network by Schrottenloher and Stevens (at CRYPTO 2022). In this paper, we introduce a new automatic model for MitM attacks on Feistel networks by generalizing the traditional {\em direct or indirect partial matching strategies} and also Sasaki's multi-round matching strategy. Besides, we find the equivalent transformations of Feistel and GFN can significantly simplify the MILP modellings. Based on our automatic model, we improve the preimage attacks on Feistel-SP-MMO, Simpira-2/-4-DM, Areion-256/-512-DM by 1-2 rounds or significantly reduce the complexities. Furthermore, we fill in the gap left by Schrottenloher and Stevens at CRYPTO 2022 on the large branch ($b>4$) Simpira-$b$'s attack and propose the first 11-round attack on Simpira-6. Besides, we significantly improve the collision attack on the ISO standard hash Lesamnta-lw by increasing the attacked round number from previous 11 to ours 17 rounds.

When generating quartets for the rectangle attack on ciphers with linear key-schedule ciphers, we find the right quartets which may suggest key candidates have to satisfy some nonlinear relationships. However, some quartets generated always violate these relationships, so that they will never suggest any key candidates. Inspired by previous rectangle frameworks, we find that guessing certain key cells before generating quartets may reduce the number of those invalid quartets. However, guessing a lot of key cells at once may lose the benefit from the early abort technique, which may lead to a higher overall complexity. To get better tradeoff, we build a new rectangle attack framework on ciphers with linear key-schedule with the purpose of reducing the overall complexity or attacking more rounds. In the tradeoff model, there are many parameters affecting the overall complexity, especially for the choices of the number and positions of key guessing cells before generating quartets. To identify optimal parameters, we build a uniform automatic tool on SKINNY as an example, which includes the optimal rectangle distinguishers for key-recovery phase, the number and positions of key guessing cells before generating quartets, the size of key counters to build that affecting the exhaustive search step, etc. Based on the automatic tool, we identify a 32-round key-recovery attack on SKINNY-128-384 in the related-key setting, which extends the best previous attack by 2 rounds. For other versions with n-2n or n-3n, we also achieve one more round than before. In addition, using the previous rectangle distinguishers, we achieve better attacks on round-reduced ForkSkinny, Deoxys-BC-384 and GIFT-64. At last, we discuss the conversion of our rectangle framework from related-key setting into single-key setting and give new single-key rectangle attack on 10-round Serpent.

At ASIACRYPT 2012, Sasaki et al. introduced the guess-and-determine approach to extend the meet-in-the-middle (MITM) preimage attack. At CRYPTO 2021, Dong et al. proposed a technique to derive the solution spaces of nonlinear constrained neutral words in the MITM preimage attack. In this paper, we try to combine these two techniques to further improve the MITM preimage attacks. Based on the previous MILP-based automatic tools for MITM attacks, we introduce new constraints due to the combination of guess-and-determine and nonlinearly constrained neutral words to build a new automatic model.As a proof of work, we apply it to the Russian national standard hash function Streebog, which is also an ISO standard. We find the first 8.5-round preimage attack on Streebog-512 compression function and the first 7.5-round preimage attack on Streebog-256 compression function. In addition, we give the 8.5-round preimage attack on Streebog-512 hash function. Our attacks extend the best previous attacks by one round. We also improve the time complexity of the 7.5-round preimage attack on Streebog-512 hash function and 6.5-round preimage attack on Streebog-256 hash function.

Rebound attack was introduced by Mendel et al. at FSE~2009 to fulfill a heavy middle round of a differential path for free, utilizing the degree of freedom from states. The inbound phase was extended to 2 rounds by Super-Sbox technique invented by Lamberger et al. at ASIACRYPT~2009 and Gilbert and Peyrin at FSE~2010. In ASIACRYPT~2010, Sasaki et al. further reduced the requirement of memory by introducing the non-full-active Super-Sbox. In this paper, we further develop this line of research by introducing Super-Inbound, which is able to connect multiple 1-round or 2-round (non-full-active) Super-Sbox inbound phases by utilizing fully the degrees of freedom from both states and key, yet without the use of large memory. This essentially extends the inbound phase by up to 3 rounds. We applied this technique to find classic or quantum collisions on several AES-like hash functions, and improved the attacked round number by 1 to 5 in targets including AES-128 and Skinny hashing modes, Saturnin-hash, and Gr{\o}stl-512. To demonstrate the correctness of our attacks, the semi-free-start collision on 6-round AES-128-MMO/MP with estimated time complexity $2^{24}$ in classical setting was implemented and an example pair was found instantly on a standard PC.

