The Legendre PRF relies on the conjectured pseudorandomness properties of the Legendre symbol with a hidden shift. Originally proposed as a PRG by Damgård at CRYPTO 1988, it was recently suggested as an efficient PRF for multiparty computation purposes by Grassi et al. at CCS 2016. Moreover, the Legendre PRF is being considered for usage in the Ethereum 2.0 blockchain. This paper improves previous attacks on the Legendre PRF and its higher-degree variant due to Khovratovich by reducing the time complexity from $O(p\log{p}/M)$ to $O(p\log^2{p}/M^2)$ Legendre symbol evaluations when $M \le \sqrt[4]{p \log^2 p}$ queries are available. The practical relevance of our improved attack is demonstrated by breaking three concrete instances of the PRF proposed by the Ethereum foundation. Furthermore, we generalize our attack in a nontrivial way to the higher-degree variant of the Legendre PRF and we point out a large class of weak keys for this construction. Lastly, we provide the first security analysis of two additional generalizations of the Legendre PRF originally proposed by Damgård in the PRG setting, namely the Jacobi PRF and the power residue PRF.

In this paper, we reevaluate the security of GIFT against differential cryptanalysis under both single-key scenario and related-key scenario. Firstly, we apply Matsui's algorithm to search related-key differential trails of GIFT. We add three constraints to limit the search space and search the optimal related-key differential trails on the limited search space. We obtain related-key differential trails of GIFT-64/128 for up to 15/14 rounds, which are the best results on related-key differential trails of GIFT so far. Secondly, we propose an automatic algorithm to increase the probability of the related-key boomerang distinguisher of GIFT by searching the clustering of the related-key differential trails utilized in the boomerang distinguisher. We find a 20-round related-key boomerang distinguisher of GIFT-64 with probability 2^-58.557. The 25-round related-key rectangle attack on GIFT-64 is constructed based on it. This is the longest attack on GIFT-64. We also find a 19-round related-key boomerang distinguisher of GIFT-128 with probability 2^-109.626. We propose a 23-round related-key rectangle attack on GIFT-128 utilizing the 19-round distinguisher, which is the longest related-key attack on GIFT-128. The 24-round related-key rectangle attack on GIFT-64 and 22-round related-key boomerang attack on GIFT-128 are also presented. Thirdly, we search the clustering of the single-key differential trails. We increase the probability of a 20-round single-key differential distinguisher of GIFT-128 from 2^-121.415 to 2^-120.245. The time complexity of the 26-round differential attack on GIFT-128 is improved from 2^124:415 to 2^123:245.

In this paper we introduce new algorithms that, based only on the independent round keys assumption, allow to practically compute the exact expected differential probability of (truncated) differentials and the expected linear potential of (multidimensional) linear hulls. That is, we can compute the exact sum of the probability or the potential of all characteristics that follow a given activity pattern. We apply our algorithms to various recent SPN ciphers and discuss the results.

In this paper, we investigate the key dependency of differentials in block ciphers by examining the results of numerous experiments applied to the substitution-permutation network (SPN) structure using 4-bit S-boxes. In particular, we consider two cipher structures: a toy 16-bit SPN and a realistic 64-bit SPN. For both ciphers, we generate many different experimental results by inserting the S-boxes used in many lightweight cipher proposals and applying different forms of round key generation. It is demonstrated that, in most circumstances, with enough rounds in the cipher, the probability distribution (across all keys) of the differential probability follows the distribution expected in the theoretically ideal scenario. However, this does not occur consistently for all S-boxes and all approaches to round key generation. Consequently, it is possible that a cipher may have more susceptibility to differential cryptanalysis for some subset of the cipher keys than is implied when employing the standard assumptions used in analyzing a cipher’s security.

Given a vectorial function $F:\mathbb{F}_2^n \mapsto \mathbb{F}_2^m$, the indicator $1_{{\cal G}_F}$ of its graph ${\cal G}_F=\{(x,F(x)); x\in \mathbb{F}_2^n\}$ allows to express the algebraic degree of $F$ in a simple way. Exploiting the formula, obtained in a previous paper, for the graph indicator of a composite function $G\circ F$, that involves only a sum of products of $1_{{\cal G}_F}$ and $1_{{\cal G}_G}$, we deduce bounds on the algebraic degree of $G\circ F$, whose efficiency comes from the fact that the algebraic degree of the product of two Boolean functions is bounded above by the sum of their algebraic degrees, while for a composition, it is bounded above by their product. One of these bounds, that depends on the algebraic degrees of $G$ and $1_{{\cal G}_F}$, is tight, general, simple, and most often efficient (for the case where it is not efficient, we give an improved bound, that is a little more complex). As far as we know, it is the first efficient upper bound ever found, that works without any condition on the vectorial functions. It provides a new criterion for the choice of S-boxes in block ciphers. It implies as a corollary a known bound assuming the divisibility of the Walsh transform values by a power of 2. It gives a better view why this latter bound works. Our results generalize to more than two functions. \\ When $F$ is a permutation, our expression of the algebraic degree of $G\circ F$ simplifies into a formula involving the algebraic degrees of the products of a coordinate function of $G$ and coordinate functions of $F^{-1}$. This implies another known bound showing that the algebraic degree of $F^{-1}$ has more impact on that of $G\circ F$ than that of $F$ itself. Our approach by graph indicators gives one more explanation to this interesting fact. Our results include all the known efficient bounds as particular cases, and clarify the reasons why they work. We also deduce the exact expression of the algebraic degree of the composition of any number of functions, leading to a bound that is much more efficient than what we obtain by applying the known bound several times. We also obtain two bounds on the algebraic degree of $G \circ F$, where $F$ is a permutation, given the divisibility by powers of 2 of some Walsh transform values of component functions of $F$ and their sums with a coordinate function of $G$. We study the generalizations of all (known and new) bounds of this kind to the composition of more than two functions.

The side-channel community recently investigated a new approach, based on deep learning, to significantly improve profiled attacks against embedded systems. Compared to template attacks, deep learning techniques can deal with protected implementations, such as masking or desynchronization, without substantial pre-processing. However, important issues are still open. One challenging problem is to adapt the methods classically used in the machine learning field (e.g. loss function, performance metrics) to the specific side-channel context in order to obtain optimal results. We propose a new loss function derived from the learning to rank approach that helps preventing approximation and estimation errors, induced by the classical cross-entropy loss. We theoretically demonstrate that this new function, called Ranking Loss (RkL), maximizes the success rate by minimizing the ranking error of the secret key in comparison with all other hypotheses. The resulting model converges towards the optimal distinguisher when considering the mutual information between the secret and the leakage. Consequently, the approximation error is prevented. Furthermore, the estimation error, induced by the cross-entropy, is reduced by up to 23%. When the ranking loss is used, the convergence towards the best solution is up to 23% faster than a model using the cross-entropy loss function. We validate our theoretical propositions on public datasets.

In this article, we present WARP, a lightweight 128-bit block cipher with a 128-bit key. It aims at small-footprint circuit in the field of 128-bit block ciphers, possibly for a unified encryption and decryption functionality. The overall structure of WARP is a variant of 32-nibble Type-2 Generalized Feistel Network (GFN), with a permutation over nibbles designed to optimize the security and efficiency. We conduct a thorough security analysis and report comprehensive hardware and software implementation results. Our hardware results show that WARP is the smallest 128-bit block cipher for most of typical hardware implementation strategies. A serialized circuit of WARP achieves around 800 Gate Equivalents (GEs), which is much smaller than previous state-of-the-art implementations of lightweight 128-bit ciphers (they need more than $1,000$ GEs). While our primary metric is hardware size, WARP also enjoys several other features, most notably low energy consumption. This is somewhat surprising, since GFN generally needs more rounds than substitution permutation network (SPN), and thus GFN has been considered to be less advantageous in this regard. We show a multi-round implementation of WARP is quite low-energy. Moreover, WARP also performs well on software: our SIMD implementation is quite competitive to known hardware-oriented 128-bit lightweight ciphers for long input, and even much better for small inputs due to the small number of parallel blocks. On 8-bit microcontrollers, the results of our assembly implementations show that WARP is flexible to achieve various performance characteristics.

Format-Preserving Encryption (FPE) is a method to encrypt non-standard domains, thus allowing for securely encrypting not only binary strings, but also special domains, e.g., social security numbers into social security numbers. The need for those resulted in a few standardized constructions such as the NIST standardized FF1 and FF3-1 and the Korean Standards FEA-1 and FEA-2. Moreover, there are currently efforts both in ANSI and in ISO to include such block ciphers to standards (e.g., the ANSI X9.124 discussing encryption for financial services). Most of the proposed FPE schemes, such as the NIST standardized FF1 and FF3-1 and the Korean Standards FEA-1 and FEA-2, are based on a Feistel construction with pseudo-random round functions. Moreover, to mitigate enumeration attacks against the possibly small domains, they all employ tweaks, which enrich the actual domain sizes. In this paper we present distinguishing attacks against Feistel-based FPEs. We show a distinguishing attack against the full FF1 with data complexity of $2^{60}$ 20-bit plaintexts, against the full FF3-1 with data complexity of $2^{40}$ 20-bit plaintexts. For FEA-1 with 128-bit, 192-bit and 256-bit keys, the data complexity of the distinguishing attack is $2^{32}$, $2^{40}$, and $2^{48}$ 8-bit plaintexts, respectively. The data complexity of the distinguishing attack against the full FEA-2 with 128-bit, 192-bit and 256-bit is $2^{56}$, $2^{68}$, and $2^{80}$ 8-bit plaintexts, respectively. Moreover, we show how to extend the distinguishing attack on FEA-1 and FEA-2 using 192-bit and 256-bit keys into key recovery attacks with time complexity $2^{136}$ (for both attacks).

This paper has four main goals. First, we show how we solved the CHES 2018 AES challenge in the contest using essentially a linear classifier combined with a SAT solver and a custom error correction method. This part of the paper has previously appeared in a preprint by the current authors (e-print report 2019/094) and later as a contribution to a preprint write-up of the solutions by the three winning teams (e-print report 2019/860). Second, we develop a novel deep neural network architecture for side-channel analysis that completely breaks the AES challenge, allowing for fairly reliable key recovery with just a single trace on the unknown-device part of the CHES challenge (with an expected success rate of roughly 70 percent if about 100 CPU hours are allowed for the equation solving stage of the attack). This solution significantly improves upon all previously published solutions of the AES challenge, including our baseline linear solution. Third, we consider the question of leakage attribution for both the classifier we used in the challenge and for our deep neural network. Direct inspection of the weight vector of our machine learning model yields a lot of information on the implementation for our linear classifier. For the deep neural network, we test three other strategies (occlusion of traces; inspection of adversarial changes; knowledge distillation) and find that these can yield information on the leakage essentially equivalent to that gained by inspecting the weights of the simpler model. Fourth, we study the properties of adversarially generated side-channel traces for our model. Partly reproducing recent work on useful features in adversarial examples in our application domain, we find that a linear classifier generalizing to an unseen device much better than our linear baseline can be trained using only adversarial examples (fresh random keys, adversarially perturbed traces) for our deep neural network. This gives a new way of extracting human-usable knowledge from a deep side channel model while also yielding insights on adversarial examples in an application domain where relatively few sources of spurious correlations between data and labels exist. The experiments described in this paper can be reproduced using code available at https://github.com/agohr/ches2018 .

