In this paper, we first demonstrate a new Differential Power Analysis (DPA) attack technique against the Grain family of stream ciphers (Grain v1 and Grain-128) by resynchronizing the cipher multiple times with the same value of the secret \emph{key} and randomly generated different initialization vectors (IVs). Subsequently, we develop a combined side channel and fault analysis attack strategy targeting various fault attack countermeasures for the Grain cipher family. We considered clock glitch induced faults occurring in practice for a hardware implementation of the cipher to devise our novel attack technique. Our proposed combined attack strategy works well even if the \emph{useful} ciphertexts are not available to the adversary. Further, the power trace classifications of a Grain cipher implementation on SASEBO G-II standard side channel evaluation board is shown in order to validate our proposed attack against the cipher. The captured power traces were analyzed using Least Squares Support Vector Machine (LS-SVM) learning algorithm based multiclass classifiers to classify the power traces into the respective Hamming distance (HD) classes. To extract power samples with high information about HD classes, Signal-to-noise ratio (SNR) metric was chosen for feature selection. The experimental results of power trace classifications of test set showed a high success rate of $98\%$ when the five largest SNR sample instants over a clock cycle were chosen as features. Our proposed attack strategy can also be extended to other stream cipher designs based on Fibonacci configured shift registers.

In the last one-and-a-half decade there has been a lot of activity towards development of cryptographic techniques for disk encryption. It has been almost canonised that an encryption scheme suitable for the application of disk encryption must be length preserving, i.e., it rules out the use of schemes like authenticated encryption where an authentication tag is also produced as a part of the ciphertext resulting in ciphertexts being longer than the corresponding plaintexts. The notion of a tweakable enciphering scheme (TES) has been formalised as the appropriate primitive for disk encryption and it has been argued that they provide the maximum security possible for a tag-less scheme. On the other hand, TESs are less efficient than some existing authenticated encryption schemes. Also TES cannot provide true authentication as they do not have authentication tags. In this paper, we analyze the possibility of the use of encryption schemes where length expansion is produced for the purpose of disk encryption. On the negative side, we argue that nonce based authenticated encryption schemes are not appropriate for this application. On the positive side, we demonstrate that deterministic authenticated encryption (DAE) schemes may have more advantages than disadvantages compared to a TES when used for disk encryption. Finally, we propose a new deterministic authenticated encryption scheme called BCTR which is suitable for this purpose. We provide the full specification of BCTR, prove its security and also report an efficient implementation in reconfigurable hardware. Our experiments suggests that BCTR performs significantly better than existing TESs and existing DAE schemes.

In this paper, we propose a new hardware friendly authen- ticated encryption (AE) scheme TriviA based on (i) a stream cipher for generating keys for the ciphertext and the tag, and (ii) a pairwise in- dependent hash to compute the tag. We have adopted one of the ISO- standardized stream ciphers for lightweight cryptography, namely Triv- ium, to obtain our underlying stream cipher. This new stream cipher has a state that is a little larger than the state of Trivium to accommodate a 128-bit secret key and IV. Our pairwise independent hash is also an adaptation of the EHC or “Encode-Hash-Combine” hash, that requires the optimum number of field multiplications and hence requires small hardware footprint. We have implemented the design in synthesizable RTL. Pre-layout synthesis, using 65 nm standard cell technology under typical operating conditions, reveals that TriviA is able to achieve a high throughput of 91.2 Gbps for an area of 24.4 KGE. We prove that our construction has at least 128-bit security for privacy and 124-bit security of authenticity under the assumption that the underlying stream cipher produces a pseudorandom bit stream.

Methods are presented to derive with the aid of the computer mathematics software system SageMath the Multivariate Quadratic equation systems (MQ) for the input and output bit variables of a cryptographic S-box starting from its algebraic expressions. Motivation to this work were the results of recent articles which we have verified and extended in an original way, to our knowledge, not yet published elsewhere. At the same time we present results contrary to the published ones which cast serious doubts on the suitability of previously presented formulas, supposed to quantify the resistance of S-boxes against algebraic attacks.

Two (so-called $C, D$) classes of permutation-based bent Boolean functions were introduced by Carlet two decades ago, but without specifying some explicit construction methods for their construction (apart from the subclass $D_0$). In this article, we look in more detail at the $C$ class, and derive some existence and nonexistence results concerning the bent functions in the $C$ class for many of the known classes of permutations over $\mathbb F_{2^n}$. Most importantly, the existence results induce generic methods of constructing bent functions in class $C$ which possibly do not belong to the completed Maiorana-McFarland class. The question whether the specific permutations and related subspaces we identify in this article indeed give bent functions outside the completed Maiorana-McFarland class remains open.