Designing symmetric ciphers for particular applications becomes a hot topic. At EUROCRYPT 2020, Naito, Sasaki and Sugawara invented the threshold implementation friendly cipher SKINNYe-64-256 to meet the requirement of the authenticated encryption PFB_Plus. Soon, Thomas Peyrin pointed out that SKINNYe-64-256 may lose the security expectation due the new tweakey schedule. Although the security issue of SKINNYe-64-256 is still unclear, Naito et al. decided to introduce SKINNYe-64-256 v2 as a response. In this paper, we give a formal cryptanalysis on the new tweakey schedule of SKINNYe-64-256 and discover unexpected differential cancellations in the tweakey schedule. For example, we find the number of cancellations can be up to 8 within 30 consecutive rounds, which is significantly larger than the expected 3 cancellations. This property is derived by the analysis of the updated functions (LFSRs) of the tweakey via linear algebra. Moreover, we take our new discoveries into rectangle, MITM and impossible differential attacks, and adapt the corresponding automatic tools with new constraints from our discoveries. Finally, we find a 41-round related-tweakey rectangle attack on SKINNYe-64-256 and leave a security margin of 3 rounds only. As STK accepts arbitrary tweakey size, but SKINNY and SKINNYe-64-256 v2 only support up to 4n tweakey size. We introduce a new design of tweakey schedule for SKINNY-64 to further extend the supported tweakey size. We give a formal proof that our new tweakey schedule inherits the security requirement of STK and SKINNY.

Simpira v2 is an AES-based permutation proposed by Gueron and Mouha at ASIACRYPT 2016. In this paper, we build an improved MILP model to count the differential and linear active Sboxes for Simpira v2, which achieves tighter bounds of the minimum number of active Sboxes for a few versions of Simpira v2. Then, based on the new model, we find some new truncated differentials for Simpira v2 and give a series (quantum) collision attacks on two versions of reduced Simpira v2.

The Meet-in-the-Middle (MITM) preimage attack is highly effective in breaking the preimage resistance of many hash functions, including but not limited to the full MD5, HAVAL, and Tiger, and reduced SHA-0/1/2. It was also shown to be a threat to hash functions built on block ciphers like AES by Sasaki in 2011. Recently, such attacks on AES hashing modes evolved from merely using the freedom of choosing the internal state to also exploiting the freedom of choosing the message state. However, detecting such attacks especially those evolved variants is difficult. In previous works, the search space of the configurations of such attacks is limited, such that manual analysis is practical, which results in sub-optimal solutions. In this paper, we remove artificial limitations in previous works, formulate the essential ideas of the construction of the attack in well-defined ways, and translate the problem of searching for the best attacks into optimization problems under constraints in Mixed-Integer-Linear-Programming (MILP) models. The MILP models capture a large solution space of valid attacks; and the objectives of the MILP models are attack configurations with the minimized computational complexity. With such MILP models and using the off-the-shelf solver, it is efficient to search for the best attacks exhaustively. As a result, we obtain the first attacks against the full (5-round) and an extended (5.5-round) version of Haraka-512 v2, and 8-round AES-128 hashing modes, as well as improved attacks covering more rounds of Haraka-256 v2 and other members of AES and Rijndael hashing modes.

When analyzing a block cipher, the first step is to search for some valid distinguishers, for example, the differential trails in the differential cryptanalysis and the linear trails in the linear cryptanalysis. A distinguisher is advantageous if it can be utilized to attack more rounds and the amount of the involved key bits during the key-recovery process is small, as this leads to a long attack with a low complexity. In this article, we propose a two-step strategy to search for such advantageous distinguishers. This strategy is inspired by the intuition that if a differential is advantageous only when some properties are satisfied, then we can predefine some constraints describing these properties and search for the differentials in the small set.As applications, our strategy is used to analyze GIFT-128, which was proposed in CHES 2017. Based on some 20-round differentials, we give the first 27-round differential attack on GIFT-128, which covers one more round than the best previous result. Also, based on two 17-round linear trails, we give the first linear hull attack on GIFT-128, which covers 22 rounds. In addition, we also give some results on two GIFT-128 based AEADs GIFT-COFB and SUNDAE-GIFT.

Automatic modelling to search distinguishers with high probability covering as many rounds as possible, such as MILP, SAT/SMT, CP models, has become a very popular cryptanalysis topic today. In those models, the optimizing objective is usually the probability or the number of rounds of the distinguishers. If we want to recover the secret key for a round-reduced block cipher, there are usually two phases, i.e., finding an efficient distinguisher and performing key-recovery attack by extending several rounds before and after the distinguisher. The total number of attacked rounds is not only related to the chosen distinguisher, but also to the extended rounds before and after the distinguisher. In this paper, we try to combine the two phases in a uniform automatic model.Concretely, we apply this idea to automate the related-key rectangle attacks on SKINNY and ForkSkinny. We propose some new distinguishers with advantage to perform key-recovery attacks. Our key-recovery attacks on a few versions of round-reduced SKINNY and ForkSkinny cover 1 to 2 more rounds than the best previous attacks.

