At FSE 2017, Gaži et al. demonstrated a pseudorandom function (PRF) distinguisher (Gaži et al., ToSC 2016(2)) on PMAC with $ \Omega(\ell q^2/2^n) $ advantage, where $ q $, $ \ell $, and $ n $, denote the number of queries, maximum permissible query length (in terms of $ n $-bit blocks), and block size of the underlying block cipher. This, in combination with the upper bounds of $ O(\ell q^2/2^n) $ (Minematsu and Matsushima, FSE 2007) and $ O(q\sigma/2^n) $ (Nandi and Mandal, J. Mathematical Cryptology 2008(2)), resolved the long-standing problem of exact security of PMAC. Gaži et al. also showed that the dependency on $ \ell $ can be dropped (i.e. $ O(q^2/2^n) $ bound up to $ \ell \leq 2^{n/2} $) for a simplified version of PMAC, called sPMAC, by replacing the Gray code-based masking in PMAC with any $ 4 $-wise independent universal hash-based masking. Recently, Naito proposed another variant of PMAC with two powering-up maskings (Naito, ToSC 2019(2)) that achieves $ \ell $-free bound of $ O(q^2/2^n) $, provided $ \ell \leq 2^{n/2} $. In this work, we first identify a flaw in the analysis of Naito's PMAC variant that invalidates the security proof. Apparently, the flaw is not easy to fix under the existing proof setup. We then formulate an equivalent problem which must be solved in order to achieve $ \ell $-free security bounds for this variant. Second, we show that sPMAC achieves $ O(q^2/2^n) $ bound for a weaker notion of universality as compared to the earlier condition of $ 4 $-wise independence.

Search for the right pairs of inputs in difference-based distinguishers is an important task for the experimental verification of the distinguishers in symmetric-key ciphers. In this paper, we develop an MILP-based approach to verify the possibility of difference-based distinguishers and extract the right pairs. We apply the proposed method to some presented difference-based trails (Related-Key Differentials (RKD), Rotational-XOR (RX)) of block ciphers \texttt{SIMECK}, and \texttt{SPECK}. As a result, we show that some of the reported RX-trails of \texttt{SIMECK} and \texttt{SPECK} are incompatible, i.e. there are no right pairs that follow the expected propagation of the differences for the trail. Also, for compatible trails, the proposed approach can efficiently speed up the search process of finding the exact value of a weak-key from the target weak-key space. For example, in one of the reported 14-round RX trails of \texttt{SPECK}, the probability of a key pair to be a weak-key is $2^{-94.91}$ when the whole key space is $2^{96}$; our method can find a key pair for it in a comparatively short time. It is worth noting that it was impossible to find this key pair using a traditional search. As another result, we apply the proposed method %and consider a search strategy for the framework of to \texttt{SPECK} block cipher, to construct longer related-key differential trails of \texttt{SPECK} which we could reach 15, 16, 17, and 19 rounds for \texttt{SPECK32/64}, \texttt{SPECK48/96}, \texttt{SPECK64/128}, and \texttt{SPECK128/256}, respectively. It should be compared with the best previous results which are 12, 15, 15, and 20 rounds, respectively, that both attacks work for a certain weak key class. It should be also considered as an improvement over the reported result of rotational XOR cryptanalysis on \texttt{SPECK}.

Traditionally, modes of Message Authentication Codes(MAC) such as Cipher Block Chaining (CBC) are instantiated using block ciphers or keyed Pseudo Random Permutations(PRP). However, one can also use domain preserving keyed Pseudo Random Functions(PRF) to instantiate MAC modes. The very first security proof of CBC-MAC, essentially modeled the PRP as a PRF. Until now very little work has been done to investigate the difference between PRP vs PRF instantiations. Only known result is the rather loose folklore PRP-PRF transition of any PRP based security proof, which looses a factor of $O(\frac{\sigma^2}{2^n})$ (domain of PRF/PRP is $\{0,1\}^n$ and adversary makes $\sigma$ many PRP/PRF calls in total). This loss is significant, considering the fact tight $\Theta(\frac{q^2}{2^n})$ security bounds have been known for PRP based EMAC and ECBC constructions (where $q$ is the total number of adversary queries). In this work, we show for many variations of encrypted CBC MACs (i.e. EMAC, ECBC, FCBC, XCBC and TCBC), random function based instantiation has a security bound $O(\frac{q\sigma}{2^n})$. This is a significant improvement over the folklore PRP/PRF transition. We also show this bound is optimal by providing an attack against the underlying PRF based CBC construction. This shows for EMAC, ECBC and FCBC, PRP instantiations are substantially more secure than PRF instantiations. Where as, for XCBC and TMAC, PRP instantiations are at least as secure as PRF instantiations.

Linear cryptanalysis considers correlations between linear input and output combiners for block ciphers and stream ciphers. Daemen and Rijmen (2007) had obtained the distributions of the correlations between linear input and output combiners of uniform random functions and uniform random permutations. The present work generalises these results to obtain the distributions of the correlations between arbitrary input and output combiners of uniform random functions and uniform random permutations.

As fault based cryptanalysis is becoming more and more of a practical threat, it is imperative to make efforts to devise suitable countermeasures. In this regard, the so-called ``infective countermeasures'' have garnered particular attention from the community due to its ability in inhibiting differential fault attacks without explicitly detecting the fault. We observe that despite being adopted over a decade ago, a systematic study of infective countermeasures is missing from the literature. Moreover, there seems to be a lack of proper security analysis of the schemes proposed, as quite a few of them have been broken promptly. Our first contribution comes in the form of a generalization of infective schemes which aids us with a better insight into the vulnerabilities, scopes for cost reduction and possible improvements. This way, we are able to propose lightweight alternatives of two existing schemes. Further we analyze shortcomings of LatinCrypt'12 and CHES'14 schemes and propose a simple patch for the former.

The Authenticated Encryption with Associated Data (AEAD) primitive, which integrates confidentiality and integrity services under a single roof, found wide-spread adoption in industry and became indispensable in practical protocol design. Recognizing this, academic research put forward a large number of candidate constructions, many of which come with provable security guarantees. Nevertheless, the recent past has shaken up with the discovery of vulnerabilities, some of them fatal, in well-regarded schemes, stemming from weak underlying primitives, flawed security arguments, implementation-level vulnerabilities, and so on. Simply reacting to such findings by replacing broken candidates by better(?) ones is in many cases unduly, costly, and sometimes just impossible. On the other hand, as attack techniques and opportunities change over time, it seems venturous to propose any specific scheme if the intended lifetime of its application is, say, twenty years. In this work we study a workable approach towards increasing the resilience against unforeseen breaks of AEAD primitives. Precisely, we consider the ability to combine two AEAD schemes into one such that the resulting AEAD scheme is secure as long as at least one of its components is (or: as long as at most one component is broken). We propose a series of such combiners, some of which work with fully generic AEAD components while others assume specific internal structures of the latter (like an encrypt-then-MAC design). We complement our results by proving the optimality of our constructions by showing the impossibility of combiners that get along with less invocations of the component algorithms.

We present practical attacks on OCB2. This mode of operation of a blockcipher was designed with the aim to provide particularly efficient and provably-secure authenticated encryption services, and since its proposal about 15 years ago it belongs to the top performers in this realm. OCB2 was included in an ISO standard in 2009. An internal building block of OCB2 is the tweakable blockcipher obtained by operating a regular blockcipher in XEX$^\ast$ mode. The latter provides security only when evaluated in accordance with certain technical restrictions that, as we note, are not always respected by OCB2. This leads to devastating attacks against OCB2's security promises: We develop a range of very practical attacks that, amongst others, demonstrate universal forgeries and full plaintext recovery. We complete our report with proposals for (provably) repairing OCB2. To our understanding, as a direct consequence of our findings, OCB2 is currently in a process of removal from ISO standards. Our attacks do not apply to OCB1 and OCB3, and our privacy attacks on OCB2 require an active adversary.

Rotational-XOR cryptanalysis is a cryptanalytic method aimed at finding distinguishable statistical properties in ARX-C ciphers, i.e., ciphers that can be described only using modular addition, cyclic rotation, XOR, and the injection of constants. In this paper we extend RX-cryptanalysis to AND-RX ciphers, a similar design paradigm where the modular addition is replaced by vectorial bitwise AND; such ciphers include the block cipher families Simon and Simeck. We analyse the propagation of RX-differences through AND-RX rounds and develop closed form formula for their expected probability. Finally, we formulate an SMT model for searching RX-characteristics in simon and simeck. Evaluating our model we find RX-distinguishers of up to 20, 27, and 35 rounds with respective probabilities of $2^{-26}, 2^{-42}$, and $2^{-54}$ for versions of simeck with block sizes of 32, 48, and 64 bits, respectively, for large classes of weak keys in the related-key model. In most cases, these are the longest published distinguishers for the respective variants of simeck. Interestingly, when we apply the model to the block cipher simon, the best distinguisher we are able to find covers 11 rounds of SIMON32 with probability $2^{-24}$. To explain the gap between simon and simeck in terms of the number of distinguished rounds we study the impact of the key schedule and the specific rotation amounts of the round function on the propagation of RX-characteristics in Simon-like ciphers.

In this paper we introduce a classification of existing re-keying-based approaches to increase the security of block cipher operation modes. We introduce the concepts of external and internal re-keying putting the focus on the second one. Whereas the external re-keying approach is widely used and provides the mechanism of key usage control on a message stream processing level, the internal re-keying approach is the first known mechanism providing such a control on a single message processing level. These approaches can be applied completely independently. The internal re-keying approach was already applied to the CTR encryption mode and yielded the CTR-ACPKM mode. This mode is currently being standardized in ISO and in IETF/IRTF (CFRG). In the current paper we apply the internal re-keying approach to the well-known GCM authenticated encryption mode. The main results of this paper are a new internally re-keyed GCM-ACPKM mode and its security bounds. The proposed mode is also passing through the last formal standardization stages in IETF (CFRG). We estimate the security of the GCM-ACPKM mode respecting standard security notions. We compare both security and performance of the GCM-ACPKM and GCM modes. The results show that changing GCM mode by integrating the ACPKM internal re-keying procedure increases security, significantly extending the lifetime of a key with a negligible loss in performance. Also we show how the re-keying approaches could increase the security of TLS 1.3 cipher suites.

In this paper we present a bitstream modification attack on the Trivium cipher, an international standard under ISO/IEC 29192-3. By changing the content of three LUTs in the bitstream, we reduce the non-linear state updating function of Trivium to a linear one. This makes it possible to recover the key from 288 keystream bits using at most $2^{19.41}$ operations. We also propose a countermeasure against bitstream modification attacks which obfuscates the bitstream using dummy and camouflaged LUTs which look legitimate to the attacker. We present an algorithm for injecting dummy LUTs directly into the bitstream without causing any performance or power penalty.

This paper proposes new symmetric cryptoalgorithms of Residue Number System and its Modified Perfect Form. According to the first method, ciphertext is regarded as a set of residues to the corresponding sets of modules (keys) and decryption or decimal number recovery from its residues takes place according to the Chinese remainder theorem. To simplify the calculations, it is proposed to use a Modified Perfect Form of Residue Number System, which leads to a decrease in the number of arithmetic operations (in particular, finding the inverse and multiplying by it) during the decryption process. Another method of symmetric encryption based on the Chinese remainder theorem can be applied when fast decryption is required. In this algorithm, the plaintext block is divided into sub-blocks that are smaller than the corresponding module and serve as remainders on dividing some number, which is a ciphertext, by these modules. Plaintext recovery is based on finding the ciphertext remainders to the corresponding modules. Examples of cryptoalgorithms implementation and their encryption schemes are given. Cryptosecurity of the proposed methods is estimated on the basis of the Prime number theorem and the Euler function. It is investigated which bitness and a number of modules are required for the developed symmetric security systems to ensure the same security level as the largest length key of the AES algorithm does. It is found that as the number of modules increases, their bitness decreases. Graphical dependencies of cryptoanalysis complexity on bitness and a number of modules are built. It is shown that with the increase of specified parameters, the cryptosecurity of the developed methods also increases.

