Hash functions and extendable output functions are some of the most fundamental building blocks in cryptography. They are often used to build commitment schemes where a committer binds themselves to some value that is also hidden from the verifier until the opening is sent. Such commitment schemes are commonly used to build signature schemes, e.g., Ed25519 via Schnorr signatures, or non-interactive zero-knowledge proofs. We specifically analyze the binding security when Ascon-Hash256 or Ascon-XOF128 is used inside of Ed25519, which is closely related to finding second preimages. While there is ample prior work on Ascon-XOF128 and Ascon-Hash256, none of it applies in this setting either because it analyzes short outputs of 64 or 128 bits or because the complexity is above the security claim and generic attack of 128 bits. We show how to exploit the setting of finding a forgery for Ed25519. We find that this setting is quite challenging due to the large 320-bit internal state combined with the 128-bit security level. We propose a second-preimage attack for 1-round Ascon-Hash256 with a complexity of 2^64 Gaussian eliminations and a random-prefix-preimage attack (also known as Nostradamus attack) for 1-round Ascon-Hash256, for the Ed25519 setting, with complexity 2^29.7 Gaussian eliminations.

The construction of building beyond-birthday-bound secure pseudorandom functions (PRFs) from the Xor-sum of 2 pseudorandom permutations (PRPs) has been known since EUROCRYPT 1998. However, the first concrete instance was only published recently at FSE 2022: the low-latency PRF Orthros. Subsequently, at ASIACRYPT 2024, Flórez-Gutiérrez et al. proposed the general framework of ZIP ciphers, where a block cipher E1 E0 is used to construct the PRF E0 E1-1 They propose the PRF ZIP-AES, as the Xor-sum of 5 AES encryption rounds and 5 decryption rounds. They discuss differential, linear, and integral distinguishers for this construction, but provide no concrete key recovery attacks. Furthermore, they propose ZIP-GIFT as a 64-bit PRF but leave cryptanalysis as future work. In this work, we provide the first third-party analysis of ZIP-AES and ZIP-GIFT. We investigate the challenges of applying classical cryptanalytic techniques to ZIP ciphers and discuss several adaptations needed for key recovery attacks in this setting. We show differential, linear, and integral key recovery attacks for both PRFs. In particular, we adapt integral key recovery techniques for ZIP ciphers, and show how to extend differential characteristics by some rounds for key recovery using truncated differential distinguishers. Our analysis deepens the understanding of the security of ZIP ciphers but does not threaten the security claims.

In modern CPU architectures, various security features to mitigate software attacks can be found. Examples of such features are logical isolation, memory tagging or shadow stacks. Basing such features on cryptographic isolation instead of logical checks can have many advantages such as lower memory overhead and more robustness against misconfiguration or low-cost physical attacks. The disadvantage of such an approach is however that the cipher that has to be introduced has a severe impact on the system performance, either in terms of additional cycles or a decrease of the maximum achievable frequency. Finally, as of today, there is no suitable low-latency cipher design available for encrypting 32-bit words as is common in microcontrollers. In this paper, we propose a 32-bit tweakable block cipher tailored to memory encryption for microcontroller units. We optimize this cipher for low latency, which we achieve by a careful selection of components for the round function and leveraging an attack scenario similar to the one used to analyze the cipher SCARF. To mitigate some attack vectors introduced by this attack scenario, we deploy a complex tweak-key schedule. Due to the shortage of suitable 32-bit designs, we compare our design to various low-latency ciphers with different block sizes. Our hardware implementation shows competitive latency numbers.