In this work we develop optimized software implementationsfor ForkAE, a second round candidate in the ongoing NIST lightweight cryptography standardization process. Moreover, we analyze the perfor-mance and efficiency of different ForkAE implementations on two em-bedded platforms: ARM Cortex-A9 and ARM Cortex-M0.First, we study portable ForkAE implementations. We apply a decryption optimization technique which allows us to accelerate decryption by up to 35%. Second, we go on to explore platform-specific software op-timizations. In platforms where cache-timing attacks are not a risk, we present a novel table-based approach to compute the SKINNY round function. Compared to the existing portable implementations, this technique speeds up encryption and decryption by 20% and 25%, respectively. Additionally, we propose a set of platform-specific optimizations for processors with parallel hardware extensions such as ARM NEON. Without relying on parallelism provided by long messages (cf. bit-sliced implementations), we focus on the primitive-level ForkSkinny parallelism provided by ForkAE to reduce encryption and decryption latency by up to 30%. We benchmark the performance of our implementations on the ARM Cortex-M0 and ARM Cortex-A9 processors and give a comparison withthe other SKINNY-based schemes in the NIST lightweight competition– SKINNY-AEAD and Romulus

In this paper, we study a group of AEAD schemes that use rekeying as a technique to increase efficiency by reducing the state size of the algorithm. We provide a unified model to study the behavior of the keys used in these schemes, called Rekey-and-Chain (RaC). This model helps understand the design of several AEAD schemes. We show generic attacks on these schemes based on the existence of certain types of weak keys. We also show that the borderline between multi-key and single-key analyses of these schemes is not solid and the analysis can be performed independent of the master key, leading sometimes to practical attacks in the multi-key setting. More importantly, the multi-key analysis can be applied in the single key setting, since each message is encrypted with a different key. Consequently, we show gaps in the security analysis of COMET and mixFeed in the single key setting, which led the designers to provide overly optimistic security claims. In the case of COMET, full key recovery can be performed with 2^64 online queries and 2^64 offline queries in the single-key setting, or 2^40 online queries per user and 2^64 offline queries in the multi-key setting with 2^24 users. In the case of mixFeed, we enhance the forgery adversarial advantage in the single-key setting with a factor of 2^67 compared to what the designers claim. More importantly, our result is just a lower bound of this advantage, since we show that the gap in the analysis of mixFeed depends on properties of the AES Key Schedule that are not well understood and require more cryptanalytic efforts to find a more tight advantage. After reporting these findings, the designers updated their security analyses and accommodated the proposed attacks.

In this work, we present a primary construction of bent functions based on cellular automata (CA). We consider the well-known characterization of bent functions in terms of Hadamard matrices and employ some recent results about mutually orthogonal Latin squares (MOLS) based on linear bipermutive CA (LBCA) to design families of Hadamard matrices of the form required for bent functions. In particular, the main question to address in this construction can be reduced to finding a large enough set of coprime polynomials over $\mathbb{F}_q$, which are used to define a set of MOLS via LBCA. This set of MOLS is, in turn, used to define a Hadamard matrix of the specific structure characterizing a bent function. We settle the existence question of such bent functions by proving that the required coprime sets exist if and only if the degree of the involved polynomials is either $1$ or $2$, and we count the resulting sets. Next, we check if the functions of $8$ variables arising from our construction are EA-equivalent to Maiorana-McFarland functions, observing that most of them are not. Finally, we show how to represent the support of these bent functions as a union of the kernels of the underlying linear CA. This allows us, in turn, to prove that the functions generated by our construction belong to the partial spread class $\mathcal{PS}^-$. In particular, we remark that for degree $1$ our construction is a particular case of the Desarguesian spread construction.

Functional Encryption (FE) allows users who hold a specific secret key (known as the functional key) to learn a specific function of encrypted data whilst learning nothing about the content of the underlying data. Considering this functionality and the fact that the field of FE is still in its infancy, we sought a route to apply this potent tool to solve the existing problem of designing decentralised additive reputation systems. To this end, we first built a symmetric FE scheme for the $\ell_1$ norm of a vector space, which allows us to compute the sum of the components of an encrypted vector (i.e. the votes). Then, we utilized our construction, along with functionalities offered by Intel SGX, to design the first FE-based decentralized additive reputation system with Multi-Party Computation. While our reputation system faces certain limitations, this work is amongst the first attempts that seek to utilize FE in the solution of a real-life problem.

The advances of the Internet of Things (IoT) have had a fundamental impact and influence in sharping our rich living experiences. However, since IoT devices are usually resource-constrained, lightweight block ciphers have played a major role in serving as a building block for secure IoT protocols. In CHES 2015, SIMECK, a family of block ciphers, was designed for resource-constrained IoT devices. Since its publication, there have been many analyses on its security. In this paper, under the one bit-flip model, we propose a new efficient fault analysis attack on SIMECK ciphers. Compared to those previously reported attacks, our attack can recover the full master key by injecting faults into only a single round of all SIMECK family members. This property is crucial, as it is infeasible for an attacker to inject faults into different rounds of a SIMECK implementation on IoT devices in the real world. Specifically, our attack is characterized by exercising a deep analysis of differential trail between the correct and faulty immediate ciphertexts. Extensive simulation evaluations are conducted, and the results demonstrate the effectiveness and correctness of our proposed attack.

The bit-sliding paper of Jean et al. (CHES 2017) showed that the smallest-size circuit for SPN based block ciphers such as AES, SKINNY and PRESENT can be achieved via bit-serial implementations. Their technique decreases the bit size of the datapath and naturally leads to a significant loss in latency (as well as the maximum throughput). Their designs complete a single round of the encryption in 168 (resp. 68) clock cycles for 128 (resp. 64) bit blocks. A follow-up work by Banik et al. (FSE 2020) introduced the swap-and-rotate technique that both eliminates this loss in latency and achieves even smaller footprints. In this paper, we extend these results on bit-serial implementations all the way to four authenticated encryption schemes from NIST LWC. Our first focus is to decrease latency and improve throughput with the use of the swap-and-rotate technique. Our block cipher implementations have the most efficient round operations in the sense that a round function of an $n$-bit block cipher is computed in exactly $n$ clock cycles. This leads to implementations that are similar in size to the state of the art, but have much lower latency (savings up to 20 percent). We then extend our technique to 4- and 8-bit implementations. Although these results are promising, block ciphers themselves are not end-user primitives, as they need to be used in conjunction with a mode of operation. Hence, in the second part of the paper, we use our serial block ciphers to bootstrap four active NIST authenticated encryption candidates: SUNDAE-GIFT, Romulus, SAEAES and SKINNY-AEAD. In the wake of this effort, we provide the smallest block-cipher-based authenticated encryption circuits known in the literature so far.

The selection criteria for NIST's Lightweight Crypto Standardization (LWC) have been slowly shifting towards the lightweight efficiency of designs, given that a large number of candidates already establish their security claims on conservative, well-studied paradigms. The research community has accumulated a decent level of experience on authenticated encryption primitives, thanks mostly to the recently completed CAESAR competition, with the advent of the NIST LWC, the de facto focus is now on evaluating efficiency of the designs with respect to hardware metrics like area, throughput, power and energy. In this paper, we focus on a less investigated metric under the umbrella term lightweight, i.e. energy consumption. Quantitatively speaking, energy is the sum total electrical work done by a voltage source and thus is a critical metric of lightweight efficiency. Among the thirty-two second round candidates, we give a detailed evaluation of the ten that only make use of a lightweight or semi-lightweight block cipher at their core. We use this pool of candidates to investigate a list of generic implementation choices that have considerable effect on both the size and the energy consumption of modes of operation circuit, which function as an authenticated encryption primitive. Besides providing energy and circuit size metrics of these candidates, our results provide useful insights for designers who wish to understand what particular choices incur significant energy consumption in AEAD schemes. In the second part of the paper we shift our focus to threshold implementations that offer protection against first order power analysis attacks. There has been no study focusing on energy efficiency of such protected implementations and as such the optimizations involved in such circuits are not well established. We explore the simplest possible protected circuit: the one in which only the state path of the underlying block cipher is shared, and we explore how design choices like number of shares, implementation of the masked s-box and the circuit structure of the AEAD scheme affect the energy consumption.

Differential power analysis (DPA) is a form of side-channel analysis (SCA) that performs statistical analysis on the power traces of cryptographic computations. DPA is applicable to many cryptographic primitives, including block ciphers, stream ciphers and even hash-based message authentication code (HMAC). At COSADE 2017, Dobraunig~et~al. presented a DPA on the fresh re-keying scheme Keymill to extract the bit relations of neighbouring bits in its shift registers, reducing the internal state guessing space from 128 to 4 bits. In this work, we generalise their methodology and combine with differential analysis, we called it differential analysis aided power attack (DAPA), to uncover more bit relations and take into account the linear or non-linear functions that feedback to the shift registers (i.e. LFSRs or NLFSRs). Next, we apply our DAPA on LR-Keymill, the improved version of Keymill designed to resist the aforementioned DPA, and breaks its 67.9-bit security claim with a 4-bit internal state guessing. We experimentally verified our analysis. In addition, we improve the previous DPA on Keymill by halving the amount of data resources needed for the attack. We also applied our DAPA to Trivium, a hardware-oriented stream cipher from the eSTREAM portfolio and reduces the key guessing space from 80 to 14 bits.

Hashing modes are ways to convert a block cipher into a hash function, and those with AES as the underlying block cipher are referred to as AES hashing modes. Sasaki in 2011, introduced the first preimage attack against AES hashing modes with the AES block cipher reduced to 7 rounds, by the method of meet-in-the-middle. In his attack, the key-schedules are not taken into account. Hence, the same attack applies to all three versions of AES. In this paper, by introducing neutral bits from the key, extra degree of freedom is gained, which is utilized in two ways, i.e., to reduce the time complexity and to extend the attack to more rounds. As an immediate result, the complexities of 7-round pseudo-preimage attacks are reduced from $2^{120}$ to $2^{104}$, $2^{96}$, and $2^{96}$ for AES-128, AES-192, and AES-256, respectively. By carefully choosing the neutral bits from the key to cancel those from the state, the attack is extended to 8 rounds for AES-192 and AES-256 with complexities $2^{112}$ and $2^{96}$. Similar results are obtained for Kiasu-BC, a tweakable block cipher based on AES-128, and interestingly the additional input tweak helps reduce the complexity and extend the attack to one more round. To the best of our knowledge, these are the first preimage attacks against 8-round AES hashing modes.

In this paper we introduce the strictly zero-correlation attack. We extend the work of Ashur and Posteuca in BalkanCryptSec 2018 and build a 0-correlation key-dependent linear trails covering the full DES. We show how this approximation can be used for a key recovery attack and empirically verify our claims through a series of experiments. To the best of our knowledge, this paper is the first to use this kind of property to leverage a meaningful attack against a symmetric-key algorithm.

Functional Encryption (FE) allows users who hold a specific secret key (known as the functional key) to learn a specific function of encrypted data whilst learning nothing about the content of the underlying data. Considering this functionality and the fact that the field of FE is still in its infancy, we sought a route to apply this potent tool to design efficient applications. To this end, we first built a symmetric FE scheme for the $\ell_1$ norm of a vector space, which allows us to compute the sum of the components of an encrypted vector. Then, we utilized our construction, to design an Order-Revealing Encryption (ORE) scheme and a privately encrypted database. While there is room for improvement in our schemes, this work is among the first attempts that seek to utilize FE for the solution of practical problems that can have a tangible effect on people's daily lives.

This report contains analysis and discussion on different versions of the TopoSign (Topographic Signature) protocol proposed by Matelski.