In recent years, Mixed Integer Linear Programming (MILP) has been widely used in cryptanalysis of symmetric-key primitives. For differential and linear cryptanalysis, MILP can be used to solve two kinds of problems: calculation of the minimum number of differentially/linearly active S-boxes, and search for the best differential/linear characteristics. There are already numerous papers published in this area. However, the efficiency is not satisfactory enough for many symmetric-key primitives. In this paper, we greatly improve the efficiency of the MILP-based search algorithm for both problems. Each of the two problems for an $r$-round cipher can be converted to an MILP model whose feasible region is the set of all possible $r$-round differential/linear characteristics. Generally, high-probability differential/linear characteristics are likely to have a low number of active S-boxes at a certain round. Inspired by the idea of a divide-and-conquer approach, we divide the set of all possible differential/linear characteristics into several smaller subsets, then separately search them. That is to say, the search of the whole set is split into easier searches of smaller subsets, and optimal solutions within the smaller subsets are combined to give the optimal solution within the whole set. In addition, we use several techniques to further improve the efficiency of the search algorithm. As applications, we apply our search algorithm to five lightweight block ciphers: PRESENT, GIFT-64, RECTANGLE, LBLOCK and TWINE. For each cipher, we obtain better results than the best-known ones obtained from the MILP method. For the minimum number of differentially/linearly active S-boxes, we reach 31/31, 16/15, 16/16, 20/20 and 20/20 rounds for the five ciphers respectively. For the best differential/linear characteristics, we reach 18/18, 15/13, 15/14, 16/15 and 15/16 rounds for the five ciphers respectively.

In this work, we study message authentication code (MAC) schemes supporting variable tag lengths. We provide a formalisation of such a scheme. Several variants of the classical Wegman- Carter MAC scheme are considered. Most of these are shown to be insecure by pointing out detailed attacks. One of these schemes is highlighted and proved to be secure. We further build on this scheme to obtain single-key variable tag length MAC schemes utilising either a stream cipher or a short-output pseudo-random function. These schemes can be efficiently instantiated using practical well known primitives.

BIG is a 128-bit block cipher proposed by Demeri et al. in 2019. The number of rounds is 18 for high security. The designer evaluated its security against linear cryptanalysis. On the other hand, it has not been reported the security of BIG against higher order differential attack, which is one of the algebraic attacks. In this paper, we focused on a higher order differential of BIG. We found a new 15-round saturation characteristc of BIG using 1-st order differential by computer experiment. Exploiting this characteristic, we show that full-round BIG can be attacked with 6 chosen plaintexts and 2^(2.7) encryption operations.

The bit-based division property (BDP) is the most effective technique for finding integral characteristics of symmetric ciphers. Recently, automatic search tools have become one of the most popular approaches to evaluating the security of designs against many attacks. Constraint-aided automatic tools for the BDP have been applied to many ciphers with simple linear layers like bit-permutation. Constructing models of complex linear layers accurately and efficiently remains hard. A straightforward method proposed by Sun \etal (called the \s method), decomposes a complex linear layer into basic operations like \texttt{COPY} and \texttt{XOR}, then models them one by one. However, this method can easily insert invalid division trails into the solution pool, which results in a quicker loss of the balanced property than the cipher itself would. In order to solve this problem, Zhang and Rijmen propose the \zr method to link every valid trail with an invertible sub-matrix of the matrix corresponding to the linear layer, and then generate linear inequalities to represent all the invertible sub-matrices. Unfortunately, the \zr method is only applicable to invertible binary matrices (defined in Definition 3). To avoid generating a huge number of inequalities for all the sub-matrices, we build a new model that only includes that the sub-matrix corresponding to a valid trail should be invertible. The computing scale of our model can be tackled by most of SMT/SAT solvers, which makes our method practical. For applications, we improve the previous BDP for LED and MISTY1. We also give the 7-round BDP results for Camellia with $FL/FL^{-1}$, which is the longest to date. Furthermore, we remove the restriction of the \zr method that the matrix has to be invertible, which provides more choices for future designs. Thanks to this, we also reproduce 5-round key-dependent integral distinguishers proposed at Crypto 2016 which cannot be obtained by either the \s or \zr methods.

The MixColumns operation is an important component providing diffusion for the AES. The branch number of it ensures that any continuous four rounds of the AES have at least 25 active S-Boxes, which makes the AES secure against the differential and linear cryptanalysis. However, the choices of the coefficients of the MixColumns matrix may undermine the AES security against some novel-type attacks. A particular property of the AES MixColumns matrix coefficient has been noticed in recent papers that \emph{each row or column of the matrix has elements that sum to zero}. Several attacks have been developed taking advantage of the coefficient property. In this paper we investigate further the influence of the specific coefficient property on the AES security. Our target, which is also one of the targets of the previous works, is a 5-round AES variant with a secret S-Box. We will show how we take advantage of the coefficient property to extract the secret key directly without any assistance of the S-Box information. Compared with the previous similar attacks, the present attacks here are the best in terms of the complexity under the chosen-plaintext scenario.

At CRYPTO '12, Landecker et al. introduced the cascaded LRW2 (or CLRW2) construction, and proved that it is a secure tweakable block cipher up to roughly $ 2^{2n/3} $ queries. Recently, Mennink presented a distinguishing attack on CLRW2 in $ 2n^{1/2}2^{3n/4} $ queries. In the same paper, he discussed some non-trivial bottlenecks in proving tight security bound, i.e. security up to $ 2^{3n/4} $ queries. Subsequently, he proved security up to $ 2^{3n/4} $ queries for a variant of CLRW2 using $ 4 $-wise independent AXU assumption and the restriction that each tweak value occurs at most $ 2^{n/4} $ times. Moreover, his proof relies on a version of mirror theory which is yet to be publicly verified. In this paper, we resolve the bottlenecks in Mennink's approach and prove that the original CLRW2 is indeed a secure tweakable block cipher up to roughly $ 2^{3n/4} $ queries. To do so, we develop two new tools: First, we give a probabilistic result that provides improved bound on the joint probability of some special collision events; Second, we present a variant of Patarin's mirror theory in tweakable permutation settings with a self-contained and concrete proof. Both these results are of generic nature, and can be of independent interests. To demonstrate the applicability of these tools, we also prove tight security up to roughly $ 2^{3n/4} $ queries for a variant of DbHtS, called DbHtS-p, that uses two independent universal hash functions.

SNOW 3G is one of the core algorithms for confidentiality and integrity in several 3GPP wireless communication standards, including the new Next Generation (NG) 5G. It is believed to be resistant to classical cryptanalysis. In this paper, we show that a key can be extracted from an unprotected FPGA implementation of SNOW 3G by a fault attack. The faults are injected by modifying the content of Look- Up Tables (LUTs) directly in the bitstream. The main challenge is to identify target LUTs whose modification reduces the non-linear state updating function of SNOW 3G to a linear one. We present an algorithm for finding all k-input LUTs implementing a given k-variable Boolean function in the bitstream. We also introduce a key independent bitstream exploration technique which reduces the complexity of some search tasks from exponential to linear. This idea has not been exploited in previous bitstream modification attacks. Finally, we propose a countermeasure which makes the identification of target LUTs an intractable problem by considerably increasing the number of candidates into target LUTs.

In this work we present a duplex-based authenticated encryption scheme Friet based on a new permutation called Friet-P. We designed Friet-P with a novel approach for cryptographic permutations and block ciphers that takes fault-attack resistance into account and that we introduce in this paper. In this method, we build a permutation $f_C$ to be embedded in a larger one, $f$ . First, we define $f$ as a sequence of steps that all abide a chosen error-correcting code $C$, i.e., that map $C$-codewords to $C$-codewords. Then, we embed $f_C$ in $f$ by first encoding its input to an element of $C$, applying $f$ and then decoding back from $C$. This last step detects a fault when the output of $f$ is not in $C$. We motivate the design of the permutation we use in Friet and report on performance in soft- and hardware. We evaluate the fault-detection capabilities of the software and simulated hardware implementations with attacks. Finally, we perform a leakage evaluation. Our code is available at https://github.com/thisimon/Friet.git.

This paper analyzes the internal keyed permutation of FlexAEAD which is a round-1 candidate of the NIST LightWeight Cryptography Competition. In our analysis, we report an iterated truncated differential leveraging on a particular property of the AES S-box that becomes useful due to the particular nature of the diffusion layer of the round function. The differential holds with a low probability of 2^-7 for one round which allows it to penetrate the same number of rounds as claimed by the designers, but with a much lower complexity. Moreover, it can be easily extended to a key-recovery attack at a little extra cost. We further report a Super-Sbox construction in the internal permutation, which is exploited using the Yoyo game to devise a 6-round deterministic distinguisher and a 7-round key recovery attack for the 128-bit internal permutation. Similar attacks can be mounted for the 64-bit and 256-bit variants. All these attacks outperform the existing results of the designers as well as other third-party results. The iterated truncated differentials can be tweaked to mount forgery attacks similar to the ones given by Eichlseder et al Success probabilities of all the reported distinguishing attacks are shown to be high. All practical attacks have been experimentally verified. To the best of our knowledge, this work reports the first key-recovery attack on the internal keyed permutation of FlexAEAD.

In this paper we exploit elementary combinatorial techniques to settle different cryptanalytic observations on RC4 that remained unproved for more than two decades. At the same time, we present new observations with theoretical proofs. We first prove the biases (non-randomness) presented by Fluhrer and McGrew (FSE 2000) two decades ago. It is surprising that though the biases have been published long back, and there are many applications of them in cryptanalysis till recent days as well, the proofs have never been presented. In this paper, we complete that task and also show that any such bias immediately provides a glimpse of hidden variables in RC4. Further, we take up the biases of two non-consecutive key-stream bytes skipping one byte in between. We show the incompleteness of such a result presented by SenGupta et al (JoC, 2013) and provide new observations and proofs in this direction relating the key-stream bytes and glimpses. Similarly, we streamline certain missed observation in the famous Glimpse theorem presented by Jenkins in 1996. Our results point out how biases of RC4 key-stream and the Glimpses of the RC4 hidden variables are related. It is evident from our results that the biases and glimpses are everywhere in RC4 and it needs further investigation as we provide very high magnitude of glimpses that were not known earlier. The new glimpses and biases that we identify in this paper may be exploited in improving practical attacks against the protocols that use RC4.

In this paper we analyse the algorithm Chaskey - a lightweight MAC algorithm for 32-bit micro controllers - with respect to rotational cryptanalysis. We perform a related-key attack over Chaskey and find a distinguisher by using rotational probabilities. Having a message $m$ we can forge and present a valid tag for some message under a related key with probability $2^{-57}$ for 8 rounds and $2^{-86}$ for all 12 rounds of the permutation for keys in a defined weak-key class. This attack can be extended to full key recovery with complexity $2^{120}$ for the full number of rounds. To our knowledge this is the first published attack targeting all 12 rounds of the algorithm. Additionally, we generalize the Markov theory with respect to a relation between two plaintexts and not their difference and apply it for rotational pairs.

In the recent trend of CAESAR competition and NIST light-weight competition, cryptographic community have witnessed the submissions of several cryptographic schemes that are build on public random permutations. Recently, in CRYPTO 2019, Chen et al. have initiated an interesting research direction in designing beyond birthday bound PRFs from public random permutations and they proposed two instances of such PRFs. In this work, we extend this research direction by proposing a nonce-based MAC build from public random permutations. We show that our proposed MAC achieves $2n/3$ bit security (with respect to the state size of the permutation) and the bound is essentially tight. Moreover, the security of the MAC degrades gracefully with the repetition of the nonce.

We characterize the ANF and the univariate representation of any vectorial function as parts of the ANF and bivariate representation of the Boolean function equal to its graph indicator. We show how this provides, when $F$ is bijective, the expression of $F^{-1}$ and/or allows deriving properties of $F^{-1}$. We illustrate this with examples and with a tight upper bound on the algebraic degree of $F^{-1}$ by means of that of $F$. We characterize by the Fourier-Hadamard transform, by the ANF, and by the bivariate representation, that a given Boolean function is the graph indicator of a vectorial function. We also give characterizations of those Boolean functions that are affine equivalent to graph indicators. We express the graph indicators of the sum, product, composition and concatenation of vectorial functions by means of the graph indicators of the functions. We deduce from these results a characterization of the bijectivity of a generic $(n,n)$-function by the fact that some Boolean function, which appears as a part of the ANF (resp. the bivariate representation) of its graph indicator, is equal to constant function 1. We also address the injectivity of $(n,m)$-functions. Finally, we study the characterization of the almost perfect nonlinearity of vectorial functions by means of their graph indicators.