Differential cryptanalysis is one of the main methods of cryptanalysis and has been applied to a wide range of ciphers. While it is very successful, it also relies on certain assumptions that do not necessarily hold in practice. One of these is the hypothesis of stochastic equivalence, which states that the probability of a differential characteristic behaves similarly for all keys. Several works have demonstrated examples where this hypothesis is violated, impacting the attack complexity and sometimes even invalidating the investigated prior attacks. Nevertheless, the hypothesis is still typically taken for granted. In this work, we propose AutoDiVer, an automatic tool that allows to thoroughly verify differential characteristics. First, the tool supports calculating the expected probability of differential characteristics while considering the key schedule of the cipher. Second, the tool supports estimating the size of the space of keys for which the characteristic permits valid pairs, and deducing conditions for these keys. AutoDiVer implements a custom SAT modeling approach and takes advantage of a combination of features of advanced SAT solvers, including approximate model counting and clause learning. To show applicability to many different kinds of block ciphers like strongly aligned, weakly aligned, and ARX ciphers, we apply AutoDiVer to GIFT, PRESENT, RECTANGLE, SKINNY, Midori, WARP, SPECK, and SPEEDY.

In 2023, NIST has selected Ascon as the new standard for lightweight cryptography. The Ascon v1.2 family provides authenticated encryption, hash functions, and extendable output functions, all using the same Ascon permutation. The main use case of Ascon is to provide efficient cryptographic primitives for resource-constraint devices. While additional primitives can be built on top of the existing Ascon functions, dedicated schemes are often more efficient. In this paper, we enrich the functionality of Ascon by providing efficient Pseudorandom Functions (PRFs), Message Authentication Codes (MACs), and a fast short-input PRF for messages up to 128 bits.

The impossible differential (ID) attack is one of the most important cryptanalytic techniques for block ciphers. There are two phases to finding an ID attack: searching for the distinguisher and building a key recovery upon it. Previous works only focused on automated distinguisher discovery, leaving key recovery as a manual post-processing task, which may lead to a suboptimal final complexity. At EUROCRYPT 2023, Hadipour et al. introduced a unified constraint programming (CP) approach based on satisfiability for finding optimal complete ID attacks in strongly aligned ciphers. While this approach was extended to weakly-aligned designs like PRESENT at ToSC 2024, its application to ARX and AndRX ciphers remained as future work. Moreover, this method only exploited ID distinguishers with direct contradictions at the junction of two deterministic transitions. In contrast, some ID distinguishers, particularly for ARX and AndRX designs, may not be detectable by checking only the existence of direct contradictions. This paper fills these gaps by extending Hadipour et al.’s method to handle indirect contradictions and adapting it for ARX and AndRX designs. We also present a similar method for identifying zero-correlation (ZC) distinguishers. Moreover, we extend our new model for finding ID distinguishers to a unified optimization problem that includes both the distinguisher and the key recovery for AndRX designs. Our method improves ID attacks and introduces new distinguishers for several ciphers, such as SIMON, SPECK, Simeck, ChaCha, Chaskey, LEA, and SipHash. For example, we achieve a one-round improvement in ID attacks against SIMON-64-96, SIMON-64-128, SIMON-128-128, SIMON-128-256 and a two-round improvement against SIMON-128- 192. These results significantly contribute to our understanding of the effectiveness of automated tools in the cryptanalysis of different design paradigms.