In this paper, we propose a formal security model and a construction methodology of interactive aggregate message authentication with detecting functionality (IAMD). The IAMD is an interactive aggregate MAC protocol which can identify invalid messages with a small amount of tag-size. Several aggregate MAC schemes that can specify invalid messages has been proposed so far by using non-adaptive group testing in the prior work. In this paper, we utilize adaptive group testing to construct IAMD scheme, and we show that the resulting IAMD scheme can identify invalid messages with a small amount of tag-size compared to the previous schemes.

This short report contains results of a brief cryptanalysis of the initialisation phase of ZUC-256. We find IV differentials that persist for 26 of the 33 initialisation rounds, and Key differentials that persist for 28 of the 33 rounds.

WAGE is a hardware-oriented authenticated cipher, which has the smallest (unprotected) hardware cost (for 128-bit security level) among the round 2 candidates of the NIST lightweight cryptography (LWC) competition. In this work, we analyze the security of WAGE against the correlation power analysis (CPA) on ARM Cortex-M4F microcontroller. Our attack detects the secret key leakage from power consumption for up to 12 (out of 111) rounds of the WAGE permutation and requires 10,000 power traces to recover the 128-bit secret key. Motivated by the CPA attack and the low hardware cost of WAGE, we propose the first optimized masking scheme of WAGE in the t-strong non-interference (SNI) security model. We investigate different masking schemes for S-boxes by exploiting their internal structures and leveraging the state-of-the-art masking techniques.To practically demonstrate the effectiveness of masking, we perform the test vector leakage assessment on the 1-order masked WAGE. We evaluate the hardware performance of WAGE for 1, 2, and 3-order security and provide a comparison with other NIST LWC round 2 candidates.

Farfalle, a permutation-based construction for building a pseudorandom function (PRF), is really versatile. It can be used for message authentication code, stream cipher, key derivation function, authenticated encryption and so on. Farfalle construction relies on a set of permutations and on so-called rolling functions: it can be split into a compression layer followed by a two-step expansion layer. As one instance of Farfalle, Xoofff is very efficient on a wide range of platforms from low-end devices to high-end processors by combining the narrow permutation Xoodoo and the inherent parallelism of Farfalle. In this paper, we present key-recovery attacks on reduced-round Xoofff. After identifying a weakness in the expanding rolling function, we first propose practical attacks on Xoofff instantiated with 1-/2-round Xoodoo in the expansion layer. We next extend such attack on Xoofff instantiated with 3-/4-round Xoodoo in the expansion layer by making use of Meet-in-the-Middle algebraic attacks and the linearization technique. All attacks proposed here -- which are independent of the details of the compression and/or middle layer -- have been practically verified (either on the "real" Xoofff or on a toy-version Xoofff with block-size of 96 bits). As a countermeasure, we discuss how to slightly modified the rolling function for free to reduce the number of attackable rounds.

For many years EM Side-Channel Attacks, which exploit the statistical link between the magnetic field radiated by secure ICs and the data they process, are a critical threat. Indeed, attackers need to find only one hotspot (position of the EM probe over the IC surface) where there is an exploitable leakage to compromise the security. As a result, designing secure ICs robust against these attacks is incredibly difficult because designers must warrant there is no hotspot over the whole IC surface. This task is all the more difficult as there is no CAD tool to compute the magnetic field radiated by ICs and hence no methodology to detect hotspots at the design stages. Within this context, this paper introduces a flow allowing predicting the EM radiations of ICs and two related methodologies. The first one aims at identifying and quantifying the dangerousness of EM hotspots at the surface of ICs, i.e. positions where to place an EM probe to capture a leakage. The second aims at locating leakage hotspots in ICs, i.e. areas in circuits from where these leakages originate.

Distinguishers on round-reduced AES have attracted considerable attention in the recent years. While the number of rounds covered in key-recovery attacks did not increase, subspace, yoyo, mixture-differential, and multiple-of-n cryptanalysis advanced the understanding of the properties of the cipher. For substitution-permutation networks, integral attacks are a suitable target for extension since they usually end after a linear layer sums several subcomponents. Based on results by Patarin, Chen et al. already observed that the expected number of collisions for a sum of permutations differs slightly from that for a random primitive. Though, their target remained lightweight primitives. The present work illustrates how the well-known integral distinguisher on three-round AES resembles a sum of PRPs and can be extended to truncated-differential distinguishers over 4 and 5 rounds. In contrast to previous distinguishers by Grassi et al., our approach allows to prepend a round that starts from a diagonal subspace. We demonstrate how the prepended round can be used for key recovery with a new differential key-recovery attack on six-round AES. Moreover, we show how the prepended round can also be integrated to form a six-round distinguisher. For all distinguishers and the key-recovery attack, our results are supported by implementations with Cid et al.'s established Small-AES version. While the distinguishers do not threaten the security of the AES, they try to shed more light on its properties.

CRAFT is a lightweight tweakable block cipher proposed at FSE 2019, which allows countermeasures against Differential Fault Attacks to be integrated into the cipher at the algorithmic level with ease. CRAFT employs a lightweight and involutory S-box and linear layer, such that the encryption function can be turned into decryption at a low cost. Besides, the tweakey schedule algorithm of CRAFT is extremely simple, where four 64-bit round tweakeys are generated and repeatedly used. Due to a combination of these features which makes CRAFT exceedingly lightweight, we find that some input difference at a particular position can be preserved through any number of rounds if the input pair follows certain truncated differential trails. Interestingly, in contrast to traditional differential analysis, the validity of this invariant property is affected by the positions where the constant additions take place. We use this property to construct ``weak-tweakey'' truncated differential distinguishes of CRAFT in the single-key model. Subsequently, we show how the tweak additions allow us to convert these weak-tweakey distinguishers into ordinary secret-key distinguishers based on which key-recovery attacks can be performed. Moreover, we show how to construct MILP models to search for truncated differential distinguishers exploiting this invariant property. As a result, we find a 15-round truncated differential distinguisher of CRAFT and extend it to a 19-round key-recovery attack with $2^{60.99}$ data, $2^{68}$ memory, $2^{94.59}$ time complexity, and success probability 80.66%. Also, we find a 14-round distinguisher with probability $2^{-43}$ (experimentally verified), a 16-round distinguisher with probability $2^{-55}$, and a 20-round weak-key distinguisher ($2^{118}$ weak keys) with probability $2^{-63}$. Experiments on round-reduced versions of the distinguishers show that the experimental probabilities are sometimes higher than predicted. Finally, we note that our result is far from threatening the security of the full CRAFT.

Periodic key rotation is a common practice designed to limit the long-term power of cryptographic keys. Key rotation refers to the process of re-encrypting encrypted content under a fresh key, and overwriting the old ciphertext with the new one. When encrypted data is stored in the cloud, key rotation can be very costly: it may require downloading the entire encrypted content from the cloud, re-encrypting it on the client's machine, and uploading the new ciphertext back to the cloud. An updatable encryption scheme is a symmetric-key encryption scheme designed to support efficient key rotation in the cloud. The data owner sends a short \emph{update token} to the cloud. This update token lets the cloud rotate the ciphertext from the old key to the new key, without learning any information about the plaintext. Recent work on updatable encryption has led to several security definitions and proposed constructions. However, existing constructions are not yet efficient enough for practical adoption, and the existing security definitions can be strengthened. In this work we make three contributions. First, we introduce stronger security definitions for updatable encryption (in the ciphertext-dependent setting) that capture desirable security properties not covered in prior work. Second, we construct two new updatable encryption schemes. The first construction relies only on symmetric cryptographic primitives, but only supports a bounded number of key rotations. The second construction supports a (nearly) unbounded number of updates, and is built from the Ring Learning with Errors (RLWE) assumption. Due to complexities of using RLWE, this scheme achieves a slightly weaker notion of integrity compared to the first. Finally, we implement both constructions and compare their performance to prior work. Our RLWE-based construction is 200x faster than a prior proposal for an updatable encryption scheme based on the hardness of elliptic curve DDH. Our first construction, based entirely on symmetric primitives, has the highest encryption throughput, approaching the performance of AES, and the highest decryption throughput on ciphertexts that were re-encrypted fewer than fifty times. For ciphertexts re-encrypted over fifty times, the RLWE construction dominates it in decryption speed.

Substitution boxes (S-boxes) based on the inversion mapping in even-characteristic finite fields are widely used components in the design of cryptographic primitives such as block ciphers (notably the AES cipher). This report focuses on the inversion mapping in finite fields GF(p^n) where p is a (small) odd prime and n is a (small) integer. We compare the differential and linear profiles of S-boxes over odd- and even-characteristic fields, which also motivates the design and analysis of AES variants operating in fields of odd-characteristic. Even for GF(2^n), the study of S-boxes which are APN permutations (odd-valued n)already shows resistance to differential and linear cryptanalysis after three rounds.

With the advances of Internet-of-Things (IoT) applications in smart cities and the pervasiveness of network devices with limited resources, lightweight block ciphers have achieved rapid development recently. Due to their relatively simple key schedule, nonlinear invariant attacks have been successfully applied to several families of lightweight block ciphers. This attack relies on the existence of a nonlinear invariant $g:\F_2^n \rightarrow \F_2$ for the round function $F_k$ so that $g(x) + g(F_k(x))$ is constant for any input value $x$. Whereas invariants of the entire $S$-box layer has been studied in terms of the corresponding cycle structure [TLS16,WRP20] (assuming the use of bijective S-boxes), a similar analysis for the linear layer has not been performed yet. In this article, we provide a theoretical analysis for specifying the minimal length of cycles for commonly used linear permutations (implementing linear layers) in lightweight block ciphers. Namely, using a suitable matrix representation, we exactly specify the minimal cycle lengths for those (efficiently implemented) linear layers that employ ShiftRows, Rotational-XOR and circular Boolean matrix operations which can be found in many well-known families of block ciphers. These results are practically useful for the purpose of finding nonlinear invariants of the entire encryption rounds since these can be specified using the intersection of cycles corresponding to the linear and S-box layer. We also apply our theoretical analysis practically and specify minimal cycle lengths of linear layers for certain families of block ciphers including some NIST candidates.

We present malleability attacks against encrypted binary executable files when they are encrypted by CBC mode of operation. While the CBC malleability is classic and has been used to attack on various real-world applications, the risk of encrypting binary executable via CBC mode on common OSs has not been widely recognized. We showed that, with a certain non-negligible probability, it is possible to manipulate the CBC-encrypted binary files so that the decryption result allows an arbitrary code execution (ACE), which is one of the most powerful exploits, even without the knowledge of plaintext binary. More specifically, for both 32- and 64-bit Linux and Windows OS, we performed a thorough analysis on the binary executable format to evaluate the practical impact of ACE on CBC encryption, and showed that the attack is possible if the adversary is able to correctly guess 13 to 25 bits of the address to inject code. In principle, our attack affects a wide range of storage/file encryption systems that adopt CBC encryption. In addition, a manual file encryption using OpenSSL API (AES-256-CBC) is affected, which is presumed to be frequently used in practice for file encryption. We provide Proof-of-Concept implementations for Linux and Windows. We have communicated our findings to the appropriate institution and have informed to vendors as an act of responsible disclosure.

This note describes some methods for adding a key commitment property to a generic (nonce-based) AEAD scheme. We analyze the the privacy bounds and key commitment guarantee of the resulting constructions, by expressing them in terms of the properties of the underlying AEAD scheme and the added key commitment primitive. We also offer concrete constructions for a key committing version of AES-GCM.