A division property is a generic tool to search for integral distinguishers, and automatic tools such as MILP or SAT/SMT allow us to evaluate the propagation efficiently. In the application to stream ciphers, it enables us to estimate the security of cube attacks theoretically, and it leads to the best key-recovery attacks against well-known stream ciphers. However, it was reported that some of the key-recovery attacks based on the division property degenerate to distinguishing attacks due to the inaccuracy of the division property. Three-subset division property (without unknown subset) is a promising method to solve this inaccuracy problem, and a new algorithm using automatic tools for the three-subset division property was recently proposed at Asiacrypt2019. In this paper, we first show that this state-of-the-art algorithm is not always efficient and we cannot improve the existing key-recovery attacks. Then, we focus on the feature of the three-subset division property without unknown subset and propose another new efficient algorithm using automatic tools. Our algorithm is more efficient than existing algorithms, and it can improve existing key-recovery attacks. In the application to Trivium, we show an 842-round key-recovery attack. We also show that an 855-round key-recovery attack, which was proposed at CRYPTO2018, has a critical flaw and does not work. As a result, our 842-round attack becomes the best key-recovery attack. In the application to Grain-128AEAD, we show that the known 184-round key-recovery attack degenerates to distinguishing attacks. Then, the distinguishing attacks are improved up to 189 rounds, and we also show the best key-recovery attack against 190 rounds. In the application to ACORN, we prove that the 772-round key-recovery attack at ISC2019 is in fact a constant-sum distinguisher. We then give new key-recovery attacks mounting to 773- and 774-round ACORN. We also verify the current best key-recovery attack on 892-round Kreyvium and recover the exact superpoly.

This paper presents WAGE, a new lightweight sponge-based authenticated cipher whose underlying permutation is based on a 37-stage Galois NLFSR over $\mathbb{F}_{2^7}$. At its core, the round function of the permutation consists of the well-analyzed Welch-Gong permutation (WGP), primitive feedback polynomial, a newly designed 7-bit SB sbox and partial word-wise XORs. The construction of the permutation is carried out such that the design of individual components is highly coupled with cryptanalysis and hardware efficiency. As such, we analyze the security of WAGE against differential, linear, algebraic and meet/miss-in-the-middle attacks. For 128-bit authenticated encryption security, WAGE achieves a throughput of 535 Mbps with hardware area of 2540 GE in ASIC ST Micro 90 nm standard cell library. Additionally, WAGE is designed with a twist where its underlying permutation can be efficiently turned into a pseudorandom bit generator based on the WG transformation (WG-PRBG) whose output bits have theoretically proved randomness properties.

In this paper, we suggest a new format for converting side channel traces to fully utilize the deep learning schemes. Due to the fact that many deep learning schemes have been advanced based on MNIST style datasets, we convert from raw-trace based on float or byte data to picture-formatted trace based on position. This is induced that the best performance can be acquired from deep learning schemes. Although the overfitting cannot be avoided in our suggestion, the accuracy for validation outperforms to previous results of side channel analysis based on deep learning. Additionally, we provide a novel criteria for attack success or fail based on statistical confidence level rather than rule of thumb. Even though the data storage is slightly increased, our suggestion can completely be recovered the correct key compared to previous results. Moreover, our suggestion scheme has a lot of potential to improve side channel attack.

Light key schedule has found many applications in lightweight blockciphers, e.g. LED, PRINTcipher and LBlock. In this paper, we study an interesting question of how to design a as light as possible key schedule from the view of provable security and revisit the four-round key-alternating Feistel cipher by Guo and Wang in Asiacrypt 18. We optimize the construction by Guo and Wang and propose a four-round key-alternating Feistel cipher with an ultra-light (in fact non-existent) key schedule. We prove our construction retain the same security level as that of Guo and Wang's construction. To the best of our knowledge, this is the first provably secure key-alternating Feistel cipher using identical round function and one n-bit master key but with ultra-light (non-existent) key schedule. We also investigate whether the same refinement works for the three-round key-alternating Feistel cipher. This time we show a distinguishing attack on such three-round construction with only four encryption queries. On the positive side, we prove that three-round key-alternating Feistel cipher with a suitable key schedule is a pseudorandom permutation. This is also the first provable-security result for three-round key-alternating Feistel cipher.

In this paper, we present all 4-bit S-boxes which are able to support BOGI logic. We exhaustively show that only 2,413 PXE classes of 4-bit S-box are BOGI-applicable among the 142,090,700 PXE classes. We evaluate the whole BOGI-applicable S-boxes in terms of the security and implementation costs. The security evaluation includes security strength of the S-boxes themselves, and how they affect the resistance of GIFT-64 against differential and linear cryptanalysis (DC and LC). The security evaluation shows that all the BOGI-applicable S-boxes fulfill the security criteria of GIFT designers as long as they have the differential uniformity and linearity as 6 and 8, respectively. It will also be shown that the security of GIFT-64 against DC and LC can be improved only by changing the S-box. Moreover, we evaluate the implementation costs of the BOGI-applicable S-boxes by finding their optimal implementation. The results show that GIFT S-box is well-chosen considering existence of fixed-points, and suggest a set of S-boxes providing the same implementation cost as GIFT S-box. Finally, we suggest a set of potentially better S-boxes for GIFT-64 based on our investigations.

LRBC is a new lightweight block cipher that has been proposed for resource-constrained IoT devices. The cipher is claimed to be secure against differential cryptanalysis and linear cryptanalysis. However, beside short state length which is only 16-bits, the structures of the cipher only use the linear operations, the its s-boxes, and this is a reason why the cipher is completely insecure against the mentioned attacks. we present a few examples to show that. Also, we show that the round function of LRBC has some structural problem and even if we fix them the cipher does not provide complete diffusion. Hence, even with replacement of the cipher s-boxes with proper s-boxes, the problem will not be fixed and it is possible to provide deterministic distinguisher for any number of round of the cipher. In addition, we show that for any fixed key, it is possible to create a full code book for the cipher with the complexity of $2^{n/2}$, which should be compared with $2^{n}$ for any secure $n$-bit block cipher.

We propose SPAE, a single pass, patent free, authenticated encryption with associated data (AEAD) for AES. The algorithm has been developped to address the needs of a growing trend in IoT systems: storing code and data on a low cost flash memory external to the main SOC. Existing AEAD algorithms such as OCB, GCM, CCM, EAX , SIV, provide the required functionality however in practice each of them suffer from various drawbacks for this particular use case. Academic contributions such as ASCON and AEGIS-128 are suitable and efficient however they require the development of new hardware accelerators and they use primitives which are not ‘approved’ by governemental institutions such as NIST, BSI, ANSSI. From a silicon manufacturer point of view, an efficient AEAD which use existing AES hardware is much more enticing: the AES is required already by most industry standards invovling symmetric encryption (GSMA, EMVco, FIDO, Bluetooth, ZigBee to name few). This paper expose the properties of an ideal AEAD for external memory encryption, present the SPAE algorithm and analyze various security aspects. Performances of SPAE on actual hardware are better than OCB, GCM and CCM.

The majority of recently demonstrated deep-learning side-channel attacks use a single neural network classifier to recover the key. The potential benefits of combining multiple classifiers have not been explored yet in the side-channel attack's context. In this paper, we show that, by combining several CNN classifiers which use different attack points, it is possible to considerably reduce (more than 40% on average) the number of traces required to recover the key from an FPGA implementation of AES by power analysis. We also show that not all combinations of classifiers improve the attack efficiency.

Scenarios in which authenticated encryption schemes output decrypted plaintext before successful verification raise many security issues. These situations are sometimes unavoidable in practice, such as when devices have insufficient memory to store an entire plaintext, or when a decrypted plaintext needs early processing due to real-time requirements. We introduce the first formalization of the releasing unverified plaintext (RUP) setting. To achieve privacy, we propose using plaintext awareness (PA) along with IND-CPA. An authenticated encryption scheme is PA if it has a plaintext extractor, which tries to fool adversaries by mimicking the decryption oracle without the secret key. Releasing unverified plaintext then becomes harmless as it is infeasible to distinguish the decryption oracle from the plaintext extractor. We introduce two notions of plaintext awareness in the symmetric-key setting, PA1 and PA2, and show that they expose a new layer of security between IND-CPA and IND-CCA. To achieve integrity of ciphertexts, INT-CTXT in the RUP setting is required, which we refer to as INT-RUP. These new security notions are used to make a classification of symmetric-key schemes in the RUP setting. Furthermore, we re-analyze existing authenticated encryption schemes, and provide solutions to fix insecure schemes.

An adjustable join ($\nadjoin$) scheme [Popa-Zeldovich 2012] is a symmetric-key primitive that enables a user to securely outsource his database to a server, and later to issue join queries for a pair of columns. When queries are extended to a list of columns, $\tp$ security of Adjoin schemes [Mironov-Segev-Shahaf 2017] does not capture the expected security. To address this deficiency, we introduce the syntax and security notion of multi-adjustable join ($\nmadjoin$) schemes. We propose a new security notion for this purpose, which we refer to as $\mtp$. The $\tp$ security of $\nadjoin$ extends to the $\mtp$ security of $\nmadjoin$ in a straightforward way. The gap between $\tp$ and $\mtp$ is filled with a sequence $\{\smtpk{k}\}_{k\in\mathbb{N}}$ of security definitions where $\smtpk{1}$ and $\smtpk{\infty}$, respectively, correspond to $\tp$ and $\mtp$. We propose constructions for achieving both $\mtp$ and $\smtpk{k}$ security levels. Our $\mtp$-secure scheme joins $m$ columns, each containing $n$ elements, in time $\mathcal{O}(n^{m-1})$. Our $\smtpk{k}$-secure scheme uses ideas from secret sharing in its construction and does the job in time $\mathcal{O}((m-1)n^{k}/k)$ with some leakage that we refer to as $k$-monotonous. It remains open if this barrier is inherent to the security definitions. Our schemes are substantially more efficient than previous ones.

Differential power analysis (DPA) is a statistical analysis of the power traces of cryptographic computations. DPA has many applications including key-recovery on linear feedback shift register based stream ciphers. In 2017, Dobraunig et. al. presented a DPA on Keymill to uncover the bit relations of neighbouring bits in the shift registers, effectively reduces the internal state guessing space to 4-bit. In this work, we generalise the analysis methodology to uncover more bit relations on both linear feedback shift registers (LFSRs) and non-linear feedback shift registers (NLFSRs) and with application to fresh re-keying scheme --- LR-Keymill. In addition, we improve the DPA on Keymill by halving the data resources needed for the attack.

The stream cipher ChaCha is an ARX type algorithm developed by Daniel Bernstein in 2008. Since its development, ChaCha has received a lot of attention and is currently being used in several systems. The most powerful cryptanalysis of reduced versions of this cipher was presented by Choudhuri and Maitra on FSE 2017 by using differential-linear cryptanalysis. In their work they show that is possible to obtain linear relations between bits from different rounds with high probability and use the proposed equations to create multi-bit differentials and improve previous attacks. In this work, we provide new linear approximations that can be used in a similar fashion but with increased efficiency. Therefore, we show that using these new equations is possible to improve the attacks against 6 and 7 rounds of ChaCha.

In early nineties Carlet [1] introduced two new classes of bent functions, both derived from the Maiorana-McFarland ($\mathcal{M}$) class, and named them $\cC$ and $ \cD$ class, respectively. Apart from a subclass of $\cD$, denoted by $\cD_0$ by Carlet, which is provably outside two main (completed) primary classes of bent functions, little is known about their efficient constructions. More importantly, both classes may easily remain in the underlying $\mathcal{M}$ class which has already been remarked in [21]. Assuming the possibility of specifying a bent function $f$ that belongs to one of these two classes (apart from $\cD_0$), the most important issue is then to determine whether $f$ is still contained in the known primary classes or lies outside their completed versions. In this article, we further elaborate on the analysis of the set of sufficient conditions given in \cite{OutsideMM} concerning the specification of bent functions in $\cC$ and $ \cD$ which are provably outside $\cM$. It is shown that these conditions, related to bent functions in class $\cD$, can be relaxed so that even those permutations whose component functions admit linear structures still can be used in the design. It is also shown that monomial permutations of the form $x^{2^r+1}$ have inverses which are never quadratic for $n >4$, which gives rise to an infinite class of bent functions in $\cC$ but outside $\cM$. Similarly, using a relaxed set of sufficient conditions for bent functions in $\cD$ and outside $\cM$, one explicit infinite class of such bent functions is identified. We also extend the inclusion property of certain subclasses of bent functions in $ \cC$ and $ \cD$, as addressed initially in [1,21], that are ultimately within the completed $\mathcal{M}$ class. Most notably, we specify {\em another generic and explicit subclass} of $\cD$, which we call $\cD_2^\star$, whose members are bent functions provably outside the completed $\mathcal{M}$ class.