At EUROCRYPT 2021, Bao et al. proposed an automatic method for systematically exploring the configuration space of meet-in-the-middle (MITM) preimage attacks. We further extend it into a constraint-based framework for finding exploitable MITM characteristics in the context of key-recovery and collision attacks by taking the subtle peculiarities of both scenarios into account. Moreover, to perform attacks based on MITM characteristics with nonlinear constrained neutral words, which have not been seen before, we present a procedure for deriving the solution spaces of neutral words without solving the corresponding nonlinear equations or increasing the overall time complexities of the attack. We apply our method to concrete symmetric-key primitives, including SKINNY, ForkSkinny, Romulus-H, Saturnin, Grostl, Whirlpool, and hashing modes with AES-256. As a result, we identify the first 23-round key-recovery attack on \skinny-$n$-$3n$ and the first 24-round key-recovery attack on ForkSkinny-$n$-$3n$ in the single-key model. Moreover, improved (pseudo) preimage or collision attacks on round-reduced Whirlpool, Grostl, and hashing modes with AES-256 are obtained. In particular, imploying the new representation of the \AES key schedule due to Leurent and Pernot (EUROCRYPT 2021), we identify the first preimage attack on 10-round AES-256 hashing.

Collision attacks on AES-like hashing (hash functions constructed by plugging AES-like ciphers or permutations into the famous PGV modes or their variants) can be reduced to the problem of finding a pair of inputs respecting a differential of the underlying AES-like primitive whose input and output differences are the same. The rebound attack due to Mendel et al. is a powerful tool for achieving this goal, whose quantum version was first considered by Hosoyamada and Sasaki at EUROCRYPT 2020. In this work, we automate the process of searching for the configurations of rebound attacks by taking related-key differentials of the underlying block cipher into account with the MILP-based approach. In the quantum setting, our model guide the search towards characteristics that minimize the resources (e.g., QRAM) and complexities of the resulting rebound attacks. We apply our method to Saturnin-hash, Skinny, and Whirlpool and improved results are obtained.

At EUROCRYPT 2020, Hosoyamada and Sasaki proposed the first dedicated quantum attack on hash functions -- a quantum version of the rebound attack exploiting differentials whose probabilities are too low to be useful in the classical setting. This work opens up a new perspective toward the security of hash functions against quantum attacks. In particular, it tells us that the search for differentials should not stop at the classical birthday bound. Despite these interesting and promising implications, the concrete attacks described by Hosoyamada and Sasaki make use of large quantum random access memories (qRAMs), a resource whose availability in the foreseeable future is controversial even in the quantum computation community. Without large qRAMs, these attacks incur significant increases in time complexities. In this work, we reduce or even avoid the use of qRAMs by performing a quantum rebound attack based on differentials with non-full-active super S-boxes. Along the way, an MILP-based method is proposed to systematically explore the search space of useful truncated differentials with respect to rebound attacks. As a result, we obtain improved attacks on \aes-\texttt{MMO}, \aes-\texttt{MP}, and the first classical collision attacks on 4- and 5-round \grostl-\texttt{512}. Interestingly, the use of non-full-active super S-box differentials in the analysis of \aes-\texttt{MMO} gives rise to new difficulties in collecting enough starting points. To overcome this issue, we consider attacks involving two message blocks to gain more degrees of freedom, and we successfully compress the qRAM demand of the collision attacks on \texttt{AES}-\texttt{MMO} and \texttt{AES}-\texttt{MP} (EUROCRYPT 2020) from $2^{48}$ to a range from $2^{16}$ to $0$, while still maintaining a comparable time complexity. To the best of our knowledge, these are the first dedicated quantum attacks on hash functions that slightly outperform Chailloux, Naya-Plasencia, and Schrottenloher's generic quantum collision attack (ASIACRYPT 2017) in a model where large qRAMs are not available. This work demonstrates again how a clever combination of classical cryptanalytic technique and quantum computation leads to improved attacks, and shows that the direction pointed out by Hosoyamada and Sasaki deserves further investigation.

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.