The design and cryptanalysis are the both sides from which we look at symmetric-key primitives. If a symmetric-key primitive is broken by a kind of cryptanalysis, it's definitely insecure. If a designer claims a symmetric-key primitive to be secure, one should demonstrate that the primitive resists against all known attacks. Differential and linear cryptanalysis are two of the most important kinds of cryptanalysis. To conduct a successful differential (linear) cryptanalysis, a differential (linear) distinguisher with significant differential probability (linear correlation) is needed. We observe that, for some lightweight symmetric-key primitives, their significant trails usually contain iterative trails. In this work, We propose an automatic tool for searching iterative trails. We model the problem of searching itrative trails as a problem of finding elementry ciucuits in a graph. Based on the iterative trails found, we further propose a method to estimate the probability (correlation) of a differential (linear hull). We apply our methods to the 256-bit KNOT permutation, PRESENT, GIFT-64 and RECTANGLE. Iterative trails are found and visualized. If iterative trails are found, we show our method can efficiently find good differentials and linear hulls. What's more, the results imply that for the primitives we test with bit permutations as their linear layers, the good differentials and linear hulls are dominated by iterative trails.

Automatic search methods have been widely used for cryptanalysis of block ciphers, especially for the most classic cryptanalysis methods -- differential and linear cryptanalysis. However, the automatic search methods, no matter based on MILP, SMT/SAT or CP techniques, can be inefficient when the search space is too large. In this paper, we improve Matsui's branch-and-bound search algorithm which is known as the first generic algorithm for finding the best differential and linear trails by proposing three new methods. The three methods, named Reconstructing DDT and LAT According to Weight, Executing Linear Layer Operations in Minimal Cost and Merging Two 4-bit S-boxes into One 8-bit S-box respectively, can efficiently speed up the search process by reducing the search space as much as possible and reducing the cost of executing linear layer operations. We apply our improved algorithm to DESL and GIFT, which are still the hard instances for the automatic search methods. As a result, we find the best differential trails for DESL (up to 14 rounds) and GIFT-128 (up to 19 rounds). The best linear trails for DESL (up to 16 rounds), GIFT-128 (up to 10 rounds) and GIFT-64 (up to 15 rounds) are also found. To the best of our knowledge, these security bounds for DESL and GIFT under single-key scenario are given for the first time. Meanwhile, it is the longest exploitable (differential or linear) trails for DESL and GIFT. Furthermore, benefiting from the efficiency of the improved algorithm, we do experiments to demonstrate that the clustering effect of differential trails for 13-round DES and DESL are both weak.

Since Keccak was selected as the SHA-3 standard, more and more permutation-based primitives have been proposed. Different from block ciphers, there is no round key in the underlying permutation for permutation-based primitives. Therefore, there is a higher risk for a differential characteristic of the underlying permutation to become incompatible when considering the dependency of difference transitions over different rounds. However, in most of the MILP or SAT based models to search for differential characteristics, only the difference transitions are involved and are treated as independent in different rounds, which may cause that an invalid one is found for the underlying permutation. To overcome this obstacle, we are motivated to design a model which automatically avoids the inconsistency in the search for differential characteristics. Our technique is to involve both the difference transitions and value transitions in the constructed model. Such an idea is inspired by the algorithm to find SHA-2 characteristics as proposed by Mendel et al. in ASIACRYPT 2011, where the differential characteristic and the conforming message pair are simultaneously searched. As a first attempt, our new technique will be applied to the Gimli permutation, which was proposed in CHES 2017. As a result, we reveal that some existing differential characteristics of reduced Gimli are indeed incompatible, one of which is found in the Gimli document. In addition, since only the permutation is analyzed in the Gimli document, we are lead to carry out a comprehensive study, covering the proposed hash scheme and the authenticated encryption (AE) scheme specified for Gimli, which has become a second round candidate of the NIST lightweight cryptography standardization process. For the hash scheme, a semi-free-start (SFS) collision attack can reach up to 8 rounds starting from an intermediate round. For the AE scheme, a state recovery attack is demonstrated to achieve up to 9 rounds. It should be emphasized that our analysis does not threaten the security of Gimli.

Deep learning approaches have become popular for Side-Channel Analysis (SCA) in the recent years. Especially Convolutional Neural Networks (CNN) due to their natural ability to overcome jitter-based as well as masking countermeasures. However, most efforts have focused on finding optimal architecture for a given dataset and bypass the need for trace pre-processing. However, trace pre-processing is a long studied topic and several proven techniques exist in the literature. There is no straightforward manner to integrate those techniques into deep learning based SCA. In this paper, we propose a generic framework which allows seamless integration of multiple, user defined pre-processing techniques into the neural network architecture. The framework is based on Multi-scale Convolutional Neural Networks (MCNN) that were originally proposed for time series analysis. MCNN are composed of multiple branches that can apply independent transformation to input data in each branch to extract the relevant features and allowing a better generalization of the model. In terms of SCA, these transformation can be used for integration of pre-processing techniques, such as phase-only correlation, principal component analysis, alignment methods etc. We present successful results on publicly available datasets. Our findings show that it is possible to design a network that can be used in a more general way to analyze side-channel leakage traces and perform well across datasets.

This document provides a simple standard specification for the Rescue-Prime family of arithmetization-oriented hash functions.

The wire probe-and-fault models are currently the most used models to provide arguments for side-channel and fault security. However, several practical attacks are not yet covered by these models. This work extends the wire fault model to include more advanced faults such as area faults and permanent faults. Moreover, we show the tile probe-and-fault adversary model from CRYPTO 2018's CAPA envelops the extended wire fault model along with known extensions to the probing model such as glitches, transitions, and couplings. In other words, tiled (tessellated) designs offer security guarantees even against advanced probe and fault adversaries. As tiled models use multi-party computation techniques, countermeasures are typically expensive for software/hardware. This work investigates a tiled countermeasure based on the ISW methodology which is shown to perform significantly better than CAPA for practical parameters.

In this paper, we prove that the nonce-based enhanced hash-then-mask MAC ($\mathsf{nEHtM}$) is secure up to $2^{\frac{3n}{4}}$ MAC queries and $2^n$ verification queries (ignoring logarithmic factors) as long as the number of faulty queries $\mu$ is below $2^\frac{3n}{8}$, significantly improving the previous bound by Dutta et al. Even when $\mu$ goes beyond $2^{\frac{3n}{8}}$, $\mathsf{nEHtM}$ enjoys graceful degradation of security. The second result is to prove the security of PRF-based $\mathsf{nEHtM}$; when $\mathsf{nEHtM}$ is based on an $n$-to-$s$ bit random function for a fixed size $s$ such that $1\leq s\leq n$, it is proved to be secure up to any number of MAC queries and $2^s$ verification queries, if (1) $s=n$ and $\mu<2^{\frac{n}{2}}$ or (2) $\frac{n}{2}<s<2^{n-s}$ and $\mu<\max\{2^{\frac{s}{2}},2^{n-s}\}$, or (3) $s\leq \frac{n}{2}$ and $\mu<2^{\frac{n}{2}}$. This result leads to the security proof of truncated $\mathsf{nEHtM}$ that returns only $s$ bits of the original tag since a truncated permutation can be seen as a pseudorandom function. In particular, when $s\leq\frac{2n}{3}$, the truncated $\mathsf{nEHtM}$ is secure up to $2^{n-\frac{s}{2}}$ MAC queries and $2^s$ verification queries as long as $\mu<\min\{2^{\frac{n}{2}},2^{n-s}\}$. For example, when $s=\frac{n}{2}$ (resp. $s=\frac{n}{4}$), the truncated $\mathsf{nEHtM}$ is secure up to $2^{\frac{3n}{4}}$ (resp. $2^{\frac{7n}{8}}$) MAC queries. So truncation might provide better provable security than the original $\mathsf{nEHtM}$ with respect to the number of MAC queries.

In this work we give several generalizations of the isotopic shift construction, introduced recently by Budaghyan et al. (2018), when the starting function is a Gold function. In particular, we derive a general construction of APN functions which covers several unclassified APN functions for $n=8$ and produces fifteen new APN functions for $n=9$.

Mixed Integer Linear Programming (MILP) is a powerful tool that helps to automate several cryptanalysis techniques for symmetric key primitives. $\textsf{Gurobi}$ is one of the most popular solvers used by researchers to obtain useful results from the MILP models corresponding to these cryptanalysis techniques. In this report, we provide a cautionary note on the use of $\textsf{Gurobi}$ in the context of bit-based division property integral attacks. In particular, we report four different examples in which $\textsf{Gurobi}$ gives contradictory results when solving the same MILP model by just changing the number of used threads or reordering some constraints.

In EUROCRYPT '96, Aiello and Venkatesan proposed two candidates for $ 2n $-bit to $ 2n $-bit pseudorandom functions (PRFs), called Benes and modified Benes (or mBenes), based on $ n $-bit to $ n $-bit PRFs. While Benes is known to be secure up to $ 2^n $ queries (Patarin, AFRICACRYPT '08), the security of mBenes has only been proved up to $ 2^{n(1-\epsilon)} $ queries for all $ \epsilon > 0 $ by Patarin and Montreuil in ICISC '05. In this work, we show that the composition of a $ 2n $-bit hash function with mBenes is a secure variable input length (VIL) PRF up to $ 2^{n-2} $ queries (given appropriate hash function bounds). We extend our analysis with block ciphers as the underlying primitive and obtain two optimally secure VIL PRFs using block ciphers. The first of these candidates requires $ 6 $ calls to the block cipher. The second candidate requires just $ 4 $ calls to the block cipher, but here the proof is based on Patarin's mirror theory. Further, we instantiate the hash function with a PMAC+/LightMAC+ like hash, to get six candidates for deterministic message authentication codes with optimal security.

We present the first deep learning-based side-channel attack on AES-128 using far field electromagnetic emissions as a side channel. Our neural networks are trained on traces captured from five different Bluetooth devices at five different distances to target and tested on four other Bluetooth devices. We can recover the key from less than 10K traces captured in an office environment at 15 m distance to target even if the measurement for each encryption is taken only once. Previous template attacks required multiple repetitions of the same encryption. For the case of 1K repetitions, we need less than 400 traces on average at 15 m distance to target. This improves the template attack presented at CHES'2020 which requires 5K traces and key enumeration up to $2^{23}$.

This article gives a rigorous mathematical treatment of generalized and closed loop invariants (CLI) which extend the standard notion of (nonlinear) invariants used in the cryptanalysis of block ciphers. Employing the cycle structure of bijective S-box components, we precisely characterize the cardinality of both generalized and CLIs. We demonstrate that for many S-boxes used in practice quadratic invariants (especially useful for mounting practical attacks in cases when the linear layer is an orthogonal matrix) might not exist, whereas there are many quadratic invariants of generalized type (alternatively quadratic CLIs). In particular, it is shown that the inverse mapping $S(x)=x^{-1}$ over $GF(2^4)$ admits quadratic CLIs that additionally possess linear structures. The use of cycle structure is further refined through a novel concept of active cycle set, which turns out to be useful for defining invariants of the whole substitution layer. We present an algorithm for finding such invariants provided the knowledge about the cycle structure of the constituent S-boxes used.