Cellular Automata (CA) have recently evolved as a good cryptographic primitive. It plays an important role in the construction of new fast, efficient and secure stream ciphers. Several studies have been made on CA based stream ciphers and we observe that the cryptographic strength of a CA based stream cipher increases with the increase in the neighbourhood radii if appropriate CA rules are employed. The current work explores the cryptographic feasibility of 5-neighbourhood CA rules also referred to as pentavalent rules. A new CA based stream cipher, CARPenter, which uses pentavalent rules have been proposed. The cipher incorporates maximum length null-boundary linear CA and a non-linear CA along with a good non-linear mixing function. This is implemented in hardware as well as software and exhibits good cryptographic properties which makes the cipher resistant to almost all attacks on stream ciphers, but with the cost of additional computing requirements. This cipher uses 16 cycles for initialization, which is the least number of cycles when compared to other existing stream ciphers.

This paper gives a new generalized key-recovery model of related-key rectangle attacks on block ciphers with linear key schedules. The model is quite optimized and applicable to various block ciphers with linear key schedule. As a proof of work, we apply the new model to two very important block ciphers, i.e. SKINNY and GIFT, which are basic modules of many candidates of the Lightweight Cryptography (LWC) standardization project by NIST. For SKINNY, we reduce the complexity of the best previous 27-round related-tweakey rectangle attack on SKINNY-128-384 from $2^{331}$ to $2^{294}$. In addition, the first 28-round related-tweakey rectangle attack on SKINNY-128-384 is given, which gains one more round than before. For the case of GIFT-64, we give the first 24-round related-key rectangle attack with a time complexity $2^{91.58}$, while the best previous attack on GIFT-64 only reaches 23 rounds at most.

We describe a somewhat homomorphic GSW-like encryption scheme, natively encrypting matrices rather than just single elements. This scheme offers much better performance than existing homomorphic encryption schemes for evaluating encrypted (nondeterministic) finite automata (NFAs). Differently from GSW, we do not know how to reduce the security of this scheme to LWE, instead we reduce it to a stronger assumption, that can be thought of as an inhomogeneous variant of the NTRU assumption. This assumption (that we term iNTRU) may be useful and interesting in its own right, and we examine a few of its properties. We also examine methods to encode regular expressions as NFAs, and in particular explore a new optimization problem, motivated by our application to encrypted NFA evaluation. In this problem, we seek to minimize the number of states in an NFA for a given expression, subject to the constraint on the ambiguity of the NFA.

We propose a nonce misuse-resistant message authentication scheme called EHE (Encrypt-Hash-Encrypt). In EHE, a message-dependent polynomial is evaluated at the point which is an encrypted nonce. The resulting polynomial hash value is encrypted again and becomes an authentication tag. We prove the prf-security of the EHE scheme and extend it to two authenticated encryption modes which follow the "encrypt-then-authenticate" paradigm.

In this work we advance the study of leakage-resilient Authenticated Encryption with Associated Data (AEAD) and lay the theoretical groundwork for building such schemes from sponges. Building on the work of Barwell et al. (ASIACRYPT 2017), we reduce the problem of constructing leakage-resilient AEAD schemes to that of building fixed-input-length function families that retain pseudorandomness and unpredictability in the presence of leakage. Notably, neither property is implied by the other in the leakage-resilient setting. We then show that such a function family can be combined with standard primitives, namely a pseudorandom generator and a collision-resistant hash, to yield a nonce-based AEAD scheme. In addition, our construction is quite efficient in that it requires only two calls to this leakage-resilient function per encryption or decryption call. This construction can be instantiated entirely from the T-sponge to yield a concrete AEAD scheme which we call SLAE. We prove this sponge-based instantiation secure in the non-adaptive leakage setting. SLAE bears many similarities and is indeed inspired by ISAP, which was proposed by Dobraunig et al. at FSE 2017. However, while retaining most of the practical advantages of ISAP, SLAE additionally benefits from a formal security treatment.

We present attacks on 21-rounds of SIMON 32/64, 21-rounds of SIMON 48/96, 25-rounds of SIMON 64/128, 35-rounds of SIMON 96/144 and 43-rounds of SIMON 128/256, often with direct recovery of the full master key without repeating the attack over multiple rounds. These attacks result from the observation that, after four rounds of encryption, one bit of the left half of the state of 32/64 SIMON depends on only 17 key bits (19 key bits for the other variants of SIMON). Further, linear cryptanalysis requires the guessing of only 16 bits, the size of a single round key of SIMON 32/64. We partition the key into smaller strings by focusing on one bit of state at a time, decreasing the cost of the exhaustive search of linear cryptanalysis to 16 bits at a time for SIMON 32/64. We also present other example linear cryptanalysis, experimentally verified on 8, 10 and 12 rounds for SIMON 32/64.

We revisit the security of various generalized Feistel networks. Concretely, for unbalanced, alternating, type-1, type-2, and type-3 Feistel networks built from random functions, we substantially improve the coupling analyzes of Hoang and Rogaway (CRYPTO 2010). For a tweakable blockcipher-based generalized Feistel network proposed by Coron et al. (TCC 2010), we present a coupling analysis and for the first time show that with enough rounds, it achieves 2n-bit security, and this provides highly secure, double-length tweakable blockciphers.

With the dawn of quantum computers, higher security than $128$ bits has become desirable for primitives and modes. During the past decade, highly secure hash functions, MACs, and encryption schemes have been built primarily on top of keyless permutations, which simplified their analyses and implementation due to the absence of a key schedule. However, the security of these modes is most often limited to the birthday bound of the state size, and their analysis may require a different security model than the easier-to-handle secret-permutation setting. Yet, larger state and key sizes are desirable not only for permutations but also for other primitives such as block ciphers. Using the additional public input of tweakable block ciphers for domain separation allows for exceptionally high security or performance as recently proposed modes have shown. Therefore, it appears natural to ask for such designs. While security is fundamental for cryptographic primitives, performance is of similar relevance. Since 2009, processor-integrated instructions have allowed high throughput for the AES round function, which already motivated various constructions based on it. Moreover, the four-fold vectorization of the AES instruction sets in Intel's Ice Lake architecture is yet another leap in terms of performance and gives rise to exploit the AES round function for even more efficient designs. This work tries to combine all aspects above into a primitive and to build upon years of existing analysis on its components. We propose Pholkos, a family of (1) highly efficient, (2) highly secure, and (3) tweakable block ciphers. Pholkos is no novel round-function design, but utilizes the AES round function, following design ideas of Haraka and AESQ to profit from earlier analysis results. It extends them to build a family of primitives with state and key sizes of $256$ and $512$ bits for flexible applications, providing high security at high performance. Moreover, we propose its usage with a $128$-bit tweak to instantiate high-security encryption and authentication schemes such as SCT, ThetaCB3, or ZAE. We study its resistance against the common attack vectors, including differential, linear, and integral distinguishers using a MILP-based approach and show an isomorphism from the AES to Pholkos-$512$ for bounding impossible-differential, or exchange distinguishers from the AES. Our proposals encrypt at around $1$--$2$ cycles per byte on Skylake processors, while supporting a much more general application range and considerably higher security guarantees than comparable primitives and modes such as PAEQ/AESQ, AEGIS, Tiaoxin346, or Simpira.

Masking is a popular countermeasure to protect cryptographic implementations against side-channel attacks (SCA). In the literature, a myriad of proposals of masking schemes can be found. They are typically defined by a masked multiplication, since this can serve as a basic building block for any nonlinear algorithm. However, when masking generic Boolean functions of algebraic degree t, it is very inefficient to construct the implementation from masked multiplications only. Further, it is not immediately clear from the description of a masked multiplication, how to efficiently implement a masked Boolean function. In this work, we fill this gap in the literature with a detailed description and investigation of a generic masking methodology for Boolean functions of any degree t at any security order d.

The boomerang attack, introduced by Wagner in 1999, is a cryptanalysis technique against block ciphers based on differential cryptanalysis. In particular it takes into consideration two differentials, one for the upper part of the cipher and one for the lower part, and it exploits the dependency of these two differentials. At Eurocrypt'18, Cid et al. introduced a new tool, called the Boomerang Connectivity Table (BCT) that permits to simplify this analysis. Next, Boura and Canteaut introduced an important parameter for cryptographic S-boxes called boomerang uniformity, that is the maximum value in the BCT. Very recently, the boomerang uniformity of some classes of permutations (in particular quadratic functions) have been studied by Li, Qu, Sun and Li, and by Mesnager, Chunming and Maosheng. In this paper we further study the boomerang uniformity of some non-quadratic differentially 4-uniform functions. In particular, we consider the case of the Bracken-Leander cubic function and three classes of 4-uniform functions constructed by Li, Wang and Yu, obtained from modifying the inverse functions.

In this work, we propose a new table-based block cipher structure, dubbed $\mathsf{FPL}$, that can be used to build white-box secure block ciphers. Our construction is a balanced Feistel cipher, where the input to each round function determines multiple indices for the underlying table via a probe function, and the sum of the values from the table becomes the output of the round function. We identify the properties of the probe function that make the resulting block cipher white-box secure in terms of weak and strong space hardness against known-space and non-adaptive chosen-space attacks. Our construction, enjoying rigorous provable security without relying on any ideal primitive, provides flexibility to the block size and the table size, and permits parallel table look-ups. We also propose a concrete instantiation of $\mathsf{FPL}$, dubbed $\mathsf{FPL}_{\mathsf{AES}}$, using (round-reduced) $\mathsf{AES}$ for the underlying table and probe functions. Our implementation shows that $\mathsf{FPL}_{\mathsf{AES}}$ provides stronger security without significant loss of efficiency, compared to existing schemes including $\mathsf{SPACE}$, $\mathsf{WhiteBlock}$ and $\mathsf{WEM}$.

This paper presents Foxtail+, a new shared-key protocol to securely authenticate resource constrained devices, such as Internet of things (IoT) devices. Foxtail+ is based on a previously proposed protocol to authenticate unaided humans, called the Foxtail protocol, which we modify for authenticating resource constrained devices. It uses a computationally lightweight function, called the Foxtail function, which makes it ideal for IoT nodes with low memory, computational, and/or battery resources. We introduce a new family of functions based on the Foxtail function, analyze its security in terms of the number of samples required to obtain the secret, and demonstrate how it is connected with the learning with rounding (LWR) problem. We then build the Foxtail+ protocol from this function family, secure against active adversaries. Finally, we implement and experimentally evaluate the performance of Foxtail+ against a similar alternate protocol, i.e., the modified version of the Hopper and Blum protocol called HB+, and a block cipher based protocol instantiated with AES. The experiments are run on an IoT device connected to a LoRa network which is an IoT specific Low-Power Wide-Area Network (LPWAN). We show that Foxtail+ outperforms HB+ in terms of overall communication and energy cost, and its parallel implementation is comparable to the AES-based protocol in terms of time and energy consumption. To our knowledge, we provide the first implementation of any member of the HB+ family of protocols that directly compares its performance against an AES-based protocol in terms of time and power consumption. Our experiments shed new light on some of the limitations of identification protocols based on lightweight primitives, of which Foxtail+ is a member, over block cipher based protocols.

In an early version of CRYPTO’17, Mennink and Neves pro- posed EWCDMD, a dual of EWCDM, and showed n-bit security, where n is the block size of the underlying block cipher. In CRYPTO’19, Chen et al. proposed permutation based design SoKAC21 and showed 2n/3- bit security, where n is the input size of the underlying permutation. In this paper we show birthday bound attacks on EWCDMD and SoKAC21, invalidating their security claims. Both attacks exploit an inherent com- position nature present in the constructions. Motivated by the above two attacks exploiting the composition nature, we consider some generic relevant composition based constructions of ideal primitives (possibly in the ideal permutation and random oracle model) and present birthday bound distinguishers for them. In particular, we demonstrate a birthday bound distinguisher against (1) a secret random permutation followed by a public random function and (2) composition of two secret random functions. Our distinguishers for SoKAC21 and EWCDMD are direct con- sequences of (1) and (2) respectively.