In the CAESAR competition, Deoxys-I and Deoxys-II are two important authenticated encryption schemes submitted by Jean et al. Recently, Deoxys-II together with Ascon, ACORN, AEGIS-128, OCB and COLM have been selected as the final CAESAR portfolio. Notably, Deoxys-II is also the primary choice for the use case “Defense in depth”. However, Deoxys-I remains to be one of the third-round candidates of the CAESAR competition. Both Deoxys-I and Deoxys-II adopt Deoxys-BC-256 and Deoxys-BC-384 as their internal tweakable block ciphers.In this paper, we investigate the security of round-reduced Deoxys-BC-256/-384 and Deoxys-I against the related-tweakey boomerang and rectangle attacks with some new boomerang distinguishers. For Deoxys-BC-256, we present 10-round related-tweakey boomerang and rectangle attacks for the popular setting (|tweak|, |key|) = (128, 128), which reach one more round than the previous attacks in this setting. Moreover, an 11-round related-tweakey rectangle attack on Deoxys-BC-256 is given for the first time. We also put forward a 13-round related-tweakey boomerang attack in the popular setting (|tweak|, |key|) = (128, 256) for Deoxys-BC-384, while the previous attacks in this setting only work for 12 rounds at most. In addition, the first 14-round relatedtweakey rectangle attack on Deoxys-BC-384 is given when (|tweak| < 98, |key| > 286), that attacks one more round than before. Besides, we give the first 10-round rectangle attack on the authenticated encryption mode Deoxys-I-128-128 with one more round than before, and we also reduce the complexity of the related-tweakey rectangle attack on 12-round Deoxys-I-256-128 by a factor of 228. Our attacks can not be applied to (round-reduced) Deoxys-II.

In this paper, we propose a key-recovery attack on Trivium reduced to 855 rounds. As the output is a complex Boolean polynomial over secret key and IV bits and it is hard to find the solution of the secret keys, we propose a novel nullification technique of the Boolean polynomial to reduce the output Boolean polynomial of 855-round Trivium. Then we determine the degree upper bound of the reduced nonlinear boolean polynomial and detect the right keys. These techniques can be applicable to most stream ciphers based on nonlinear feedback shift registers (NFSR). Our attack on 855-round Trivium costs time complexity $$2^{77}$$. As far as we know, this is the best key-recovery attack on round-reduced Trivium. To verify our attack, we also give some experimental data on 721-round reduced Trivium.

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.

This paper studies the Keccak-based authenticated encryption (AE) scheme Ketje Sr against cube-like attacks. Ketje is one of the remaining 16 candidates of third round CAESAR competition, whose primary recommendation is Ketje Sr. Although the cube-like method has been successfully applied to Ketje’s sister ciphers, including Keccak-MAC and Keyak – another Keccak-based AE scheme, similar attacks are missing for Ketje. For Ketje Sr, the state (400-bit) is much smaller than Keccak-MAC and Keyak (1600-bit), thus the 128-bit key and cubes with the same dimension would occupy more lanes in Ketje Sr. Hence, the number of key bits independent of the cube sum is very small, which makes the divide-and-conquer method (it has been applied to 7-round attack on Keccak-MAC by Dinur et al.) can not be translated to Ketje Sr trivially. This property seems to be the barrier for the translation of the previous cube-like attacks to Ketje Sr. In this paper, we evaluate Ketje Sr against the divide-and-conquer method. Firstly, by applying the linear structure technique, we find some 32/64-dimension cubes of Ketje Sr that do not multiply with each other as well as some bits of the key in the first round. In addition, we introduce the new dynamic variable instead of the auxiliary variable (it was used in Dinur et al.’s divide-and-conquer attack to reduce the diffusion of the key) to reduce the diffusion of the key as well as the cube variables. Finally, we successfully launch a 6/7-round1 key recovery attack on Ketje Sr v1 and v2 (v2 is presented for the 3rd round CAESAR competition.). In 7-round attack, the complexity of online phase for Ketje Sr v1 is 2113, while for Ketje Sr v2, it is 297 (the preprocessing complexity is the same). We claim 7-round reduced Ketje Sr v2 is weaker than v1 against our attacks. In addition, some results on other Ketje instances and Ketje Sr with smaller nonce are given. Those are the first results on Ketje and bridge the gaps of cryptanalysis between its sister ciphers – Keyak and the Keccak keyed modes.

Since Knudsen and Rijmen proposed the known-key attacks in ASIACRYPT 2007, the open-key model becomes more and more popular. As the other component of the open-key model, chosen-key model was applied to the full attacks on AES-256 by Biryukov et al. in CRYPTO 2009. In this paper, we explore how practically the chosen-key model affect the real-world cryptography and show that 11-round generic Feistel-SP block cipher is no longer safe in its hashing modes (MMO and MP mode) as there exist collision attacks. This work improves Sasaki and Yasuda’s collision attacks by 2 rounds with two interesting techniques. First, we for the first time use the available degrees of freedom in the key to reduce the complexity of the inbound phase, which extends the previous 5-round inbound differential to a 7-round one. This results in a 12-round chosen-key distinguisher of Feistel-SP block cipher. Second, inspired by the idea of Wang et al., we construct collisions using two blocks. The rebound attack is used in the second compression function. We carefully balance the freedom of the first block and the complexity of the rebound attack, and extend the chosen-key attack to a 11-round collision attack on its hashing modes (MMO and MP mode).