In 2017, Ward Beullenset al.submitted Lifted Unbalanced Oil andVinegar, which is a modification to the Unbalanced Oil and Vinegar Schemeby Patarin. Previously, Dinget al.proposed the Subfield Differential Attack which prompted a change of parameters by the authors of LUOV for the sec-ond round of the NIST post quantum standardization competition. In this paper we propose a modification to the Subfield Differential Attack called the Nested Subset Differential Attack which fully breaks half of the pa-rameter sets put forward. We also show by experimentation that this attack ispractically possible to do in under 210 minutes for the level I security param-eters and not just a theoretical attack. The Nested Subset Differential attack isa large improvement of the Subfield differential attack which can be used inreal world circumstances. Moreover, we will only use what is called the "lifted"structure of LUOV, and our attack can be thought as a development of solving"lifted" quadratic systems.

In CRYPTO 2015, Cogliati et al. have proposed one-round tweakable Even-Mansour (\textsf{1-TEM}) cipher constructed out of a single $n$-bit public permutation $\pi$ and a uniform and almost XOR-universal hash function \textsf{H} as $(k, t, x) \mapsto \textsf{H}_k(t) \oplus \pi(\textsf{H}_k(t) \oplus x)$, where $t$ is the tweak, and $x$ is the $n$-bit message. Authors have shown that its two-round extension, which we refer to as \textsf{2-TEM}, obtained by cascading $2$-independent instances of the construction gives $2n/3$-bit security and $r$-round cascading gives $rn/r+2$-bit security. In ASIACRYPT 2015, Cogliati and Seurin have shown that four-round tweakable Even-Mansour cipher, which we refer to as \textsf{4-TEM}, constructed out of four independent $n$-bit permutations $\pi_1, \pi_2, \pi_3, \pi_4$ and two independent $n$-bit keys $k_1, k_2$, defined as $$k_1 \oplus t \oplus \pi_4(k_2 \oplus t \oplus \pi_3(k_1 \oplus t \oplus \pi_2(k_2 \oplus t \oplus \pi_1(k_1 \oplus t \oplus x)))),$$ is secure upto $2^{2n/3}$ adversarial queries. In this paper, we have shown that if we replace two independent permutations of \textsf{2-TEM} (Cogliati et al., CRYPTO 2015) with a single $n$-bit public permutation, then the resultant construction still guarrantees security upto $2^{2n/3}$ adversarial queries. Using the results derived therein, we also show that replacing the permutation $(\pi_4, \pi_3)$ with $(\pi_1, \pi_2)$ in the above equation preserves security upto $2^{2n/3}$ adversarial queries.

In the modified CTR (CounTeR) mode known as CTR2, nonces are encrypted before constructing sequences of counters from them. This way we have only probabilistic guarantees for non-overlapping of the sequences. We show that these guarantees, and therefore the security guarantees of CTR2, are strong enough in two standard scenarios: random nonces and non-repeating nonces. We also show how to extend CTR2 to an authenticated encryption mode which we call CHE (Counter-Hash-Encrypt). To extend, we use one invocation of polynomial hashing and one additional block encryption.

Chameleon-hashes are collision-resistant hash-functions parametrized by a public key. If the corresponding secret key is known, arbitrary collisions for the hash can be found. Recently, Derler et al. (PKC '20) introduced the notion of fully collision-resistant chameleon-hashes. Full collision-resistance requires the intractability of finding collisions, even with full-adaptive access to a collision-finding oracle. Their construction combines simulation-sound extractable (SSE) NIZKs with perfectly correct IND-CPA secure public-key encryption (PKE) schemes. We show that, instead of perfectly correct PKE, non-interactive commitment schemes are sufficient. For the first time, this gives rise to efficient instantiations from plausible post-quantum assumptions and thus candidates of chameleon-hashes with strong collision-resistance guarantees and long-term security guarantees. On the more theoretical side, our results relax the requirement to not being dependent on public-key encryption.

Fresh rekeying is a well-established method to protect a primitive or mode against side-channel attacks: an easy to protect but cryptographically not so involved function generates a subkey from the master key, and this subkey is then used for the block encryption of a single or a few messages. It is an efficient way to achieve side-channel protection, but current solutions only achieve birthday bound security in the block size of the cipher and thus halve its security (except if more involved primitives are employed). We present generalized solutions to parallel block cipher rekeying that, for the first time, achieve security beyond the birthday bound in the block size $n$. The first solution involves, next to the subkey generation, one multiplication and the core block cipher call and achieves $2^{2n/3}$ security. The second solution makes two block cipher calls, and achieves optimal $2^n$ security. Our third solution uses a slightly larger subkey generation function but requires no adaptations to the core encryption and also achieves optimal security. The construction seamlessly generalizes to permutation based fresh rekeying. Central to our schemes is the observation that fresh rekeying and generic tweakable block cipher design are two very related topics, and we can take lessons from the advanced results in the latter to improve our understanding and development of the former. We subsequently use these rekeying schemes in a constructive manner to deliver three authenticated encryption modes that achieve beyond birthday bound security and are easy to protect against side-channel attacks.

In this paper we present an analysis of the SpoC cipher, a second round candidate of the NIST Lightweight Crypto Standardization process. First we present a differential analysis on the sLiSCP-light permutation, a core element of SpoC. Then we propose a series of attacks on both versions of SpoC, namely round-reduced differential tag forgery and message recovery attacks, as well as a time-memory trade-off key-recovery attack on the full round version of Spoc-64. Finally, we present an observation regarding the constants used in the sLiSCP-light permutation. To the best of our knowledge, this paper represents the first third-party analysis on both SpoC cipher and the sLiSCP-light permutation.

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-MMO, AES-MP, and the first classical collision attacks on 4- and 5-round Grostl-512. Interestingly, the use of non-full-active super S-box differentials in the analysis of AES-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 AES-MMO and AES-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.

Only the method to estimate the upper bound of the algebraic degree on block ciphers is known so far, but it is not useful for the designer to guarantee the security. In this paper we provide meaningful lower bounds on the algebraic degree of modern block ciphers.

We show that the underlying permutation of ChaCha20 stream cipher does not behave as a random permutation for up to 17 rounds with respect to rotational cryptanalysis. In particular, we derive a lower and an upper bound for the rotational probability through ChaCha quarter round, we show how to extend the bound to a full round and then to the full permutation. The obtained bounds show that the probability to find what we call a parallel rotational collision is, for example, less than $2^{-488}$ for 17 rounds of ChaCha permutation, while for a random permutation of the same input size, this probability is $2^{-511}$. We remark that our distinguisher is not an attack to ChaCha20 stream cipher, but rather a theoretical analysis of its internal permutation from the point of view of rotational cryptanalysis.

Since it was proposed in 2015 as a generalization of integral properties, the division property has evolved into a powerful tool for probing the structures of Boolean functions whose algebraic normal forms are not available. We capture the most essential elements for the detection of division properties from a pure algebraic perspective, proposing a technique named as monomial prediction, which can be employed to determine the presence or absence of a monomial in any product of the coordinate functions of a vectorial Boolean function $\boldsymbol f$ by counting the number of the so-called monomial trails across a sequence of simpler functions whose composition is $\boldsymbol f$. Under the framework of the monomial prediction, we formally prove that most algorithms for detecting division properties in literature raise no false alarms but may miss. We also establish the equivalence between the monomial prediction and the three-subset bit-based division property without unknown subset presented at EUROCRYPT 2020, and show that these two techniques are perfectly accurate. The monomial prediction technique can be regarded as a purification of the definitions of the division properties without resorting to external multisets. This algebraic formulation gives more insights into division properties and inspires new search strategies. With the monomial prediction, we obtain the exact algebraic degrees of TRIVIUM up to 834 rounds for the first time. In the context of cube attacks, we are able to explore a larger search space in limited time and recover the exact algebraic normal forms of complex superpolies with the help of a divide-and-conquer strategy. As a result, we identify more cubes with smaller dimensions, leading to improvements of some near-optimal attacks against 840-, 841- and 842-round TRIVIUM.

We provide a novel electro-magnetic (EM) side-channel resistant symmetric-key authentication mechanism for small devices that uses a Benes network to permute the on-board authentication-key before computing a MAC of a challenge with the key. The permutation itself is derived from the challenge using a hash function acting as a random oracle. The solution has interesting applications such as forgery detection of currency bills.

This paper presents the first third-party security analysis of \tinyjambu, which is one of 32 second-round candidates in NIST's lightweight cryptography standardization process. TinyJAMBU adopts an NLFSR based keyed-permutation that computes only a single NAND gate as a non-linear component per round. The designers evaluated the minimum number of active AND gates, however such a counting method neglects the dependency between multiple AND gates. There also exist previous works considering such dependencies with stricter models, however those are known to be too slow. In this paper, we present a new model that provides a good balance of efficiency and accuracy by only taking into account the first-order correlation of AND gates that frequently occurs in TinyJAMBU. With the refined model, we show a 338-round differential with probability $2^{-62.68}$ that leads to a forgery attack breaking 64-bit security. This implies that the security margin of TinyJAMBU with respect to the number of unattacked rounds is approximately 12%. We also show a differential on full 384 rounds with probability $2^{-70.64}$, thus the security margin of full rounds with respect to the data complexity, namely the gap between the claimed security bits and the attack complexity, is less than 8 bits. Our attacks also point out structural weaknesses of the mode that essentially come from the minimal state size to be lightweight.

This note describes several attacks on the MALICIOUS framework for creating backdoored tweakable block ciphers. It is shown that, although the embedded malicious tweak pair itself is hard to recover, it is feasible to find additional weak tweak pairs that can be used to mount key-recovery attacks. Full-round attacks on most instances of LowMC-M are given. Our attacks are far from optimized and significant future improvements are to be expected. We focus on low-data attacks, since these are the most relevant for typical use-cases of LowMC. In addition, this implies that our attacks can not be prevented by limiting the amount of data that can be encrypted using the weak tweak pair. Despite our findings, we believe that the MALICIOUS framework can be used to create backdoored variants of LowMC provided that the parameters are modified.

We analyze the multi-user security of the streaming encryption in Google's Tink library via an extended version of the framework of nonce-based online authenticated encryption of Hoang et al. (CRYPTO'15) to support random-access decryption. We show that Tink's design choice of using random nonces and a nonce-based key-derivation function indeed improves the concrete security bound. We then give two better alternatives that are more robust against randomness failure. In addition, we show how to efficiently instantiate the key-derivation function via AES, instead of relying on HMAC-SHA256 like the current design in Tink. To accomplish this we give a multi-user analysis of the XOR-of-permutation construction of Bellare, Krovetz, and Rogaway (EUROCRYPT'98).

We study the security of CTR-DRBG, one of NIST's recommended Pseudorandom Number Generator (PRNG) designs. Recently, Woodage and Shumow (Eurocrypt' 19), and then Cohney et al. (S&P' 20) point out some potential vulnerabilities in both NIST specification and common implementations of CTR-DRBG. While these researchers do suggest counter-measures, the security of the patched CTR-DRBG is still questionable. Our work fills this gap, proving that CTR-DRBG satisfies the robustness notion of Dodis et al. (CCS'13), the standard security goal for PRNGs.

S-boxes are the only source of non-linearity in many symmetric primitives. While they are often defined as being functions operating on a small space, some recent designs propose the use of much larger ones (e.g., 32 bits). In this context, an S-box is then defined as a subfunction whose cryptographic properties can be estimated precisely. We present a 64-bit ARX-based S-box called Alzette, which can be evaluated in constant time using only 12 instructions on modern CPUs. Its parallel application can also leverage vector (SIMD) instructions. One iteration of Alzette has differential and linear properties comparable to those of the AES S-box, and two are at least as secure as the AES super S-box. As the state size is much larger than the typical 4 or 8 bits, the study of the relevant cryptographic properties of Alzette is not trivial. We further discuss how such wide S-boxes could be used to construct round functions of 64-, 128- and 256-bit (tweakable) block ciphers with good cryptographic properties that are guaranteed even in the related-tweak setting. We use these structures to design a very lightweight 64-bit block cipher (CRAX) which outperforms SPECK-64/128 for short messages on micro-controllers, and a 256-bit tweakable block cipher (TRAX) which can be used to obtain strong security guarantees against powerful adversaries (nonce misuse, quantum attacks).