In Crypto'05, Bellare et al. proved an $O(\ell q^2 /2^n)$ bound for the PRF (pseudorandom function) security of the CBC-MAC based on an $n$-bit random permutation $\Pi$, provided $\ell < 2^{n/3}$. Here an adversary can make at most $q$ prefix-free queries each having at most $\ell$ many ``blocks'' (elements of $\{0,1\}^n$). In the same paper an $O(\ell^{o(1)} q^2 /2^n)$ bound for EMAC (or encrypted CBC-MAC) was proved, provided $\ell < 2^{n/4}$. Both proofs are based on {\bf structure graphs} representing all collisions among ``intermediate inputs'' to $\Pi$ during the computation of CBC. The problem of bounding PRF-advantage is shown to be reduced to bounding the number of structure graphs satisfying certain collision patterns. In the present paper, we show that the Lemma 10 in the Crypto '05 paper, stating an important result on structure graphs, is incorrect. This is due to the fact that the authors overlooked certain structure graphs. This invalidates the proofs of the PRF bounds. In ICALP '06, Pietrzak improved the bound for EMAC by showing a tight bound $O(q^2/2^n)$ under the restriction that $\ell < 2^{n/8}$. As he used the same flawed lemma, this proof also becomes invalid. In this paper, we have revised and sometimes simplified these proofs. We revisit structure graphs in a slightly different mathematical language and provide a complete characterization of certain types of structure graphs. Using this characterization, we show that PRF security of CBC-MAC is about $\sigma q /2^n$ provided $\ell < 2^{n/3}$ where $ \sigma $ is the total number of blocks in all queries. We also recover tight bound for PRF security of EMAC with a much relaxed constraint ($ \ell < 2^{n/4} $) than the original ($ \ell < 2^{n/8} $).

In this paper we spot light on dedicated quantum collision attacks on concrete hash functions, which has not received much attention so far. In the classical setting, the generic complexity to find collisions of an $n$-bit hash function is $O(2^{n/2})$, thus classical collision attacks based on differential cryptanalysis such as rebound attacks build differential trails with probability higher than $2^{-n/2}$. By the same analogy, generic quantum algorithms such as the BHT algorithm find collisions with complexity $O(2^{n/3})$. With quantum algorithms, a pair of messages satisfying a differential trail with probability $p$ can be generated with complexity $p^{-1/2}$. Hence, in the quantum setting, some differential trails with probability up to $2^{-2n/3}$ that cannot be exploited in the classical setting may be exploited to mount a collision attack in the quantum setting. In particular, the number of attacked rounds may increase. In this paper, we attack two international hash function standards: AES-MMO and Whirlpool. For AES-MMO, we present a $7$-round differential trail with probability $2^{-80}$ and use it to find collisions with a quantum version of the rebound attack, while only $6$ rounds can be attacked in the classical setting. For Whirlpool, we mount a collision attack based on a $6$-round differential trail from a classical rebound distinguisher with a complexity higher than the birthday bound. This improves the best classical attack on 5 rounds by 1. We also show that those trails are optimal in our approach. Our results have two important implications. First, there seems to exist a common belief that classically secure hash functions will remain secure against quantum adversaries. Indeed, several second-round candidates in the NIST post-quantum competition use existing hash functions, say SHA-3, as quantum secure ones. Our results disprove this common belief. Second, our observation suggests that differential trail search should not stop with probability $2^{-n/2}$ but should consider up to $2^{-2n/3}$. Hence it deserves to revisit the previous differential trail search activities.

Side-channel analysis constitutes a powerful attack vector against crypto- graphic implementations. Techniques such as power and electromagnetic side-channel analysis have been extensively studied to provide an efficient way to recover the secret key used in cryptographic algorithms. To protect against such attacks, countermea- sure designers have developed protection methods, such as masking and hiding, to make the attacks harder. However, due to significant overheads, these protections are sometimes deployed only at the beginning and the end of encryption, which are the main targets for side-channel attacks. In this paper, we present a methodology for side-channel assisted differential crypt- analysis attack to target middle rounds of block cipher implementations. Such method presents a powerful attack vector against designs that normally only protect the beginning and end rounds of ciphers. We generalize the attack to SPN based ciphers and calculate the effort the attacker needs to recover the secret key. We provide experimental results on 8-bit and 32-bit microcontrollers. We provide case studies on state-of-the-art symmetric block ciphers, such as AES, SKINNY, and PRESENT. Furthermore, we show how to attack shuffling-protected implementations.

In this paper we develop a number of generic techniques and algorithms in spectral analysis of large linear approximations for use in cryptanalysis. We apply the developed tools for cryptanalysis of ZUC-256 and give a distinguishing attack with complexity around $2^{236}$. Although the attack is only $2^{20}$ times faster than exhaustive key search, the result indicates that ZUC-256 does not provide a source with full 256-bit entropy in the generated keystream, which would be expected from a 256-bit key. To the best of our knowledge, this is the first known academic attack on full ZUC-256 with a computational complexity that is below exhaustive key search.

Logic locking has been proposed as strong protection of intellectual property (IP) against security threats in the IC supply chain especially when the fabrication facility is untrusted. Such techniques use additional locking circuitry to inject incorrect behavior into the digital functionality when the key is incorrect. A family of attacks known as "SAT attacks" provides a strong mathematical formulation to find the correct key of locked circuits. Many conventional SAT-resilient logic locking schemes fail to inject sufficient error into the circuit when the key is incorrect: there are usually very few (or only one) input minterms that cause any error at the circuit output. The state-of-the-art stripped functionality logic locking (SFLL) technique provides a wide spectrum of configurations that introduced a trade-off between security (i.e. SAT attack complexity) and effectiveness (i.e. the amount of error injected by a wrong key). In this work, we prove that such a trade-off is universal among all logic locking techniques. In order to attain high effectiveness of locking without compromising security, we propose a novel secure and effective logic locking scheme, called Strong Anti-SAT (SAS). SAS has the following significant improvements over existing techniques. (1) We prove that SAS's security against SAT attack is not compromised by increases in effectiveness. (2) In contrast to prior work which focused solely on the circuit-level locking impact, we integrate SAS-locked modules into an 80386 processor and show that SAS has a high application-level impact. (3) SAS's hardware overhead is smaller than that of existing techniques.

Linear transformations are applied to the white-box cryptographic implementation for the diffusion effect to prevent key-dependent intermediate values from being analyzed. However, it has been shown that there still exists a correlation before and after the linear transformation, and thus this is not enough to protect the key against statistical analysis. So far, the Hamming weight of rows in the invertible matrix has been considered the main cause of the key leakage from the linear transformation. In this study, we present an in-depth analysis of the distribution of intermediate values and the characteristics of block invertible binary matrices. Our mathematical analysis and experimental results show that the balanced distribution of the key-dependent intermediate value is the main cause of the key leakage.

Linear cryptanalysis is considered to be one of the strongest techniques in the cryptanalyst’s arsenal. In most cases, Matsui’s Algorithm 2 is used for the key recovery part of the attack. The success rate analysis of this algorithm is based on an assumption regarding the bias of a linear approximation for a wrong key, known as the wrong-key-randomization hypothesis. This hypothesis was refined by Bogdanov and Tischhauser to take into account the stochastic nature of the bias for a wrong key. We provide further refinements to the analysis of Matsui’s Algorithm 2 by considering sampling without replacement. This paper derives the distribution of the observed bias for wrong keys when sampling is done without replacement and shows that less data are required in this scenario. It also develops formulas for the success probability and the required data complexity when this approach is taken. The formulas predict that the success probability may reach a peak and then decrease as more pairs are considered. We provide a new explanation for this behavior and derive the conditions for encountering it. We empirically verify our results and compare them to previous work.

We analyze the authenticated encryption algorithm of ORANGE, a submission to the NIST lightweight cryptography standardization process. We show that it is practically possible to craft forgeries out of two observed transmitted messages that encrypt the same plaintext. The authors of ORANGE have confirmed the attack, and they discuss a fix for this attack in their second-round submission of ORANGE to the NIST lightweight cryptography competition.

Deoxys-BC is the core internal tweakable block cipher of the authenticated encryption schemes Deoxys-I and Deoxys-II. Deoxys-II is one of the six schemes in the final portfolio of the CAESAR competition, while Deoxys-I is a 3rd round candidate. By well studying the new method proposed by Cid et al. at ToSC 2017 and BDT technique proposed by Wang and Peyrin at ToSC 2019, we find a new 11-round related-tweakey boomerang distinguisher of Deoxys-BC-384 with probability of $2^{-118.4}$, and give a related-tweakey rectangle attack on 13-round Deoxys-BC-384 with a data complexity of $2^{125.2}$ and time complexity of $2^{186.7}$, and then apply it to analyze 13-round Deoxys-I-256-128 in this paper. This is the first time that an attack on 13-round Deoxys-I-256-128 is given, while the previous attack on this version only reaches 12 rounds.

In the CAESAR competition, Deoxys-I and Deoxys-II are two important authenticated encryption schemes submitted by Jean et al. Recently, Deoxys-II together with Ascon, ACORN, AEGIS-128, OCB and COLM have been selected as the final CAESAR portfolio. Notably, Deoxys-II is also the primary choice for the use case ``Defense in depth''. However, Deoxys-I remains to be one of the third-round candidates of the CAESAR competition. Both Deoxys-I and Deoxys-II adopt Deoxys-BC-256 and Deoxys-BC-384 as their internal tweakable block ciphers. In this paper, we investigate the security of round-reduced Deoxys-BC-256/-384 and Deoxys-I against the related-tweakey boomerang and rectangle attacks with some new boomerang distinguishers. For Deoxys-BC-256, we present 10-round related-tweakey boomerang and rectangle attacks for the popular setting $(|tweak|,|key|)=(128,128)$, which reach one more round than the previous attacks in this setting. Moreover, an 11-round related-tweakey rectangle attack on Deoxys-BC-256 is given for the first time. We also put forward a 13-round related-tweakey boomerang attack in the popular setting $(|tweak|,|key|)=(128,256)$ for Deoxys-BC-384, while the previous attacks in this setting only work for 12 rounds at most. In addition, the first 14-round related-tweakey rectangle attack on Deoxys-BC-384 is given when $(|tweak|<98,|key|>286)$, that attacks one more round than before. Besides, we give the first 10-round rectangle attack on the authenticated encryption mode Deoxys-I-128-128 with one more round than before, and we also reduce the complexity of the related-tweakey rectangle attack on 12-round Deoxys-I-256-128 by a factor of $2^{28}$. Our attacks can not be applied to (round-reduced) Deoxys-II.

Using recent results on solving the equation $X^{2^k+1}+X+a=0$ over a finite field $\GF{2^n}$, we address an open question raised by the first author in WAIFI 2014 concerning the APN-ness of the Kasami functions $x\mapsto x^{2^{2k}-2^k+1}$ with $gcd(k,n)=1$, $x\in\GF{2^n}$

Conditional differential attacks were proposed by Knellwolf et al. at ASIACRYPT 2010 which targeted at cryptographic primitives based on non-linear feedback shift registers. The main idea of conditional differential attacks lies in controlling the propagation of a difference through imposing some conditions on public/key variables. In this paper, we improve the conditional differential attack by introducing the mixed integer linear programming (MILP) method to it. Let $J=\{f_i(\boldsymbol{x},\boldsymbol{v})=\gamma_i| 1\le i\le N\}$ be a set of conditions that we want to impose, where $\boldsymbol{x}=(x_1,x_2,\ldots,x_n)$ (resp. $ \boldsymbol{v}=(v_1,v_2,\ldots,v_n)$) represents key (resp. public) variables and $\gamma_i \in\{0,1\}$ needs evaluating. Previous automatic conditional differential attacks evaluate $\gamma_1,\gamma_2,\ldots,\gamma_N$ just in order with the preference to zero. Based on the MILP method, conditions in $J$ could be automatically analysed together. In particular, to enhance the effect of conditional differential attacks, in our MILP models, we are concerned with minimizing the number of 1's in $\{\gamma_1,\gamma_2,\ldots,\gamma_N\}$ and maximizing the number of weak keys. ~~~We apply our method to analyse the security of Trivium. As a result, key-recovery attacks are preformed up to the 978-round Trivium and non-randomness is detected up to the 1108-round Trivium of its 1152 rounds both in the weak-key setting. All the results are the best known so far considering the number of rounds and could be experimentally verified. Hopefully, the new method would provide insights on conditional differential attacks and the security evaluation of Trivium.

In this paper we provide a theoretical argument towards an unsolved question related to Mantin's ``Digraph Repetition Bias" (Eurocrypt 2005) that is observed in the key-stream of RC4. The open question, that depends on the observation that arrival of four consecutive same bytes (of the form $AAAA$) in RC4 key-stream is slightly negatively biased, was posed by Bricout et al [Des. Codes Cryptogr. (2018) 86:743-770] in 2016. Moreover, for the first time, we consider the ``Reverse Digraph Repetition Bias" and show that there is significant negative bias in arrival of $ABBA$ ($A, B$ two distinct bytes) in RC4 key-stream.