Gentry’s bootstrapping technique is the most famous method of obtaining fully homomorphic encryption. In this paper I propose a new fully homomorphic encryption scheme on non-associative octonion ring over finite field without bootstrapping technique. The security of the proposed fully homomorphic encryption scheme is based on computational difficulty to solve the multivariate algebraic equations of high degree while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. Because proposed fully homomorphic encryption scheme is based on multivariate algebraic equations with high degree or too many variables, it is against the Gröbner basis attack, the differential attack, rank attack and so on. The key size of this system and complexity for enciphering/deciphering become to be small enough to handle.

Let P be chosen uniformly from the set P := Perm(S), the set of all permutations over a set S of size N. In Crypto 2015, Minaud and Seurin proved that for any unbounded time adversary A, making at most q queries, the distinguishing advantage between P^r (after sampling P, compose it for r times) and P, denoted Delta(P^r ; P), is at most (2r + 1)q/N. In this paper we provide an alternative simple proof of this result for an upper bound 2q(r+1)^2/N by using well known coefficient H-technique.

This paper analyses the cryptography used in the Open Smart Grid Protocol (OSGP). The authenticated encryption (AE) scheme deployed by OSGP is a non-standard composition of RC4 and a home-brewed MAC, the ``OMA digest''. We present several practical key-recovery attacks against the OMA digest. The first and basic variant can achieve this with a mere $13$ queries to an OMA digest oracle and negligible time complexity. A more sophisticated version breaks the OMA digest with only $4$ queries and a time complexity of about $2^{25}$ simple operations. A different approach only requires one arbitrary valid plaintext-tag pair, and recovers the key in an average of $144$ \emph{message verification} queries, or one ciphertext-tag pair and $168$ \emph{ciphertext verification} queries. Since the encryption key is derived from the key used by the OMA digest, our attacks break both confidentiality and authenticity of OSGP.

In this article, we analyse the known-key security of the standardized PRESENT lightweight block cipher. Namely, we propose a known-key distinguisher on the full PRESENT, both 80- and 128-bit key versions. We first leverage the very latest advances in differential cryptanalysis on PRESENT, which are as strong as the best linear cryptanalysis in terms of number of attacked rounds. Differential properties are much easier to handle for a known-key distinguisher than linear properties, and we use a bias on the number of collisions on some predetermined input/output bits as distinguishing property. In order to reach the full PRESENT, we eventually introduce a new meet-in-the-middle layer to propagate the differential properties as far as possible. Our techniques have been implemented and verified on the small scale variant of PRESENT. While the known-key security model is very generous with the attacker, it makes sense in practice since PRESENT has been proposed as basic building block to design lightweight hash functions, where no secret is manipulated. Our distinguisher can for example apply to the compression function obtained by placing PRESENT in a Davies-Meyer mode. We emphasize that this is the very first attack that can reach the full number of rounds of the PRESENT block cipher.

In this paper, we present improved preimage attacks on the reduced-round \texttt{GOST} hash function family, which serves as the new Russian hash standard, with the aid of techniques such as the rebound attack, the Meet-in-the-Middle preimage attack and the multicollisions. Firstly, the preimage attack on 5-round \texttt{GOST-256} is proposed which is the first preimage attack for \texttt{GOST-256} at the hash function level. Then we extend the (previous) attacks on 5-round \texttt{GOST-256} and 6-round \texttt{GOST-512} to 6.5 and 7.5 rounds respectively by exploiting the involution property of the \texttt{GOST} transposition operation. Secondly, inspired by the preimage attack on \texttt{GOST-256}, we also study the impacts of four representative truncation patterns on the resistance of the Meet-in-the-Middle preimage attack against \texttt{AES}-like compression functions, and propose two stronger truncation patterns which make it more difficult to launch this type of attack. Based on our investigations, we are able to slightly improve the previous pseudo preimage attacks on reduced-round \texttt{Grøstl-256}.

The \texttt{Whirlwind} hash function, which outputs a 512-bit digest, was designed by Barreto $et\ al.$ and published by \textit{Design, Codes and Cryptography} in 2010. In this paper, we provide a thorough cryptanalysis on \texttt{Whirlwind}. Firstly, we focus on security properties at the hash function level by presenting (second) preimage, collision and distinguishing attacks on reduced-round \texttt{Whirlwind}. In order to launch the preimage attack, we have to slightly tweak the original Meet-in-the-Middle preimage attack framework on \texttt{AES}-like compression functions by partially fixing the values of the state. Based on this slightly tweaked framework, we are able to construct several new and interesting preimage attacks on reduced-round \texttt{Whirlpool} and \texttt{AES} hashing modes as well. Secondly, we investigate security properties of the reduced-round components of \texttt{Whirlwind}, including semi-free-start and free-start (near) collision attacks on the compression function, and a limited-birthday distinguisher on the inner permutation. As far as we know, our results are currently the best cryptanalysis on \texttt{Whirlwind}.