Symmetric Searchable Encryption (SSE) is an encryption technique that allows users to search directly on their outsourced encrypted data while preserving the privacy of both the files and the queries. Unfortunately, majority of the SSE schemes allows users to either decrypt the whole ciphertext or nothing at all. In this paper, we propose a novel scheme based on traditional symmetric primitives, that allows data owners to bind parts of their ciphertexts with specific policies. Inspired by the concept of Attribute-Based Encryption (ABE) in the public setting, we design a scheme through which users can recover only certain parts of an encrypted document if and only if they retain a set of attributes that satisfy a policy. Our construction satisfies the important notion of forward privacy while at the same time supports the multi-client model by leveraging SGX functionality for the synchronization of users. To prove the correctness of our approach, we provide a detailed simulation-based security analysis coupled with an extensive experimental evaluation that shows the effectiveness of our scheme.

We report the successful recovery of the key to a Zip archive containing only two encrypted files. The attack improves on our 2001 ciphertext-only attack, which required five encrypted files. The main innovations are a new differential meet-in-the-middle attack for the initial stages and the use of lattice reduction to recover the internal state of the truncated linear congruential generator.

While many similarities between Machine Learning and cryptanalysis tasks exists, so far no major result in cryptanalysis has been reached with the aid of Machine Learning techniques. One exception is the recent work of Gohr, presented at Crypto 2019, where for the first time, conventional cryptanalysis was combined with the use of neural networks to build a more efficient distinguisher and, consequently, a key recovery attack on Speck32/64. On the same line, in this work we propose two Deep Learning (DL) based distinguishers against the Tiny Encryption Algorithm (TEA) and its evolution RAIDEN. Both ciphers have twice block and key size compared to Speck32/64. We show how these two distinguishers outperform a conventional statistical distinguisher, with no prior information on the cipher, and a differential distinguisher based on the differential trails presented by Biryukov and Velichkov at FSE 2014. We also present some variations of the DL-based distinguishers, discuss some of their extra features, and propose some directions for future research.

Differential cryptanalysis of block ciphers requires the identification of differential characteristics with high probability. For block ciphers with large block sizes and number of rounds, identifying these characteristics is computationally intensive. The branch-and-bound algorithm was proposed by Matsui to automate this task. Since then, numerous improvements were made to the branch-and-bound algorithm by bounding the number of active s-boxes, incorporating a meet-in-the-middle approach, and adapting it to various block cipher architectures. Although mixed-integer linear programming (MILP) has been widely used to evaluate the differential resistance of block ciphers, MILP is still inefficient for clustering singular differential characteristics to obtain differentials (also known as the differential effect). The branch-and-bound method is still better suited for the task of trail clustering. However, it requires enhancements before being feasible for block ciphers with large block sizes, especially for a large number of rounds. Motivated by the need for a more efficient branch-and-bound algorithm to search for block cipher differentials, we propose a GPU-accelerated branch-and-bound algorithm. The proposed approach substantially increases the performance of the differential cluster search. We were able to derive a branch enumeration and evaluation kernel that is 5.95 times faster than its CPU counterpart. To showcase its practicality, the proposed algorithm is applied on TRIFLE-BC, a 128-bit block cipher. By incorporating a meet-in-the-middle approach with the proposed GPU kernel, we were able to improve the search efficiency (on 20 rounds of TRIFLE-BC) by approximately 58 times as compared to the CPU-based approach. Differentials consisting of up to 50 million individual characteristics can be constructed for 20 rounds of TRIFLE, leading to slight improvements to the overall differential probabilities. Even for larger rounds (43 rounds), the proposed algorithm is still able to construct large clusters of over 500 thousand characteristics. This result depicts the practicality of the proposed algorithm in constructing large differentials even for a 128-bit block cipher, which could be used to improve cryptanalytic findings against other block ciphers in the future.

We study anonymity of probabilistic encryption (pE) and probabilistic authenticated encryption (pAE). We start by providing concise game-based security definitions capturing anonymity for both pE and pAE, and then show that the commonly used notion of indistinguishability from random ciphertexts (IND\($\)) indeed implies the anonymity notions for both pE and pAE. This is in contrast to a recent work of Chan and Rogaway (Asiacrypt 2019), where it is shown that IND\($\)-secure nonce-based authenticated encryption can only achieve anonymity if a sophisticated transformation is applied. Moreover, we also show that the Encrypt-then-MAC paradigm is anonymity-preserving, in the sense that if both the underlying probabilistic MAC (pMAC) and pE schemes are anonymous, then also the resulting pAE scheme is. Finally, we provide a composable treatment of anonymity using the constructive cryptography framework of Maurer and Renner (ICS 2011). We introduce adequate abstractions modeling various kinds of anonymous communication channels for many senders and one receiver in the presence of an active man-in-the-middle adversary. Then we show that the game-based notions indeed are anonymity-preserving, in the sense that they imply constructions between such anonymous channels, thus generating authenticity and/or confidentiality as expected, but crucially retaining anonymity if present.

A report on the selection process of the STARK friendly hash (SFH) function for standardization by the Ethereum Foundation. The outcome of this process, described here, is our recommendation to use the Rescue function over a prime field of size approximately $ 2^{61}$ in sponge mode with $12$ field elements per state. With an Appendix by Jean-Charles Faugere and Ludovic Perret of CryptoNext Security.

This epos tells the origin story of Rescue, a family of cryptographic algorithms in the Marvellous cryptoverse.

The SHA-1 hash function was designed in 1995 and has been widely used during two decades. A theoretical collision attack was first proposed in 2004 [WYY05], but due to its high complexity it was only implemented in practice in 2017, using a large GPU cluster [SBK+17]. More recently, an almost practical chosen-prefix collision attack against SHA-1 has been proposed [LP19]. This more powerful attack allows to build colliding messages with two arbitrary prefixes, which is much more threatening for real protocols. In this paper, we report the first practical implementation of this attack, and its impact on real-world security with a PGP/GnuPG impersonation attack. We managed to significantly reduce the complexity of collisions attack against SHA-1: on an Nvidia GTX 970, identical-prefix collisions can now be computed with a complexity of $2^{61.2}$ rather than $2^{64.7}$, and chosen-prefix collisions with a complexity of $2^{63.4}$ rather than $2^{67.1}$. When renting cheap GPUs, this translates to a cost of 11k US\$ for a collision, and 45k US\$ for a chosen-prefix collision, within the means of academic researchers. Our actual attack required two months of computations using 900 Nvidia GTX 1060 GPUs (we paid 75k US\$ because GPU prices were higher, and we wasted some time preparing the attack). Therefore, the same attacks that have been practical on MD5 since 2009 are now practical on SHA-1. In particular, chosen-prefix collisions can break signature schemes and handshake security in secure channel protocols (TLS, SSH). We strongly advise to remove SHA-1 from those type of applications as soon as possible. We exemplify our cryptanalysis by creating a pair of PGP/GnuPG keys with different identities, but colliding SHA-1 certificates. A SHA-1 certification of the first key can therefore be transferred to the second key, leading to a forgery. This proves that SHA-1 signatures now offers virtually no security in practice. The legacy branch of GnuPG still uses SHA-1 by default for identity certifications, but after notifying the authors, the modern branch now rejects SHA-1 signatures (the issue is tracked as CVE-2019-14855).

The Luby-Rackoff construction, or the Feistel construction, is one of the most important approaches to construct secure block ciphers from secure pseudorandom functions. The 3-round and 4-round Luby-Rackoff constructions are proven to be secure against chosen-plaintext attacks (CPAs) and chosen-ciphertext attacks (CCAs), respectively, in the classical setting. However, Kuwakado and Morii showed that a quantum superposed chosen-plaintext attack (qCPA) can distinguish the 3-round Luby-Rackoff construction from a random permutation in polynomial time. In addition, Ito et al. showed a quantum superposed chosen-ciphertext attack (qCCA) that distinguishes the 4-round Luby-Rackoff construction. Since Kuwakado and Morii showed the result, a problem of much interest has been how many rounds are sufficient to achieve provable security against quantum query attacks. This paper answers this fundamental question by showing that 4-rounds suffice against qCPAs. Concretely, we prove that the 4-round Luby-Rackoff construction is secure up to $O(2^{n/6})$ quantum queries. We also prove that the bound is tight by showing an attack that distinguishes the 4-round Luby-Rackoff construction from a random permutation with $O(2^{n/6})$ quantum queries. Our result is the first to demonstrate the tight security of a typical block-cipher construction against quantum query attacks, without any algebraic assumptions. To give security proofs, we use an alternative formalization of Zhandry's compressed oracle technique.

An adversary with $S$ bits of memory obtains a stream of $Q$ elements that are uniformly drawn from the set $\{1,2,\ldots,N\}$, either with or without replacement. This corresponds to sampling $Q$ elements using either a random function or a random permutation. The adversary's goal is to distinguish between these two cases. This problem was first considered by Jaeger and Tessaro (EUROCRYPT 2019), which proved that the adversary's advantage is upper bounded by $\sqrt{Q \cdot S/N}$. Jaeger and Tessaro used this bound as a streaming switching lemma which allowed proving that known time-memory tradeoff attacks on several modes of operation (such as counter-mode) are optimal up to a factor of $O(\log N)$ if $Q \cdot S \approx N$. However, the bound's proof assumed an unproven combinatorial conjecture. Moreover, if $Q \cdot S \ll N$ there is a gap between the upper bound of $\sqrt{Q \cdot S/N}$ and the $Q \cdot S/N$ advantage obtained by known attacks. In this paper, we prove a tight upper bound (up to poly-logarithmic factors) of $O(\log Q \cdot Q \cdot S/N)$ on the adversary's advantage in the streaming distinguishing problem. The proof does not require a conjecture and is based on a hybrid argument that gives rise to a reduction from the unique-disjointness communication complexity problem to streaming.

We consider a collision search problem (CSP), where given a parameter $C$, the goal is to find $C$ collision pairs in a random function $f:[N] \rightarrow [N]$ (where $[N] = \{0,1,\ldots,N-1\})$ using $S$ bits of memory. Algorithms for CSP have numerous cryptanalytic applications such as space-efficient attacks on double and triple encryption. The best known algorithm for CSP is parallel collision search (PCS) published by van Oorschot and Wiener, which achieves the time-space tradeoff $T^2 \cdot S = \tilde{O}(C^2 \cdot N)$ for $S = \tilde{O}(C)$. In this paper, we prove that any algorithm for CSP satisfies $T^2 \cdot S = \tilde{\Omega}(C^2 \cdot N)$ for $S = \tilde{O}(C)$, hence the best known time-space tradeoff is optimal (up to poly-logarithmic factors in $N$). On the other hand, we give strong evidence that proving similar unconditional time-space tradeoff lower bounds on CSP applications (such as breaking double and triple encryption) may be very difficult, and would imply a breakthrough in complexity theory. Hence, we propose a new restricted model of computation and prove that under this model, the best known time-space tradeoff attack on double encryption is optimal.