Integral, impossible-differential (ID), and zero-correlation (ZC) attacks are three of the most important attacks on block ciphers. However, manually finding these attacks can be a daunting task, which is why automated methods are becoming increasingly important. Most automatic tools regarding integral, ZC, and ID attacks have focused only on finding distinguishers rather than complete attacks. At EUROCRYPT 2023, Hadipour et al. proposed a generic and efficient constraint programming (CP) model based on satisfiability for finding ID, ZC, and integral distinguishers. This new model can be extended to a unified CP model for finding full key recovery attacks. However, it has limitations, including determining the contradiction location beforehand and a cell-wise model unsuitable for weakly aligned ciphers like Ascon and PRESENT. They also deferred developing a CP model for the partial-sum technique in key recovery as future work. In this paper, we enhance Hadipour et al.’s method in several ways. First, we remove the limitation of determining the contradiction location in advance. Second, we show how to extend the distinguisher model to a bit-wise model, considering the internal structure of S-boxes and keeping the model based on satisfiability. Third, we introduce a CP model for the partial-sum technique for the first time. To show the usefulness and versatility of our approach, we apply it to various designs, from strongly aligned ones like ForkSKINNY and QARMAv2 to weakly aligned ones such as Ascon and PRESENT, yielding significantly improved results. To mention a few of our results, we improve the integral distinguisher of QARMAv2-128 (resp. QARMAv2-64) by 7 (resp. 5) rounds, and the integral distinguisher of ForkSKINNY by 1 round, only thanks to our cell-wise distinguisher modelings. By using our new bit-wise modeling, our tool can find a group of 2155 5-round ID and ZC distinguishers for Ascon in only one run, taking a few minutes on a regular laptop. The new CP model for the partial-sum technique enhances integral attacks on all SKINNY variants, notably improving the best attack on SKINNY-n-n in the single-key setting by 1 round. We also enhance ID attacks on ForkSKINNY and provide the first analysis of this cipher in a limited reduced-round setting. Our methods are generic and applicable to other block ciphers.

In 2023, NIST has selected Ascon as the new standard for lightweight cryptography. The Ascon v1.2 family provides authenticated encryption, hash functions, and extendable output functions, all using the same Ascon permutation. The main use case of Ascon is to provide efficient cryptographic primitives for resource-constraint devices. While additional primitives can be built on top of the existing Ascon functions, dedicated schemes are often more efficient. In this paper, we enrich the functionality of Ascon by providing efficient Pseudorandom Functions (PRFs), Message Authentication Codes (MACs), and a fast short-input PRF for messages up to 128 bits.

We consider pre-image attacks on a version of Ascon-Xof where the number of rounds in pa has been reduced to 2 and the length of the hash value H is truncated to 64 bits. Hence, it is expected to hit this value with a probability of 2−64 and thus, the expected workload to find a pre-image is around 264. For simplicity, we consider the round-reduced variant of Ascon-Xof without round constants and with an all-zero equivalent IV. If we then take a look at the output of the S-box of the first round, we see that the 3 bits SL 0,0,i, S L 0,1,i, and S L 0,3,i of the S-box output depend on the input bit S N 0,0,i, while the bits SL 0,2,i = 1 and S L 0,4,i = 0. Hence, after the application of the linear layer, bit i of the first word SN 1,0,i = Σ0,i(S N 0,0), bit i of the second word SN 1,1,i = Σ1,i(S N 0,0), bit i of the third word SN 1,2,i = 1, bit i of the fourth word SN 1,3,i = Σ3,i(S N 0,0), and bit i of the fifth word SN 1,4,i = 0. Due to the word-wise structure of Ascon’s linear layer, we only have to obey the first bit of the ANF of the S-box and get:

In 1994, Langford and Hellman introduced differential-linear (DL) cryptanalysis, with the idea of decomposing the block cipher E into two parts, E_u and E_ℓ , such that E_u exhibits a high-probability differential trail, while E_ℓ has a high-correlation linear trail. Combining these trails forms a distinguisher for E, assuming independence between E_u and E_ℓ . The dependency between the two parts of DL distinguishers remained unaddressed until EUROCRYPT 2019, where Bar-On et al. [3] introduced the DLCT framework, resolving the issue up to one S-box layer. However, extending the DLCT framework to formalize the dependency between the two parts for multiple rounds remained an open problem. In this paper, we first tackle this problem from the perspective of boomerang analysis. By examining the relationships between DLCT, DDT, and LAT, we introduce a set of new tables facilitating the formulation of dependencies between the two parts of the DL distinguisher across multiple rounds. Then, we introduce a highly versatile and easy-to-use automatic tool for exploring DL distinguishers, inspired by automatic tools for boomerang distinguishers. This tool considers the dependency between differential and linear trails across multiple rounds. We apply our tool to various symmetric-key primitives, and in all applications, we either present the first DL distinguishers or enhance the best-known ones. We achieve successful results against Ascon, AES, SERPENT, PRESENT, SKINNY, TWINE, CLEFIA, WARP, LBlock, Simeck, and KNOT. Furthermore, we demonstrate that, in some cases, DL distinguishers outperform boomerang distinguishers significantly.