The all-subkeys recovery (ASR) attack is an extension of the meet-in-the-middle attack, which allows evaluating the security of a block cipher without analyzing its key scheduling function. Combining the ASR attack with some advanced techniques such as the function reduction and the repetitive ASR attack, we show the improved ASR attacks on the 7-round reduced FOX64 and FOX128. Moreover, the improved ASR attacks on the 119-, 105- and 99-round reduced KATAN32, KATAN48 and KATAN64, and the 42-round reduced SHACAL-2 are also presented, respectively. As far as we know, all of those attacks are the best single-key attacks with respect to the number of attacked rounds in literature.

A side-channel analysis of multiplication in GF(2^{128}) has recently been published by Belaïd, Fouque and Gérard at Asiacrypt 2014, with an application to AES-GCM. Using the least significant bit of the Hamming weight of the multiplication result, the authors have shown how to recover the secret multiplier efficiently. However such least significant bit is very sensitive to noise measurement; this implies that without averaging their attack can only work for high signal-to-noise ratios (SNR > 128). In this paper we describe a new side-channel attack against the multiplication in GF(2^{128}) that uses the most significant bits of the Hamming weight. We show that much higher values of noise can be then tolerated. For instance with an SNR equal to 8, the key can be recovered using 2^{20} consumption traces with time and memory complexities respectively equal to 2^{51.68} and 2^{36}. We moreover show that the new method can be extended to attack the fresh re-keying countermeasure proposed by Medwed, Standaert, Großschädl and Regazzoni at Africacrypt 2010.

We study how to construct efficient tweakable block ciphers in the Random Permutation model, where all parties have access to public random permutation oracles. We propose a construction that combines, more efficiently than by mere black-box composition, the CLRW construction (which turns a traditional block cipher into a tweakable block cipher) of Landecker et al. (CRYPTO 2012) and the iterated Even-Mansour construction (which turns a tuple of public permutations into a traditional block cipher) that has received considerable attention since the work of Bogdanov et al. (EUROCRYPT 2012). More concretely, we introduce the (one-round) tweakable Even-Mansour (TEM) cipher, constructed from a single $n$-bit permutation $P$ and a uniform and almost XOR-universal family of hash functions $(H_k)$ from some tweak space to $\{0,1\}^n$, and defined as $(k,t,x)\mapsto H_k(t)\oplus P(H_k(t)\oplus x)$, where $k$ is the key, $t$ is the tweak, and $x$ is the $n$-bit message, as well as its generalization obtained by cascading $r$ independently keyed rounds of this construction. Our main result is a security bound up to approximately $2^{2n/3}$ adversarial queries against adaptive chosen-plaintext and ciphertext distinguishers for the two-round TEM construction, using Patarin's H-coefficients technique. We also provide an analysis based on the coupling technique showing that asymptotically, as the number of rounds $r$ grows, the security provided by the $r$-round TEM construction approaches the information-theoretic bound of $2^n$ adversarial queries.

A detailed overview of the problems, solutions and experience of the first international student's Olympiad in cryptography, NSUCRYPTO'2014, is given. We start with rules of participation and description of rounds. All 15 problems of the Olympiad and their solutions are considered in detail. There are discussed solutions of the mathematical problems related to cipher constructing such as studying of differential characteristics of S-boxes, S-box masking, determining of relations between cyclic rotation and additions modulo $2$ and $2^n$, constructing of special linear subspaces in $\mathbb{F}_2^n$; problems about the number of solutions of the equation $F(x)+F(x+a)=b$ over the finite field $\mathbb{F}_{2^n}$ and APN functions. Some unsolved problems in symmetric cryptography are also considered.

The fully homomorphic symmetric encryption scheme \emph{MORE} encrypts keys by conjugation with a random invertible matrix over an RSA modulus. We provide a two known-ciphertexts cryptanalysis recovering a linear dependence among the two encrypted keys.