In the context of linear cryptanalysis of block ciphers, let $p_0$ (resp. $p_1$) be the probability that a particular linear approximation holds for the right (resp. a wrong) key choice. The standard right key randomisation hypothesis states that $p_0$ is a constant $p\neq 1/2$ and the standard wrong key randomisation hypothesis states that $p_1=1/2$. Using these hypotheses, the success probability $P_S$ of the attack can be expressed in terms of the data complexity $N$. The resulting expression for $P_S$ is a monotone increasing function of $N$. Building on earlier work by Daemen and Rijmen (2007), Bogdanov and Tischhauser (2014) argued that $p_1$ should be considered to be a random variable. They postulated the adjusted wrong key randomisation hypothesis which states that $p_1$ follows a normal distribution. A non-intuitive consequence was that the resulting expression for $P_S$ is no longer a monotone increasing function of $N$. A later work by Blondeau and Nyberg (2017) argued that $p_0$ should also be considered to be a random variable and they postulated the adjusted right key randomisation hypothesis which states that $p_0$ follows a normal distribution. In this work, we revisit the key randomisation hypotheses. While the argument that $p_0$ and $p_1$ should be considered to be random variables is indeed valid, we consider the modelling of their distributions by normal to be inappropriate. Being probabilities, the support of the distributions of $p_0$ and $p_1$ should be subsets of $[0,1]$ which does not hold for normal distributions. We show that if $p_0$ and $p_1$ follow any distributions with supports which are subsets of $[0,1]$, and $E[p_0]=p$ and $E[p_1]=1/2$, then the expression for $P_S$ that is obtained is exactly the same as the one obtained using the standard key randomisation hypotheses. Consequently, $P_S$ is a monotone increasing function of $N$ even when $p_0$ and $p_1$ are considered to be random variables.

A memory-hard function (MHF) $f_n$ with parameter $n$ can be computed in sequential time and space $n$. Simultaneously, a high amortized parallel area-time complexity (aAT) is incurred per evaluation. In practice, MHFs are used to limit the rate at which an adversary (using a custom computational device) can evaluate a security sensitive function that still occasionally needs to be evaluated by honest users (using an off-the-shelf general purpose device). The most prevalent examples of such sensitive functions are Key Derivation Functions (KDFs) and password hashing algorithms where rate limits help mitigate off-line dictionary attacks. As the honest users' inputs to these functions are often (low-entropy) passwords special attention is given to a class of side-channel resistant MHFs called iMHFs. Essentially all iMHFs can be viewed as some mode of operation (making $n$ calls to some round function) given by a directed acyclic graph (DAG) with very low indegree. Recently, a combinatorial property of a DAG has been identified (called ``depth-robustness'') which results in good provable security for an iMHF based on that DAG. Depth-robust DAGs have also proven useful in other cryptographic applications. Unfortunately, up till now, all known very depth-robust DAGs are impractically complicated and little is known about their exact (i.e. non-asymptotic) depth-robustness both in theory and in practice. In this work we build and analyze (both formally and empirically) several exceedingly simple and efficient to navigate practical DAGs for use in iMHFs and other applications. For each DAG we: - Prove that their depth-robustness is asymptotically maximal. - Prove bounds of at least $3$ orders of magnitude better on their exact depth-robustness compared to known bounds for other practical iMHF. - Implement and empirically evaluate their depth-robustness and aAT against a variety of state-of-the art (and several new) depth-reduction and low aAT attacks. We find that, against all attacks, the new DAGs perform significantly better in practice than Argon2i, the most widely deployed iMHF in practice. Along the way we also improve the best known empirical attacks on the aAT of Argon2i by implementing and testing several heuristic versions of a (hitherto purely theoretical) depth-reduction attack. Finally, we demonstrate practicality of our constructions by modifying the Argon2i code base to use one of the new high aAT DAGs. Experimental benchmarks on a standard off-the-shelf CPU show that the new modifications do not adversely affect the impressive throughput of Argon2i (despite seemingly enjoying significantly higher aAT).

ARX-KW is a family of key wrapping construction based on add-rotate-xor primitives: the pseudo-random function SipHash for authentication and the stream cipher ChaCha for confidentiality. This paper presents ARX-KW, proposes a specific instantiation of ARX-KW and details the design decisions that were made.

Tweakable TWINE (T-TWINE) is a new lightweight tweakable block cipher family proposed by Sakamoto $et$ $al$. at IWSEC 2019. T-TWINE is the first Tweakable Block Cipher (TBC) that is built on Generalized Feistel Structure (GFS). It is based on the TWINE block cipher in addition to a simple tweak scheduling based on SKINNY’s tweakey schedule. Similar to TWINE, it has two versions, namely, T-TWINE-80 and T-TWINE-128, both have a block length of 64 bits and employ keys of length 80 and 128 bits, respectively. In this paper, we present impossible differential attacks against reduced-round versions of T-TWINE-80 and T-TWINE-128. First, we present an 18-round impossible differential distinguisher against T-TWINE. Then, using this distinguisher, we attack 25 and 27 rounds of T-TWINE-80 and T-TWINE-128, respectively.

As the need for lightweight cryptography has grown even more due to the evolution of the Internet of Things, it has become a greater challenge for cryptographers to design ultra lightweight stream ciphers in compliance with the rule of thumb that the internal state size should be at least twice as the key size to defend against generic Time-Memory-Data Tradeoff (TMDT) attacks. However, recently in 2015, Armknecht and Mikhalev sparked a new light on designing keystream generators (KSGs), which in turn yields stream ciphers, with small internal states, called KSG with Keyed Update Function (KSG with KUF), and gave a concrete construction named Sprout. But, currently, security analysis of KSGs with KUF in a general setting is almost non-existent. Our contribution in this paper is two-fold. 1) We give a general mathematical setting for KSGs with KUF, and for the first time, analyze a class of such KSGs, called KSGs with Boolean Keyed Feedback Function (KSG with Boolean KFF), generically. In particular, we develop two generic attack algorithms applicable to any KSG with Boolean KFF having almost arbitrary output and feedback functions where the only requirement is that the secret key incorporation is biased. We introduce an upper bound for the time complexity of the first algorithm. Our extensive experiments validate our algorithms and assumptions made thereof. 2) We study Sprout to show the effectiveness of our algorithms in a practical instance. A straightforward application of our generic algorithm yields one of the most successful attacks on Sprout.

Deep learning based side-channel analysis has seen a rise in popularity over the last few years. A lot of work is done to understand the inner workings of the neural networks used to perform the attacks and a lot is still left to do. However, finding a metric suitable for evaluating the capacity of the neural networks is an open problem that is discussed in many articles. We propose an answer to this problem by introducing an online evaluation metric dedicated to the context of side-channel analysis and use it to perform early stopping on existing convolutional neural networks found in the literature. This metric compares the performance of a network on the training set and on the validation set to detect underfitting and overfitting. Consequently, we improve the performance of the networks by finding their best training epoch and thus reduce the number of traces used by 30%. The training time is also reduced for most of the networks considered.

Password authenticated key establishment (PAKE) is a cryptographic primitive that allows two parties who share a low-entropy secret (a password) to securely establish cryptographic keys in the absence of public key infrastructure. We propose the first quantum-resistant password-authenticated key exchange scheme based on supersingular elliptic curve isogenies. The scheme is built upon supersingular isogeny Diffie-Hellman, and uses the password to generate permutations which obscure the auxiliary points. We include elements of a security proof, and discuss roadblocks to obtaining a proof in the BPR model. We also include some performance results.

Authenticated encryption (AE) schemes are widely used to secure communications because they can guarantee both confidentiality and authenticity of a message. In addition to the standard AE security notion, some recent schemes offer extra robustness, i.e. they maintain security in some misuse scenarios. In particular, Ashur, Dunkelman and Luykx proposed a generic AE construction at CRYPTO'17 that is secure even when releasing unverified plaintext (the RUP setting), and a concrete instantiation, GCM-RUP. The designers proved that GCM-RUP is secure up to the birthday bound in the nonce-respecting model. In this paper, we perform a birthday-bound universal forgery attack against GCM-RUP, matching the bound of the proof. While there are simple distinguishing attacks with birthday complexity on GCM-RUP, our attack is much stronger: we have a partial key recovery leading to universal forgeries. For reference, the best known universal forgery attack against GCM requires $2^{2n/3}$ operations, and many schemes do not have any known universal forgery attacks faster than $2^n$. This suggests that GCM-RUP offers a different security trade-off than GCM: stronger protection in the RUP setting, but more fragile when the data complexity reaches the birthday bound. In order to avoid this attack, we suggest a minor modification of GCM-RUP that seems to offer better robustness at the birthday bound.

This work introduces a new class of Algorithm Substitution Attack (ASA) on Symmetric Encryption Schemes. ASAs were introduced by Bellare, Paterson and Rogaway in light of revelations concerning mass surveillance. An ASA replaces an encryption scheme with a subverted version that aims to reveal information to an adversary engaged in mass surveillance, while remaining undetected by users. Previous work posited that a particular class of AEAD scheme (satisfying certain correctness and uniqueness properties) is resilient against subversion. Many if not all real-world constructions - such as GCM, CCM and OCB - are members of this class. Our results stand in opposition to those prior results. We present a potent ASA that generically applies to any AEAD scheme, is undetectable in all previous frameworks and which achieves successful exfiltration of user keys. We give even more efficient non-generic attacks against a selection of AEAD implementations that are most used in practice.In contrast to prior work, our new class of attack targets the decryption algorithm rather than encryption. We argue that this attack represents an attractive opportunity for a mass surveillance adversary. Our work serves to refine the ASA model and contributes to a series of papers that raises awareness and understanding about what is possible with ASAs.

This paper presents a novel, yet efficient secret-key authentication and MAC, which provide post-quantum security promise, whose security is reduced to the quantum-safe conjectured hardness of Mersenne Low Hamming Combination (MERS) assumption recently introduced by Aggarwal, Joux, Prakash, and Santha (CRYPTO 2018). Our protocols are very suitable to weak devices like smart card and RFID tags.

Linear cryptanalysis is an important evaluation method for cryptographic primitives against key recovery attack. In this paper, we revisit the Walsh transformation for linear correlation calculation of modular addition, and an efficient algorithm is proposed to construct the input-output mask space of specified correlation weight. By filtering out the impossible large correlation weights in the first round, the search space of the first round can be substantially reduced. We introduce a new construction of combinational linear approximation table (cLAT) for modular addition with two inputs. When one input mask is fixed, another input mask and the output mask can be obtained by the \textit{Spliting-Lookup-Recombination} approach. We first split the $n$-bit fixed input mask into several sub-vectors, then, to find the corresponding bits of other masks, and in the recombination phase, pruning conditions can be used. By this approach, a large number of search branches in the middle rounds can be pruned. With the combination of the optimization strategies and the branch-and-bound search algorithm, we can improve the search efficiency for linear characteristics on ARX ciphers. The linear hulls for SPECK32/48/64 with higher average linear potential ($ALP$) than existing results have been obtained. For SPARX variants, a 11-round linear trail and a 10-round linear hull have been found for SPARX-64, a 10-round linear trail and a 9-round linear hull are obtained for SPARX-128. For Chaskey, a 5-round linear trail with correlation of $2^{-61}$ have been obtained. For CHAM-64, the 34/35-round optimal linear characteristics with correlation of $2^{-31}$/$2^{-33}$ are found.

Motivated by the algorithm of differential probability calculation of Lipmaa and Moriai, we revisit the differential properties of modular addition. We propose an efficient approach to generate the input-output difference tuples with non-zero probabilities. A novel construction of combinational DDT, which makes it possible to obtain all valid output differences for fixed input differences. According to the upper bound of differential probability of modular addition, combining the optimization strategies with branch and bound search algorithm, we can reduce the search space of the first round and prune the invalid difference branches of the middle rounds. Applying this tool, the provable optimal differential trails covering more rounds for SPECK32/48/64 with tight probabilities can be found, and the differentials with larger probabilities are also obtained. In addition, the optimal differential trails cover more rounds than exisiting results for SPARX variants are obtained. A 12-round differential with a probability of $2^{-54.83}$ for SPARX-64, and a 11-round differential trail with a probability of $2^{-53}$ for SPARX-128 are found. For CHAM-64/128 and CHAM-128/*, the 39/63-round differential characteristics we find cover 3/18 rounds more than the known results respectively.

This document contains supplementary material to the paper with the same title available from the proceedings of the International Conference on Information Security and Cryptology (ICISC) 2019. In this supplementary material, we demonstrate that the random fault attack strategy described in the full paper can be applied to ciphers in the MORUS family, resulting in partial state recovery for these ciphers.