Impossible differential (ID), zero-correlation (ZC), and integral attacks are a family of important attacks on block ciphers. For example, the impossible differential attack was the first cryptanalytic attack on 7 rounds of AES. Evaluating the security of block ciphers against these attacks is very important but also challenging: Finding these attacks usually implies a combinatorial optimization problem involving many parameters and constraints that is very hard to solve using manual approaches. Automated solvers, such as Constraint Programming (CP) solvers, can help the cryptanalyst to find suitable attacks. However, previous CP-based methods focus on finding only the ID, ZC, and integral distinguishers, often only in a limited search space. Notably, none can be extended to a unified optimization problem for finding full attacks, including efficient key-recovery steps. In this paper, we present a new CP-based method to search for ID, ZC, and integral distinguishers and extend it to a unified constraint optimization problem for finding full ID, ZC, and integral attacks. To show the effectiveness and usefulness of our method, we applied it to several block ciphers, including SKINNY, CRAFT, SKINNYe-v2, and SKINNYee. For the ISO standard block cipher SKINNY, we significantly improve all existing ID, ZC, and integral attacks. In particular, we improve the integral attacks on SKINNY- n -3 n and SKINNY- n -2 n by 3 and 2 rounds, respectively, obtaining the best cryptanalytic results on these variants in the single-key setting. We improve the ZC attack on SKINNY- n - n (SKINNY- n -2 n ) by 2 (resp. 1) rounds. We also improve the ID attacks on all variants of SKINNY. Particularly, we improve the time complexity of the best previous single-tweakey (related-tweakey) ID attack on SKINNY-128-256 (resp. SKINNY-128-384) by a factor of 2 22.57 (resp. 2 15.39 ). On CRAFT, we propose a 21-round (20-round) ID (resp. ZC) attack, which improves the best previous single-tweakey attack by 2 (resp. 1) rounds. Using our new model, we also provide several practical integral distinguishers for reduced-round SKINNY, CRAFT, and Deoxys-BC. Our method is generic and applicable to other strongly aligned block ciphers.

In this paper, we propose SassCache, a secure skewed associative cache with keyed index mapping. For this purpose, we design a new two-layered, low-latency cryptographic construction with configurable output coverage based on state-of-the-art cryptographic primitives. Based on this construction, SassCache is the first secure randomized cache with secure spacing. Victim cache lines automatically hide in locations the attacker cannot reach after less than 1 access on average. Consequently, attackers cannot evict the cache line, no matter which and how many memory accesses they perform. Our security analysis shows that all existing techniques for eviction set construction fail, and state-of-the-art attacks only apply to 1 in 3 million addresses, where SassCache is still as secure as ScatterCache. Compared to standard caches, Sass Cache has a single-threaded performance penalty of 1:75% on the last-level cache hit rate in the SPEC2017 benchmark, and an average decrease of 11:7 p.p. in hit rate for MiBench, GAP and Scimark for our high-security settings.