In this paper we analyze the security of the compression function of SHA-1 against collision attacks, or equivalently free-start collisions on the hash function. While a lot of work has been dedicated to the analysis of SHA-1 in the past decade, this is the first time that free-start collisions have been considered for this function. We exploit the additional freedom provided by this model by using a new start-from-the-middle approach in combination with improvements on the cryptanalysis tools that have been developed for SHA-1 in the recent years. This results in particular in better differential paths than the ones used for hash function collisions so far. Overall, our attack requires about $2^{50}$ evaluations of the compression function in order to compute a one-block free-start collision for a 76-step reduced version, which is so far the highest number of steps reached for a collision on the SHA-1 compression function. We have developed an efficient GPU framework for the highly branching code typical of a cryptanalytic collision attack and used it in an optimized implementation of our attack on recent GTX-970 GPUs. We report that a single cheap US$350 GTX-970 is sufficient to find the collision in less than 5 days. This showcases how recent mainstream GPUs seem to be a good platform for expensive and even highly-branching cryptanalysis computations. Finally, our work should be taken as a reminder that cryptanalysis on SHA-1 continues to improve. This is yet another proof that the industry should quickly move away from using this function.

At CRYPTO 2012, Knellwolf and Khovratovich presented a differential formulation of advanced meet-in-the-middle techniques for preimage attacks on hash functions. They demonstrated the usefulness of their approach by significantly improving the previously best known attacks on SHA-1 from CRYPTO~2009, increasing the number of attacked rounds from a 48-round one-block pseudo-preimage without padding and a 48-round two-block preimage without padding to a 57-round one-block preimage without padding and a 57-round two-block preimage with padding, out of 80 rounds for the full function. In this work, we exploit further the differential view of meet-in-the-middle techniques and generalize it to higher-order differentials. Despite being an important technique dating from the mid-90's, this is the first time higher-order differentials have been applied to meet-in-the-middle preimages. We show that doing so may lead to significant improvements to preimage attacks on hash functions with a simple linear message expansion. We extend the number of attacked rounds on SHA-1 to give a 62-round one-block preimage without padding, a 56-round one-block preimage with padding, and a 62-round two-block preimage with padding. We also apply our framework to the more recent SHA-3 finalist BLAKE and its newer variant BLAKE2, and give an attack for a 2.75-round preimage with padding, and a 7.5-round pseudo-preimage on the compression function.

We propose new generic key recovery attacks on Feistel-type block ciphers. The proposed attack is based on the all subkeys recovery approach presented in SAC 2012, which determines all subkeys instead of the master key. This enables us to construct a key recovery attack without taking into account a key scheduling function. With our advanced techniques, we apply several key recovery attacks to Feistel-type block ciphers. For instance, we show 8-, 9- and 11-round key recovery attacks on n-bit Feistel ciphers with 2n-bit key employing random keyed F-functions, random F-functions, and SP-type F-functions, respectively. Moreover, thanks to the meet-in-the-middle approach, our attack leads to low-data complexity. To demonstrate the usefulness of our approach, we show a key recovery attack on the 8-round reduced CAST-128, which is the best attack with respect to the number of attacked rounds. Since our approach derives the lower bounds on the numbers of rounds to be secure under the single secret key setting, it can be considered that we unveil the limitation of designing an efficient block cipher by a Feistel scheme such as a low-latency cipher.

Securely sharing the same secret key among multiple parties is the main concern in symmetric cryptography that is the workhorse of modern cryptography due to its simplicity and fast speed. Typically asymmetric cryptography is used to set up a shared secret between parties, after which the switch to symmetric cryptography can be made. In this paper, we introduce a novel key exchange protocol based on physical hardware implementation to establish a shared secret between parties rather than relying on mathematical implementation of asymmetric cryptography. In particular, the key exchange is dependent on a new security concept named as virtual proof of reality or simply virtual proof (VP) that enables proof of a physical statement over untrusted digital communication channels between two parties (a prover and a verifier) residing in two separate local systems. We firstly exploit the VP to secure key exchange and further prove it by using experimental data. The key transferred in this protocol is only seen by the prover and hidden from not only the adversary but also the verifier. While only the verifier can successfully discover it.

At ASIACRYPT 1991, Even and Mansour introduced a block cipher construction based on a single permutation. Their construction has since been lauded for its simplicity, yet also criticized for not providing the same security as other block ciphers against generic attacks. In this paper, we prove that if a small number of plaintexts are encrypted under multiple independent keys, the Even-Mansour construction surprisingly offers similar security as an ideal block cipher with the same block and key size. Note that this multi-key setting is of high practical relevance, as real-world implementations often allow frequent rekeying. We hope that the results in this paper will further encourage the use of the Even-Mansour construction, especially when the secure and efficient implementation of a key schedule would result in a significant overhead.