Lai-Massey scheme is a well-known block cipher structure which has been used in the design of the ciphers PES, IDEA, WIDEA, FOX and MESH. Recently, the lightweight block cipher FLY applied this structure in the construction of a lightweight $8 \times 8$ S-box from $4 \times 4$ ones. In the current paper, firstly we investigate the linear, differential and algebraic properties of the general form of S-boxes used in FLY, mathematically. Then, based on this study, a new cipher structure is proposed which we call generalized Lai-Massey scheme or GLM. We give upper bounds for the maximum average differential probability (MADP) and maximum average linear hull (MALH) of GLM and after examination of impossible differentials and zero-correlations of one round of this structure, we show that two rounds of GLM do not have any structural impossible differentials or zero-correlations. As a measure of structural security, we prove the pseudo-randomness of GLM by the H-coefficient method.

In CRYPTO 2017, Dai, Hoang, and Tessaro introduced the {\em Chi-square method} ($\chi^2$ method) which can be applied to obtain an upper bound on the statistical distance between two joint probability distributions. The authors applied this method to prove the {\em pseudorandom function security} (PRF-security) of sum of two random permutations. In this work, we revisit their proof and find a non-trivial gap in the proof and describe how to plug this gap as well; this has already been done by Dai {\em et al.} in the revised version of their CRYPTO 2017 paper. A complete, correct, and transparent proof of the full security of the sum of two random permutations construction is much desirable, especially due to its importance and two decades old legacy. The proposed $\chi^2$ method seems to have potential for application to similar problems, where a similar gap may creep into a proof. These considerations motivate us to communicate our observation in a formal way.\par On the positive side, we provide a very simple proof of the PRF-security of the {\em truncated random permutation} construction (a method to construct PRF from a random permutation) using the $\chi^2$ method. We note that a proof of the PRF-security due to Stam is already known for this construction in a purely statistical context. However, the use of the $\chi^2$ method makes the proof much simpler.

SipHash is a family of ARX-based MAC algorithms optimized for short inputs. Already, a lot of implementations and applications for SipHash have been proposed, whereas the cryptanalysis of SipHash still lags behind. In this paper, we study the property of truncated differential in SipHash and find out the output bits with the most imbalanced differential biases. Making use of these results, we construct distinguishers with practical complexity $2^{10}$ for SipHash-2-1 and $2^{36}$ for SipHash-2-2. We further reveal the relations between the value of output bias and the difference after first modular addition step, which is directly determined by corresponding key bits. Based on these relations, we propose a key recovery method for SipHash-2-1 that can obtain a nonuniform distribution of the 128-bit key through several bias tests. It is found that the highest probability can reach $2^{-41}$ and the nonuniform distribution can lead to a $2^{29}$ gain of search cost in average.

We propose a general method for security evaluation of SNOW 2.0-like ciphers against correlation attacks that are built similarly to known attacks on SNOW 2.0. Unlike previously known methods, the method we propose is targeted at security proof and allows obtaining lower bounds for efficiency of attacks from the class under consideration directly using parameters of stream cipher components similarly to techniques for security proofs of block ciphers against linear cryptanalysis. The method proposed is based upon automata-theoretic approach to evaluation the imbalance of discrete functions. In particular, we obtain a matrix representation and upper bounds for imbalance of an arbitrary discrete function being realized by a sequence of finite automata. These results generalize a number of previously known statements on matrix (linear) representations for imbalance of functions having specified forms, and may be applied to security proofs for other stream ciphers against correlation attacks. Application of this method to SNOW 2.0 and Strumok ciphers shows that any of the considered correlation attacks on them over the field of the order 256 has an average time complexity not less than $2^{146.20}$ and $2^{249.40}$ respectively, and requires not less than $2^{142.77}$ and, respectively, $2^{249.38}$ keystream symbols.

This work introduces \sym{FAST} which is a new family of tweakable enciphering schemes. Several instantiations of \sym{FAST} are described. These are targeted towards two goals, the specific task of disk encryption and a more general scheme suitable for a wide variety of practical applications. A major contribution of this work is to present detailed and careful software implementations of all of these instantiations. For disk encryption, the results from the implementations show that \sym{FAST} compares very favourably to the IEEE disk encryption standards XCB and EME2 as well as the more recent proposal AEZ. \sym{FAST} is built using a fixed input length pseudo-random function and an appropriate hash function. It uses a single-block key, is parallelisable and can be instantiated using only the encryption function of a block cipher. The hash function can be instantiated using either the Horner's rule based usual polynomial hashing or hashing based on the more efficient Bernstein-Rabin-Winograd polynomials. Security of \sym{FAST} has been rigorously analysed using the standard provable security approach and concrete security bounds have been derived. Based on our implementation results, we put forward \sym{FAST} as a serious candidate for standardisation and deployment.

The proliferation of small embedded devices having growing but still limited computing and data storage facilities, and the related development of cloud services with extensive storage and computing means, raise nowadays new privacy issues because of the outsourcing of data processing. This has led to a need for symmetric cryptosystems suited for hybrid symmetric-FHE encryption protocols, ensuring the practicability of the FHE solution. Recent ciphers meant for such use have been introduced, such as LowMC, Kreyvium, FLIP, and Rasta. The introduction of stream ciphers devoted to symmetric-FHE frameworks such as FLIP and its recent modification has in its turn posed new problems on the Boolean functions to be used in them as filter functions. We recall the state of the art in this matter and present further studies (without proof).

Differential branch number and linear branch number are critical for the security of symmetric ciphers. The recent trend in the designs like PRESENT block cipher, ASCON authenticated encryption shows that applying S-boxes that have nontrivial differential and linear branch number can significantly reduce the number of rounds. As we see in the literature that the class of 4 x 4 S-boxes have been well-analysed, however, a little is known about the n x n S-boxes for n >= 5. For instance, the complete classification of 5 x 5 affine equivalent S-boxes is still unknown. Therefore, it is challenging to obtain “the best” S-boxes with dimension >= 5 that can be used in symmetric cipher designs. In this article, we present a novel approach to construct S-boxes that identifies classes of n x n S-boxes (n = 5, 6) with differential branch number 3 and linear branch number 3, and ensures other cryptographic properties. To the best of our knowledge, we are the first to report 6 x 6 S-boxes with linear branch number 3, differential branch number 3, and with other good cryptographic properties such as nonlinearity 24 and differential uniformity 4.

We investigate constructing message authentication schemes from symmetric cryptographic primitives, with the goal of achieving security when most intermediate values during tag computation and verification are leaked (i.e., mode-level leakage-resilience). Existing efficient proposals typically follow the plain Hash-then-MAC paradigm $T=MAC_K(H(M))$. When the domain of the MAC function $MAC_K$ is $\{0,1\}^{128}$, e.g., when instantiated with the AES, forgery is possible within time $2^{64}$ and data complexity 1. To dismiss such cheap attacks, we propose two modes: LRW1-based Hash-then-MAC (LRWHM) that is built upon the LRW1 tweakable blockcipher of Liskov, Rivest, and Wagner, and Rekeying Hash-then-MAC (RHM) that employs internal rekeying. Built upon secure AES implementations, LRWHM is provably secure up to (beyond-birthday) $2^{78.3}$ time complexity, while RHM is provably secure up to $2^{121}$ time. Thus in practice, their main security threat is expected to be side-channel key recovery attacks against the AES implementations. Finally, we benchmark the performance of instances of our modes based on the AES and SHA3 and confirm their efficiency.

In this paper, we propose a new method to launch a more efficient algebraic cryptanalysis. Algebraic cryptanalysis aims at finding the secret key of a cipher by solving a collection of polynomial equations that describe the internal structure of the cipher, while chosen correlated plaintexts, as what appear in higher order differential cryptanalysis and its derivatives such as cube attack or integral cryptanalysis, forces many linear relation between intermediate state bits in the cipher. In this paper, we take these polynomial relations into account, so it become possible to simplify the equation system arising from algebraic cryptanalysis, and consequently solve the polynomial system more efficiently. We take advantage of Universal Proning technique to provide an efficient method to recover such linear polynomials. Another important parameter in algebraic cryptanalysis of ciphers is to effectively describe the cipher. We employ FWBW representation of S-boxes together with Universal Proning to help provide a more powerful algebraic cryptanalysis based on Gröbner-basis computation. We show our method is more efficient than doing algebraic cryptanalysis with MQ representation, and also than employing MQ together with Universal Proning. To show the effectiveness of our approach, we applied it for the cryptanalysis of several light weight block ciphers. A by-product of employing this approach is that we have achieved such an efficiency to algebraic cryptanalyse 12-round LBlock, 6-round MIBS, 7-round PRESENT and 9-round SKINNY light-weight block ciphers, so far.

Authenticity can be compromised by information leaked via side-channels (e.g., power consumption). Examples of attacks include direct key recoveries and attacks against the tag verification which may lead to forgeries. At FSE 2018, Berti et al. described two authenticated encryption schemes which provide authenticity assuming a “leak-free implementation” of a Tweakable Block Cipher (TBC). Precisely, security is guaranteed even if all the intermediate computations of the target implementation are leaked in full but the TBC long-term key. Yet, while a leak-free implementation reasonably models strongly protected implementations of a TBC, it remains an idealized physical assumption that may be too demanding in many cases, in particular, if hardware engineers mitigate the leakage to a good extent but (due to performance constraints) do not reach leak-freeness. In this paper, we get rid of this important limitation by introducing the notion of “Strong Unpredictability with Leakage” for BC's and TBC's. It captures the hardness for an adversary to provide a fresh and valid input/output pair for a (T)BC, even having oracle access to the (T)BC, its inverse and their leakages. This definition is game-based and may be verified/falsified by laboratories. Based on it, we then provide two Message Authentication Codes (MAC) which are secure if the (T)BC on which they rely are implemented in a way that maintains a sufficient unpredictability. Thus, we improve the theoretical foundations of leakage-resilient MAC and extend them towards engineering constraints that are easier to achieve in practice.

Tweakable block ciphers are increasingly becoming a common primitive to build new resilient modes as well as a concept for multiple dedicated designs. While regular block ciphers define a family of permutations indexed by a secret key, tweakable ones define a family of permutations indexed by both a secret key and a public tweak. In this work we formalize and study a generic framework for building such a tweakable block cipher based on regular block ciphers, the iterated tweakable FX construction, which includes many such previous constructions of tweakable block ciphers. Then we describe a cryptanalysis from which we can derive a provable security upper-bound for all constructions following this tweakable iterated FX strategy. Concretely, the cryptanalysis of r rounds of our generic construction based on n-bit block ciphers with \kap-bit keys requires O(2^{r(n + \kap)/(r+1)}) online and offline queries. For r = 2 rounds this interestingly matches the proof of the particular case of XHX2 by Lee and Lee (ASIACRYPT 2018) thus proving for the first time its tightness. In turn, the XHX and XHX2 proofs show that our generic cryptanalysis is information theoretically optimal for 1 and 2 rounds.

Differential Power Analysis and Differential Fault Analysis threaten the security of even the most trustworthy cryptographic primitives. It is important we protect their implementation such that no sensitive information is leaked using side channels and it withstands injected faults or combined physical attacks. In this work, we propose security notions tailored against advanced physical attacks consisting of both faults and probes on circuit wires. We then transform the security notions to composable security notions. The motivation for this research includes the ease of verification time; the creation of secure components; and the isolation of primitives in larger protocols such as modes of operations. We dub our notion NINA, which forms the link between the established Non-Interference (NI) property and our composable active security property, Non-Accumulation (NA). To illustrate the NINA property, we use it to prove the security of two multiplication gadgets: an error checking duplication gadget and an error correcting duplication gadget. The NINA proofs for error detecting gadgets capture the effect of Statistical Ineffective Fault Analysis (SIFA), an attack vector which threatens most current masked implementations. Additionally, we study error correcting techniques. We show that error correcting gadgets can attain the Independent NINA property. A stronger property which captures a clear separation between the effect of faults and probes. Thus, we show that clever error correcting gadgets improve on error detecting ones by achieving significant higher levels of combined security along with guaranteed output delivery.

Given the links between nonlinearity properties and the related tables such as LAT, DDT, BCT and ACT that have appeared in the literature, the boomerang connectivity table BCT seems to be an outlier as it cannot be derived from the others using Walsh-Hadamard transform. In this paper, a brief unified summary of the existing links for general vectorial Boolean functions is given first and then a link between the autocorrelation and boomerang connectivity tables is established.