In this work we study the leakage resilience of authenticated encryption schemes. We show that, if one settles for non-adaptive leakage, leakage-resilient authenticated encryption schemes can be built solely from leakage-resilient pseudorandom functions. Degabriele et al. (ASIACRYPT 2019) introduce the FGHF' construction which allows to build leakage-resilient authenticated encryption schemes from functions which, under leakage, retain both pseudorandomness and unpredictability. We revisit their construction and show the following. First, pseudorandomness and unpredictability do not imply one another in the leakage setting. Unfortunately, this entails that any instantiation of the FGHF' construction indeed seems to require a function that is proven both pseudorandom and unpredictable under leakage. Second, however, we show that the unpredictability requirement is an artefact that stems from the underlying composition theorem of the N2 construction given by Barwell et al. (ASIACRYPT 2017). By recasting this composition theorem, we show that the unpredictability requirement is unnecessary for the FGHF' construction. Thus, leakage-resilient AEAD schemes can be obtained by instantiating the FGHF' construction with functions that are solely pseudorandom under leakage.

Keyed and unkeyed cryptographic permutations often iterate simple round functions. Substitution-permutation networks (SPNs) are an approach that is popular since the mid 1990s. One of the new directions in the design of these round functions is to reduce the substitution (S-Box) layer from a full one to a partial one, uniformly distributed over all the rounds. LowMC and Zorro are examples of this approach. A relevant freedom in the design space is to allow for a highly non-uniform distribution of S-Boxes. However, choosing rounds that are so different from each other is very rarely done, as it makes security analysis and implementation much harder. We develop the design strategy Hades and an analysis framework for it, which despite this increased complexity allows for security arguments against many classes of attacks, similar to earlier simpler SPNs. The framework builds upon the wide trail design strategy, and it additionally allows for security arguments against algebraic attacks, which are much more of a concern when algebraically simple S-Boxes are used. Subsequently, this is put into practice by concrete instances and benchmarks for a use case that generally benefits from a smaller number of S-Boxes and showcases the diversity of design options we support: A candidate cipher natively working with objects in GF(p), for securing data transfers with distributed databases using secure multiparty computation (MPC). Compared to the currently fastest design MiMC, we observe significant improvements in online bandwidth requirements and throughput with a simultaneous reduction of preprocessing effort, while having a comparable online latency.

Recent years have seen a major involvement of deep learning architecture in the cryptanalysis of various lightweight ciphers. The present study is inspired by the work of Gohr and Baksi et al. in the field to develop a deep neural network-based differential distinguisher for round reduced PRESENT lightweight block cipher. We present a multi-layer perceptron network which can distinguish between 3-6 rounds of PRESENT cipher data and a randomly generated data with a significantly high probability. We also discuss the possible improvements in the original approach of the differential distinguisher presented by Baksi et al.

PudgyTurtle is a way to use keystream to encode plaintext before XOR-based (stream cipher-like) encryption. It makes stream ciphers less efficient -- a typical implementation requiring about five times as much keystream and producing about twice as much ciphertext -- but also more robust against time-memory-data tradeoff attacks. PudgyTurtle can operate alongside any keystream generator, and thus functions somewhat like an encryption mode for stream ciphers. Here, we introduce the mechanics or PudgyTurtle and discuss its design motivations.

In this article, we propose two new families of very lightweight and efficient authenticated encryption with associated data (AEAD) modes, Romulus and Remus, that provide security beyond the birthday bound with respect to the block-length $n$. The former uses a tweakable block cipher (TBC) as internal primitive and can be proven secure in the standard model. The later uses a block cipher (BC) as internal primitive and can be proven secure in the ideal cipher model. Both our modes allow to switch very easily from nonce-respecting to nonce-misuse scenario. Previous constructions, such as ThetaCB, are quite computationally efficient, yet needing a large memory for implementation, which makes them unsuitable for platforms where lightweight cryptography should play a key role. Romulus and Remus break this barrier by introducing a new architecture evolved from a BC mode COFB. They achieve the best of what can be possible with TBC -- the optimal computational efficiency (rate-1 operation) and the minimum state size of a TBC mode (i.e., $(n+t)$-bit for $n$-bit block, $t$-bit tweak TBC), with almost equivalent provable security as ThetaCB. Actually, our comparisons show that both our designs present superior performances when compared to all other recent lightweight AEAD modes, being BC-based, TBC-based or sponge-based, in the nonce-respecting or nonce-misuse scenario. We eventually describe how to instantiate Romulus and Remus modes using the Skinny lightweight tweakable block cipher proposed at CRYPTO 2016, including the hardware implementation results.

Cryptographic primitives have been designed to be secure against mathematical attacks in a black-box model. Such primitives can be implemented in a way that they are also secure against physical attacks, in a grey-box model. One of the most popular techniques for this purpose is masking. The increased security always comes with a high price tag in terms of implementation cost. In this work, we look at how the traditional design principles of symmetric primitives can be at odds with the optimization of the implementations and how they can evolve to be more suitable for embedded systems. In particular, we take a comparative look at the round 2 candidates of the NIST lightweight competition and their implementation properties in the world of masking.

Terakey is an encryption system whose confidentiality can be demonstrated from first principles, without making assumptions about the computational difficulty of certain mathematical problems. It employs a key that is much larger than the anticipated volume of message traffic. It is based on the one-time pad, but addresses the risk of key reuse stochastically. Conventional cryptographic techniques can be used to ameliorate infrequent byte collisions. The large size of the key reduces the risk of key exfiltration and facilitates physical security measures to maintain a secure chain of control for the key. Terakey also serves as a potential alternative for comparison with quantum key distribution technology, arguably providing equivalent security with fewer complications.

Bitstream reverse engineering is traditionally associated with Intellectual Property (IP) theft. Another, less known, threat deriving from that is bitstream modification attacks. It has been shown that the secret key can be extracted from FPGA implementations of cryptographic algorithms by injecting faults directly into the bitstream. Such bitstream modification attacks rely on changing the content of Look Up Tables (LUTs). Therefore, related countermeasures aim to make the task of identifying a LUT more difficult (e.g. by masking its content). However, recent advances in FPGA reverse engineering revealed information on how interconnects are encoded in the bitstream of Xilinx 7 series FPGAs. In this paper, we show that this knowledge can be used to break or weaken existing countermeasures, as well as improve existing attacks. Furthermore, a straightforward attack that re-routes the key to an output pin becomes possible. We demonstrate our claims on an FPGA implementation of SNOW 3G stream cipher. The presented results show that there is an urgent need for stronger bitstream protection methods.

In this report, we cryptanalyse the Rescue hash function. In particular, we look at linear and differential cryptanalysis of Rescue, how multiplicative subgroups are propagated by the round function and at rebound attacks. Overall, we do not find any direct threat to the security of Rescue.

Since Keccak was selected as the SHA-3 standard, both its hash mode and keyed mode have attracted lots of third-party cryptanalysis. Especially in recent years, there is progress in analyzing the collision resistance and preimage resistance of round-reduced Keccak. However, for the preimage attacks on round-reduced Keccak-384/512, we found that the linear relations leaked by the hash value are not well exploited when utilizing the current linear structures. To make full use of the $320+64\times2=448$ and 320 linear relations leaked by the hash value of Keccak-512 and Keccak-384, respectively, we propose a dedicated algebraic attack by expressing the output as a quadratic Boolean equation system in terms of the input. Such a quadratic Boolean equation system can be efficiently solved with linearization techniques. Consequently, we successfully improved the preimage attacks on 2/3/4 rounds of Keccak-384 and 2/3 rounds of Keccak-512. Since similar $\theta$ and $\chi$ operations exist in the round function of Xoodoo, we make a study of the permutation and construct a practical zero-sum distinguisher for 12-round Xoodoo. Although 12-round Xoodoo is the underlying permutation used in Xoodyak, which has been selected by NIST for the second round in the Lightweight Cryptography Standardization process, such a distinguisher will not lead to an attack on Xoodyak.

Recently, in Asiacrypt 2019, Bonnetain et. al have shown attacks by quantum adversaries on FX construction and Even-Mansour Cipher without using superposition queries to the encryption oracle. In this work, we use a similar approach to mount new attacks on HCTR and HCH construction. In addition, we mount attacks on HCTR, Tweakable-HCTR and HCH using the superposition queries to the encryption oracle using strategies proposed by Leander and May in Asiacrypt 2017 and Kaplan et. al in Crypto 2016.

This paper initiates the study of the provable security of authenticated encryption (AE) in the memory-bounded setting. Recent works – Tessaro and Thiruvengadam (TCC '18), Jaeger and Tessaro (EUROCRYPT '19), and Dinur (EUROCRYPT '20) – focus on confidentiality, and look at schemes for which trade-offs between the attacker's memory and its data complexity are inherent. Here, we ask whether these results and techniques can be lifted to the full AE setting, which additionally asks for integrity. We show both positive and negative results. On the positive side, we provide tight memory-sensitive bounds for the security of GCM and its generalization, CAU (Bellare and Tackmann, CRYPTO '16). Our bounds apply to a restricted case of AE security which abstracts the deployment within protocols like TLS, and rely on a new memory-tight reduction to corresponding restricted notions of confidentiality and integrity. In particular, our reduction uses an amount of memory which linearly depends on that of the given adversary, as opposed to only imposing a constant memory overhead as in earlier works (Auerbach et al., CRYPTO '17). On the negative side, we show that a large class of black-box reductions cannot generically lift confidentiality and integrity security to a joint definition of AE security in a memory-tight way.

The side-channel community recently investigated a new approach, based on deep learning, to significantly improve profiled attacks against embedded systems. Previous works have shown the benefit of using convolutional neural networks (CNN) to limit the effect of some countermeasures such as desynchronization. Compared with template attacks, deep learning techniques can deal with trace misalignment and the high dimensionality of the data. Pre-processing is no longer mandatory. However, the performance of attacks depends to a great extent on the choice of each hyperparameter used to configure a CNN architecture. Hence, we cannot perfectly harness the potential of deep neural networks without a clear understanding of the network’s inner-workings. To reduce this gap, we propose to clearly explain the role of each hyperparameters during the feature selection phase using some specific visualization techniques including Weight Visualization, Gradient Visualization and Heatmaps. By highlighting which features are retained by filters, heatmaps come in handy when a security evaluator tries to interpret and understand the efficiency of CNN. We propose a methodology for building efficient CNN architectures in terms of attack efficiency and network complexity, even in the presence of desynchronization. We evaluate our methodology using public datasets with and without desynchronization. In each case, our methodology outperforms the previous state-of-the-art CNN models while significantly reducing network complexity. Our networks are up to 25 times more efficient than previous state-of-the-art while their complexity is up to 31810 times smaller. Our results show that CNN networks do not need to be very complex to perform well in the side-channel context.

The sponge duplex is a popular mode of operation for constructing authenticated encryption schemes. In fact, one can assess the popularity of this mode from the fact that around $ 25 $ out of the $ 56 $ round 1 submissions to the ongoing NIST lightweight cryptography (LwC) standardization process are based on this mode. Among these, $14$ sponge-type constructions are selected for the second round consisting of $32$ submissions. In this paper, we generalize the duplexing interface of the duplex mode, which we call Transform-then-Permute. It encompasses Beetle as well as a new sponge-type mode SpoC (both are round 2 submissions to NIST LwC). We show a tight security bound for Transform-then-Permute based on $b$-bit permutation, which reduces to finding an exact estimation of the expected number of multi-chains (defined in this paper). As a corollary of our general result, authenticated encryption advantage of Beetle and SpoC is about $\frac{T(D+r2^r)}{2^b}$ where $T$, $D$ and $r$ denotes the number of offline queries (related to time complexity of the attack), number of construction queries (related to data complexity) and rate of the construction (related to efficiency). Previously the same bound has been proved for Beetle under the limitation that $ T << min\{2^r, 2^{b/2}\} $ (that compels to choose larger permutation with higher rate). In the context of NIST LwC requirement, SpoC based on $ 192 $-bit permutation achieves the desired security with $ 64 $-bit rate, which is not achieved by either duplex or Beetle (as per the previous analysis).