The hash function Romulus-H is a finalist in the NIST Lightweight Cryptography competition. It is based on the Hirose double block-length (DBL) construction which is provably secure when used with an ideal block cipher. However, in practice, ideal block ciphers can only be approximated. Therefore, the security of concrete instantiations must be cryptanalyzed carefully; the security margin may be higher or lower than in the secret-key setting. So far, the Hirose DBL construction has been studied with only a few other block ciphers, like IDEA and AES. However, Romulus-H uses Hirose DBL with the SKINNY block cipher where only very little analysis has been published so far. In this work, we present the first practical analysis of Romulus-H. We propose a new framework for finding collisions in hash functions based on the Hirose DBL construction. This is in contrast to previous work that only focused on free-start collisions. Our framework is based on the idea of joint differential characteristics which capture the relationship between the two block cipher calls in the Hirose DBL construction. To identify good joint differential characteristics, we propose a combination of MILP and CP models. Then, we use these characteristics in another CP model to find collisions. Finally, we apply this framework to Romulus-H and find practical collisions of the hash function for 10 out of 40 rounds and practical semi-free-start collisions for up to 14 rounds.

. We introduce the tweakable block cipher QARMAv2 . It is a redesign of QARMA to improve its security bounds and allow for longer tweaks, while keeping very similar latency and area values. The wider tweak input caters to both specific use cases and the design of modes of operation with higher security bounds. This is achieved through new key and tweak schedules, revised S-Box and linear layer choices, adjustments to the 128-bit version, and a more comprehensive security analysis. The new cipher offers competitive latency and area in fully unrolled HW implementations. Some of our results may be of independent interest. This includes new MILP models of certain classes of diffusion matrices, the comparative analysis of a full reflection cipher against an iterative half-cipher, and our boomerang attack framework.

We introduce the QARMAv2 family of tweakable block ciphers. It is a redesign of QARMA (from FSE 2017) to improve its security bounds and allow for longer tweaks, while keeping similar latency and area. The wider tweak input caters to both specific use cases and the design of modes of operation with higher security bounds. This is achieved through new key and tweak schedules, revised S-Box and linear layer choices, and a more comprehensive security analysis. QARMAv2 offers competitive latency and area in fully unrolled hardware implementations. Some of our results may be of independent interest. These include: new MILP models of certain classes of diffusion matrices; the comparative analysis of a full reflection cipher against an iterative half-cipher; our boomerang attack framework; and an improved approach to doubling the width of a block cipher.

In this paper, we present CSI:Rowhammer, a principled hardware-software co-design Rowhammer mitigation with cryptographic security and integrity guarantees, that does not focus on any specific properties of Rowhammer. We design a new memory error detection mechanism based on a low-latency cryptographic MAC and an exception mechanism initiating a software-level correction routine. The exception handler uses a novel instruction-set extension for the error correction and resumes execution afterward. In contrast to regular ECCDRAM that remains exploitable if more than 2 bits are flipped, CSI:Rowhammer maintains the security level of the cryptographic MAC. We evaluate CSI:Rowhammer in a gem5 proof-of-concept implementation. Under normal conditions, we see latency overheads below 0.75% and no memory overhead compared to off-the-shelf ECC-DRAM. While the average latency to correct a single bitflip is below 20 ns (compared to a range from a few nanoseconds to several milliseconds for state-of-the-art ECC memory), CSI:Rowhammer can detect any number of bitflips with overwhelming probability and correct at least 8 bitflips in practical time constraints.

The guess-and-determine technique is one of the most widely used techniques in cryptanalysis to recover unknown variables in a given system of relations. A subset of the unknown variables is guessed such that the remaining unknowns can be deduced using the relations. Applications include state recovery for stream ciphers and key-bridging in key-recovery attacks on block ciphers. Since the attack complexity depends on the number of guessed variables, it is essential to find small guess bases. In this paper, we present Autoguess, an easy-to-use tool to search for a minimal guess basis. We propose several new modeling techniques to harness SAT/SMT, MILP, and Gröbner basis solvers. We demonstrate their usefulness in guess-and-determine attacks on stream ciphers and block ciphers, as well as finding key-bridges for block ciphers. Moreover, integrating our CP models for the key-bridging technique into the previous CP-based frameworks to search for distinguishers, we propose a unified and general CP model to find key-recovery-friendly distinguishers for both linear and nonlinear key schedules.