Obtaining compact, while cryptographically strong, S-boxes is a challenging task required for hardware implementations of lightweight cryptography. Contrarily to 4-bit permutations design which is somewhat well understood, 8-bit permutations have mainly been investigated only through structured S-boxes built from 4-bit ones by means of Feistel, MISTY or SPN schemes. In this paper, we depart from this common habit and search for compact designs directly in the space of 8-bit permutations. We propose two methods for searching good and compact 8-bit S-boxes. One is derived from an adaptation to 8-bit circuits of a systematic bottom-up exploration already used in previous works for 4-bit permutations. The other is the use of a genetic algorithm that samples solutions in the 8-bit permutations space and makes them evolve toward predefined criteria. Contrarily to similar previous attempts, we chose to encode permutations by their circuits rather than by their tables, which allows to optimize non only w.r.t the cryptographic quality but also w.r.t. compactness. We obtain results which show competitive compared to structured designs and we provide an overview of the relation between quality and compactness in the range of rather small 8-bit circuits. Beside, we also exhibit a 8-gate circuit made of only AND and XOR gates that represents a 4-bit permutation belonging to an optimal equivalence class. This shows that such optimal class can be instantiated by threshold implementation friendly circuits with no extra cost compared to previous works.

ASCON is an authenticated encryption, selected as the first choice for a lightweight use case in the CAESAR competition in February 2019. In this work, we investigate vulnerabilities of ASCON against fault analysis. We observe that the use of 128-bit random nonce makes it resistant against many cryptanalysis techniques like differential, linear, etc. and their variants. However, XORing the key just before releasing the tag T (a public value) creates a trivial attack path. Also, the S-Box demonstrates a non-random behavior towards subset cryptanalysis. We observe that if the 3rd bit of the S-box input is set to zero, then XoR of the last two output bits is zero, with a probability of $0.625$, i.e., this characteristic is present in 10 out of 16 cases. Our subset fault analysis(SSFA) attack uses this property to retrieve the 128-bit secret key. The SSFA attack can uniquely retrieve the key of full-round ASCON with the complexity of $2^{64}$.

SNOW 3G is a stream cipher designed in 2006 by ETSI/SAGE, serving in 3GPP as one of the standard algorithms for data confidentiality and integrity protection. It is also included in the 4G LTE standard. In this paper we derive vectorized linear approximations of the finite state machine in SNOW 3G. In particular, we show one 24-bit approximation with a bias around $2^{-37}$ and one byte-oriented approximation with a bias around $2^{-40}$. We then use the approximations to launch attacks on SNOW 3G. The first approximation is used in a distinguishing attack resulting in an expected complexity of $2^{172}$ and the second one can be used in a standard fast correlation attack resulting in key recovery in an expected complexity of $2^{177}$. If the key length in SNOW 3G would be increased to 256 bits, the results show that there are then academic attacks on such a version faster than the exhaustive key search.

Subterranean 2.0 designed by Daemen, Massolino and Rotella is a Round 2 candidate of the NIST Lightweight Cryptography Standardization process. In the official document of Subterranean 2.0, the designers have analyzed the state collisions in unkeyed absorbing by reducing the number of rounds to absorb the message from 2 to 1. However, little cryptanalysis of the authenticated encryption scheme Subterranean-SAE is made. For Subterranean-SAE, the designers introduce 8 blank rounds to separate the controllable input and output, and expect that 8 blank rounds can achieve a sufficient diffusion. Therefore, it is meaningful to investigate the security by reducing the number of blank rounds. Moreover, the designers make no security claim but expect a non-trivial effort to achieve full-state recovery in a nonce-misuse scenario. In this paper, we present the first practical full-state recovery attack in a nonce-misuse scenario with data complexity of $2^{13}$ 32-bit blocks. In addition, in a nonce-respecting scenario and if the number of blank rounds is reduced to 4, we can mount a key-recovery attack with $2^{122}$ calls to the internal permutation of Subterranean-SAE and $2^{69.5}$ 32-bit blocks. A distinguishing attack with $2^{33}$ calls to the internal permutation of Subterranean-SAE and $2^{33}$ 32-bit blocks is achieved as well. Our cryptanalysis does not threaten the security claim for Subterranean-SAE and we hope it can enhance the understanding of Subterranean-SAE.

We formalize and analyze the general suffix keyed sponge construction, a pseudorandom function built on top of a cryptographic permutation. The construction hashes its data using the (keyless) sponge construction, transforms part of the state using the secret key, and generates the tag from the output of a final permutation call. In its simplest form, if the key and tag size are at most the rate of the sponge, one can see the suffix keyed sponge as a simple sponge function evaluation whose input is the plaintext appended with the key. The suffix keyed sponge is, however, much more general: the key and tag size may exceed the rate without any need to make extra permutation calls. We prove that the suffix keyed sponge construction achieves birthday-bound PRF security in the capacity, even if key and tag size exceed the rate. Furthermore, we prove that if the absorption of the key into the state happens in a leakage resilient manner, the suffix keyed sponge itself is leakage resilient as well. Our findings show that the suffix keyed sponge compares favorably with the hash-then-MAC construction. For instance, to reach a security level of $k$ bits, the side-channel protected component in the suffix keyed sponge just needs to process $k$ bits of input besides the key, whereas schemes following the hash-then-MAC construction need a side-channel protected MAC function that processes $2k$ bits of input besides the key. Moreover, even if we just consider black-box attacks, the MAC function in a hash-then-MAC scheme needs to be cryptographically strong whereas in the suffix keyed sponge the key may be absorbed by a simple XOR. The security proofs are performed using the H-coefficient technique, and make effective use of the multicollision limit function results of Daemen et al. (ASIACRYPT 2017), both for arguing that state manipulation larger than the rate is tolerated after key processing and for upper bounding the amount of leakage an attacker may gain about the secret key.

Authenticated encryption schemes are usually expected to offer confidentiality and authenticity. In case of release of unverified plaintext (RUP), an adversary gets separated access to the decryption and verification functionality, and has more power in breaking the scheme. Andreeva et al. (ASIACRYPT 2014) formalized RUP security using plaintext awareness, informally meaning that the decryption functionality gives no extra power in breaking confidentiality, and INT-RUP security, covering authenticity in case of RUP. We describe a single, unified model, called AERUP security, that ties together these notions: we prove that an authenticated encryption scheme is AERUP secure if and only if it is conventionally secure, plaintext aware, and INT-RUP secure. We next present ANYDAE, a generalization of SUNDAE of Banik et al. (ToSC 2018/3). ANYDAE is a lightweight deterministic scheme that is based on a block cipher with block size $n$ and arbitrary mixing functions that all operate on an $n$-bit state. It is particularly efficient for short messages, it does not rely on a nonce, and it provides maximal robustness to a lack of secure state. Whereas SUNDAE is not secure under release of unverified plaintext (a fairly simple attack can be mounted in constant time), ANYDAE is. We make handy use of the AERUP security model to prove that ANYDAE achieves both conventional security as RUP security, provided that certain modest conditions on the mixing functions are met. We describe two simple instances, called MONDAE and TUESDAE, that conform to these conditions and that are competitive with SUNDAE, in terms of efficiency and optimality.

A new approach to invariant subspaces and nonlinear invariants is developed. This results in both theoretical insights and practical attacks on block ciphers. It is shown that, with minor modifications to some of the round constants, Midori-64 has a nonlinear invariant with $2^{96}$ corresponding weak keys. Furthermore, this invariant corresponds to a linear hull with maximal correlation. By combining the new invariant with integral cryptanalysis, a practical key-recovery attack on 10 rounds of unmodified Midori-64 is obtained. The attack works for $2^{96}$ weak keys and irrespective of the choice of round constants. The data complexity is $1.25 \cdot 2^{21}$ chosen plaintexts and the computational cost is dominated by $2^{56}$ block cipher calls. Finally, it is shown that similar techniques lead to a practical key-recovery attack on MANTIS-4. The full key is recovered using 640 chosen plaintexts and the attack requires about $2^{56}$ block cipher calls. Finally, it is shown that similar techniques lead to a practical key-recovery attack on Mantis-4. The full key is recovered using roughly $350$ chosen plaintexts and the attack requires about $2^{56}$ block cipher calls. Furthermore, given less than $350$ additional chosen ciphertexts under a related tweak, $2^{18}$ block cipher calls suffice to recover the full key.

\textsf{HCTR}, proposed by Wang et al., is one of the most efficient candidates of tweakable enciphering schemes that turns an $n$-bit block cipher into a variable input length tweakable block cipher. Wang et al. have shown that \textsf{HCTR} offers a cubic security bound against all adaptive chosen plaintext and chosen ciphertext adversaries. Later in FSE 2008, Chakraborty and Nandi have improved its bound to $O(\sigma^2 / 2^n)$, where $\sigma$ is the total number of blocks queried and $n$ is the block size of the block cipher. In this paper, we propose \textbf{tweakable \textsf{HCTR}} that turns an $n$-bit tweakable block cipher to a variable input length tweakable block cipher by replacing all the block cipher calls of \textsf{HCTR} with tweakable block cipher. We show that when there is no repetition of the tweak, tweakable \textsf{HCTR} enjoys the optimal security against all adaptive chosen plaintext and chosen ciphertext adversaries. However, if the repetition of the tweak is limited, then the security of the construction remains close to the security bound in no repetition of the tweak case. Hence, it gives a graceful security degradation with the maximum number of repetition of tweaks.

As perfect building blocks for the diffusion layers of many symmetric-key primitives, the construction of MDS matrices with light-weight circuits has received much attention from the symmetric-key community. One promising way of realizing low-cost MDS matrices is based on the iterative construction: a low-cost matrix becomes MDS after rising it to a certain power. To be more specific, if $A^t$ is MDS, then one can implement $A$ instead of $A^t$ to achieve the MDS property at the expense of an increased latency with $t$ clock cycles. In this work, we identify the exact lower bound of the number of nonzero blocks for a $4 \times 4$ block matrix to be potentially iterative-MDS. Subsequently, we show that the theoretically lightest $4 \times 4$ iterative MDS block matrix (whose entries or blocks are $4 \times 4$ binary matrices) with minimal nonzero blocks costs at least 3 XOR gates, and a concrete example achieving the 3-XOR bound is provided. Moreover, we prove that there is no hope for previous constructions (GFS, LFS, DSI, and spares DSI) to beat this bound. Since the circuit latency is another important factor, we also consider the lower bound of the number of iterations for certain iterative MDS matrices. Guided by these bounds and based on the ideas employed to identify them, we explore the design space of lightweight iterative MDS matrices with other dimensions and report on improved results. Whenever we are unable to find better results, we try to determine the bound of the optimal solution. As a result, the optimality of some previous results is proved.

Division property is a new cryptanalysis method introduced by Todo at Eurocrypt'15 that proves to be very efficient on block ciphers and stream ciphers. It can be viewed as a generalization or a more precise version of integral cryptanalysis, that allows to take into account bit properties. However, it is very cumbersome to study the propagation of a given division property through the layers of a block cipher. Fortunately, computer-aided techniques can be used to this end and many new results have been found. Nonetheless, we claim that the previous techniques do not consider the full search space. Indeed, we show that even if the previous techniques fail to find a distinguisher based on the division property over a given function $E$, we can find a distinguisher over a linearly equivalent function, i.e. over $L_{out} \circ E \circ L_{in}$ with $L_{out}$ and $L_{in}$ being linear mappings, and such distinguisher is still relevant. We first show that the representation of the block cipher heavily influences the propagation of the division property, and exploiting this, we give an algorithm to efficiently search for such linear mappings $L_{out}$ and $L_{in}$. As a result, we are able to exhibit a new distinguisher over 10 rounds of RECTANGLE, while the previous best known distinguisher was over 9 rounds. Our algorithm also allows us to rule out such distinguisher over strictly more than 9 rounds of PRESENT, which is the highest known number of rounds on which we can build an integral distinguisher. Finally, we also give some insight about the construction of an S-box to strengthen a block cipher against our technique. We first prove that if an S-box satisfies a certain criteria, then using this S-box is optimal in term of resistance against classical division property. According to this, we exhibit some stronger variants of RECTANGLE and PRESENT, on which the maximum number of rounds we can distinguish is 2 rounds lower than the original, thus more secure against division property.

We draw attention to a gap between theory and usage of nonce-based symmetric encryption, under which the way the former treats nonces can result in violation of privacy in the latter. We bridge the gap with a new treatment of nonce-based symmetric encryption that modifies the syntax (decryption no longer takes a nonce), upgrades the security goal (asking that not just messages, but also nonces, be hidden) and gives simple, efficient schemes conforming to the new definitions. We investigate both basic security (holding when nonces are not reused) and advanced security (misuse resistance, providing best-possible guarantees when nonces are reused).