We present several improvements to the framework of differential-linear attacks with a special focus on ARX ciphers. As a demonstration of their impact, we apply them to Chaskey and ChaCha and we are able to significantly improve upon the best attacks published so far.

In this article, we analyse the security of the authenticated encryption mode JAMBU, a submission to the CAESAR competition that remains currently unbroken. We show that the security claims of this candidate regarding its nonce-misuse resistance can be broken. More precisely, we explain a technique to guess in advance a ciphertext block corresponding to a plaintext that has never been queried before (nor its prefix), thus breaking the confidentiality of the scheme when the attacker can make encryption queries with the same nonce. Our attack is very practical as it requires only about 2^{32} encryption queries and computations (instead of the 2^{128} claimed by the designers). Our cryptanalysis has been fully implemented in order to verify our findings. Moreover, due to the small tag length of JAMBU, we show how this attack can be extended in the nonce-respecting scenario to break confidentiality in the adaptative chosen-ciphertext model (IND-CCA2) with 2^{96} computations, with message prefixes not previously queried.

The use of deep learning in side-channel analysis has been more and more prominent recently. In particular, Convolution Neural Networks (CNN) are very efficient tools to extract the secret information from side-channel traces. Previous work regarding the use of CNN in side-channel has been mostly proposed through practical results. Zaid et al. have proposed a theoretical methodology in order to better understand the convolutional part of CNN and to understand how to construct an efficient CNN in the side-channel context [ZBHV19]. The proposal of Zaid et al. has been recently questioned by [WAGP20]. However this revisit is based on wrong assumptions and misinterpretations. Hence, many of the claims of [WAGP20] are unfounded regarding [ZBHV19]. In this paper, we clear out the potential misunderstandings brought by [WAGP20] and explain more thoroughly the contributions of [ZBHV19].

We provide a simple and complete proof of the famous Pi&#8853;Pj Theorem in the particular case where &#958;max=2. This Theorem gives a lower bound for the number of solutions of simple linear systems of equations in the case where all the variables have to be pairwise distinct. Such systems often occur in cryptographic proofs of security, and this particular Theorem can be used to prove that the function x&#8614;P(0||x)&#8853;P(1||x) is an optimally secure pseudorandom function when P is a uniformly random permutation.

Database management systems (DBMS) are one of cloud services with great interests in industry and business. In such services, since there is no trust in the cloud servers, the databases are encrypted prior to outsourcing. One of the most challenging issues in designing these services is supporting SQL join queries on the encrypted database. The multi-adjustable join scheme (M-Adjoin) [Khazaei-Rafiee 2019], an extension of Adjoin [Popa-Zeldovich 2012 and Mironov-Segev-Shahaf 2017], is a symmetric-key primitive that supports the join queries for a list of column labels on an encrypted database. In previous works, the following security notions were introduced for Adjoin and M-Adjoin schemes: 3Partition, M3Partition and M3P k , for every integer k . Additionally, simulation-based and indistinguishability-based security notions have been defined by Mironov et al. for Adjoin scheme. In this paper, we extend their results to M-Adjoin and study the relations between all security notions for M-Adjoin. Some non-trivial relations are proved which resolve some open problems raised by [Mironov-Segev-Shahaf 2017].

PMAC is a rate-1, parallelizable, block-cipher-based message authentication code (MAC), proposed by Black and Rogaway (EUROCRYPT 2002). Improving the security bound is a main research topic for PMAC. In particular, showing a tight bound is the primary goal of the research, since Luykx et al.'s paper (EUROCRYPT 2016). Regarding the pseudo-random-function (PRF) security of PMAC, a collision of the hash function, or the difference between a random permutation and a random function offers the lower bound $\Omega(q^2/2^n)$ for $q$ queries and the block cipher size $n$. Regarding the MAC security (unforgeability), a hash collision for MAC queries, or guessing a tag offers the lower bound $\Omega(q_m^2/2^n + q_v/2^n)$ for $q_m$ MAC queries and $q_v$ verification queries (forgery attempts). The tight upper bound of the PRF-security $O(q^2/2^n)$ of PMAC was given by Gaž et el. (ToSC 2017, Issue 1), but their proof requires a 4-wise independent masking scheme that uses 4 $n$-bit random values. Open problems from their work are: (1) find a masking scheme with three or less random values with which PMAC has the tight upper bound for PRF-security; (2) find a masking scheme with which PMAC has the tight upper bound for MAC-security. In this paper, we consider PMAC with three powering-up masks that uses three random values for the masking scheme. We show that the PMAC has the tight upper bound $O(q^2/2^n)$ for PRF-security, which answers the open problem (1), and the tight upper bound $O(q_m^2/2^n + q_v/2^n)$ for MAC-security, which answers the open problem (2). Note that these results deal with two-key PMAC, thus showing tight upper bounds of PMACs with single-key and/or with two (or one) powering-up masks are open problems.

An increasing number of lightweight cryptographic primitives have been published recently. Some of these proposals are ARX primitives, which have shown a great performance in software. Rotational-XOR cryptanalysis is a statistical technique to attack ARX primitives. In this paper, a computer tool to speed up and make easier the security evaluation of ARX block ciphers against rotational-XOR cryptanalysis is shown. Our tool takes a Python implementation of an ARX block cipher and automatically finds an optimal rotational-XOR characteristic. Compared to most of the automated tools, which only support a small set of primitives, our tool supports any ARX block cipher and it is executed with a simple shell command.

Nowadays, the resistance against algebraic attacks and fast algebraic attacks are considered as an important cryptographic property for Boolean functions used in stream ciphers. Both attacks are very powerful analysis concepts and can be applied to symmetric cryptographic algorithms used in stream ciphers. The notion of algebraic immunity has received wide attention since it is a powerful tool to measure the resistance of a Boolean function to standard algebraic attacks. Nevertheless, an algebraic tool to handle the resistance to fast algebraic attacks is not clearly identified in the literature. In the current paper, we propose a new parameter to measure the resistance of a Boolean function to fast algebraic attack. We also introduce the notion of fast immunity profile and show that it informs both on the resistance to standard and fast algebraic attacks. Further, we evaluate our parameter for two secondary constructions of Boolean functions. Moreover, A coding-theory approach to the characterization of perfect algebraic immune functions is presented. Via this characterization, infinite families of binary linear complementary dual codes (or LCD codes for short) are obtained from perfect algebraic immune functions. The binary LCD codes presented in this paper have applications in armoring implementations against so-called side-channel attacks (SCA) and fault non-invasive attacks, in addition to their applications in communication and data storage systems.

Bit permutation based block ciphers, like PRESENT and GIFT, are well-known for their extreme lightweightness in hardware implementation. However, designing such ciphers comes with one major challenge - to ensure strong cryptographic properties simply depending on the combination of three components, namely S-box, a bit permutation and a key addition function. Having a wrong combination of components could lead to weaknesses. In this article, we studied the interaction between these components, improved the theoretical security bound of GIFT and highlighted the potential pitfalls associated with a bit permutation based primitive design. We also conducted analysis on TRIFLE, a first-round candidate for the NIST lightweight cryptography competition, where our findings influenced the elimination of TRIFLE from second-round of the NIST competition. In particular, we showed that internal state bits of TRIFLE can be partially decrypted for a few rounds even without any knowledge of the key.

Persistent fault analysis (PFA) consists in guessing block cipher secret keys by biasing their substitution box. This paper improves the original attack of Zhang et al. on AES-128 presented at CHES 2018. By a thorough analysis, the exact probability distribution of the ciphertext (under a uniformly distributed plaintext) is derived, and the maximum likelihood key recovery estimator is computed exactly. Its expression is turned into an attack algorithm, which is shown to be twice more efficient in terms of number of required encryptions than the original attack of Zhang et al. This algorithm is also optimized from a computational complexity standpoint. In addition, our optimal attack is naturally amenable to key enumeration, which expedites full 16- bytes key extraction. Various tradeoffs between data and computational complexities are investigated.

Skinny is a lightweight tweakable block cipher which received a great deal of cryptanalytic attention following its elegant structure and efficiency. Inspired by the Skinny competitions, multiple attacks on it were reported in different settings (e.g. single vs. related-tweakey) using different techniques (impossible differentials, meet-in-the-middle, etc.). In this paper we revisit some of these attacks, identify issues with several of them, and offer a series of improved attacks which were experimentally verified. Our best attack can attack up to 18 rounds using $2^{60}$ chosen ciphertexts data, $2^{116}$ time, and $2^{112}$ memory.

Spook is one of the 32 candidates that has made it to the second round of the NIST Lightweight Cryptography Standardization process, and is particularly interesting since it proposes differential side channel resistance. In this paper, we present practical distinguishers of the full 6-step version of the underlying permutations of Spook, namely Shadow-512 and Shadow-384, solving challenges proposed by the designers on the permutation. We also propose practical forgeries with 4-step Shadow for the S1P mode of operation in the nonce misuse scenario, which is allowed by the CIML2 security game considered by the authors. All the results presented in this paper have been implemented.

Leakage-resilient encryption is a powerful tool to protect data confidentiality against side channel attacks. In this work, we introduce a new and strong leakage setting to counter backdoor (or Trojan horse) plus covert channel attack, by relaxing the restrictions on leakage. We allow \emph{bounded} leakage at \emph{anytime} and \emph{anywhere} and over \emph{anything}. Our leakage threshold (e.g. 10000 bits) could be much larger than typical secret key (e.g. AES key or RSA private key) size. Under such a strong leakage setting, we propose an efficient encryption scheme which is semantic secure in standard setting (i.e. without leakage) and can tolerate strong continuous leakage. We manage to construct such a secure scheme under strong leakage setting, by hiding partial (e.g. $1\%$) ciphertext as secure as we hide the secret key using a small amount of more secure hardware resource, so that it is almost equally difficult for any adversary to steal information regarding this well-protected partial ciphertext or the secret key. We remark that, the size of such well-protected small portion of ciphertext is chosen to be much larger than the leakage threshold. We provide concrete and practical examples of such more secure hardware resource for data communication and data storage. Furthermore, we also introduce a new notion of computational entropy, as a sort of computational version of Kolmogorov complexity. Our quantitative analysis shows that, hiding partial ciphertext is a powerful countermeasure, which enables us to achieve higher security level than existing approaches in case of backdoor plus covert channel attacks. We also show the relationship between our new notion of computational entropy and existing relevant concepts, including Shannon-Entropy, Yao-Entropy, Hill-Entropy, All-or-Nothing Transform, and Exposure Resilient Function. This new computation entropy formulation may have independent interests.

Side-channel analysis has seen rapid adoption of deep learning techniques over the past years. While many paper focus on designing efficient architectures, some works have proposed techniques to boost the efficiency of existing architectures. These include methods like data augmentation, oversampling, regularization etc. In this paper, we compare data augmentation and oversampling (particularly SMOTE and its variants) on public traces of two side-channel protected AES. The techniques are compared in both balanced and imbalanced classes setting, and we show that adopting SMOTE variants can boost the attack efficiency in general. Further, we report a successful key recovery on ASCAD(desync=100) with 180 traces, a 50% improvement over current state of the art.