Differential Fault Attack (DFA) has received serious attention in cryptographic literature and very recently such attacks have been mounted against several popular stream ciphers for example Grain v1, MICKEY 2.0 and Trivium, that are parts of the eStream hardware profile. The basic idea of the fault attacks consider injection of faults and the most general set-up should consider faults at random location and random time. Then one should identify the exact location and the exact timing of the fault (as well as multi bit faults) with the help of fault signatures. In this paper we consider this most general set-up and solve the problem of fault attack under a general framework, where probabilistic signatures are exploited. Our ideas subsume all the existing DFAs against the Grain family, MICKEY 2.0 and Trivium. In the process we provide improved fault attacks for all the versions of Grain family and also for MICKEY 2.0 (the attacks against Trivium are already quite optimal and thus there is not much scope to improve). Our generalized method can also take care of the cases where certain parts of the keystream bits are missing for authentication purpose. In particular, we show that the unsolved problem of identifying the faults in random time for Grain 128a can be solved in this manner. Our techniques can easily be applied to mount fault attack on any stream cipher of similar kind.

We consider the problem of recovering the internal specification of a general SP-network consisting of three linear layers (A) interleaved with two Sbox layers (S) (denoted by ASASA for short), given only black-box access to the scheme. The decomposition of such general ASASA schemes was first considered at ASIACRYPT 2014 by Biryukov et al. which used the alleged difficulty of this problem to propose several concrete block cipher designs as candidates for white-box cryptography. In this paper, we present several attacks on general ASASA schemes that significantly outperform the analysis of Biryukov et al. As a result, we are able to break all the proposed concrete ASASA constructions with practical complexity. For example, we can decompose an ASASA structure that was supposed to provide $64$-bit security in roughly $2^{28}$ steps, and break the scheme that supposedly provides $128$-bit security in about $2^{41}$ time. Whenever possible, our findings are backed up with experimental verifications.

We introduce and study the iterated random permutation problem, which asks how hard it is to distinguish, in a black-box way, the r-th power of a random permutation from a uniformly random permutation of a set of size N. We show that this requires Omega(N) queries (even for a two-sided, adaptive adversary). As a direct application of this result, we show that cascading a block cipher with the same key cannot degrade its security (as a pseudorandom permutation) more than negligibly.

It is well known that three and four rounds of balanced Feistel cipher or Luby-Rackoff (LR) encryption for two blocks messages are pseudorandom permutation (PRP) and strong pseudorandom permutation (SPRP) respectively. A {\bf block} is $n$-bit long for some positive integer $n$ and a (possibly keyed) {\bf block-function} is a nonlinear function mapping all blocks to themselves, e.g. blockcipher. XLS (eXtended Latin Square) with three blockcipher calls was claimed to be SPRP and later which is shown to be wrong. Motivating with these observations, we consider the following questions in this paper: {\em What is the minimum number of invocations of block-functions required to achieve PRP or SPRP security over $\ell$ blocks inputs}? To answer this question, we consider all those length-preserving encryption schemes, called {\bf linear encryption mode}, for which only nonlinear operations are block-functions. Here, we prove the following results for these encryption schemes: (1) At least $2\ell$ (or $2\ell-1$) invocations of block-functions are required to achieve SPRP (or PRP respectively). These bounds are also tight. (2) To achieve the above bound for PRP over $\ell > 1$ blocks, either we need at least two keys or it can not be {\em inverse-free} (i.e., need to apply the inverses of block-functions in the decryption). In particular, we show that a single-keyed block-function based, inverse-free PRP needs $2\ell$ invocations. (3) We show that 3-round LR using a single-keyed pseudorandom function (PRF) is PRP if we xor a block of input by a masking key.

Fault injection has become over the years one of the most dangerous threats for embedded devices such as smartcards. It is thus mandatory for any embedded system to implement efficient protections against this hazard. Among the various countermeasures suggested so far, the idea of infective computation seems fascinating, probably due to its aggressive strategy. Originally conceived to protect asymmetric cryptosystems, infective computation has been recently adapted to symmetric systems. This paper investigates the security of a new symmetric infective countermeasure suggested at CHES 2014. By noticing that the number of executed rounds is not protected, we develop four different attacks allowing one to efficiently recover the secret key of the underlying cryptosystem by using any of the three most popular fault models used in literature.

The iterated Even-Mansour cipher is a construction of a block cipher from $r$ public permutations $P_1,\ldots,P_r$ which abstracts in a generic way the structure of key-alternating ciphers. The indistinguishability of this construction from a truly random permutation by an adversary with oracle access to the inner permutations $P_1,\ldots,P_r$ has been investigated in a series of recent papers. This construction has also been shown to be (fully) indifferentiable from an ideal cipher for a sufficient number of rounds (five or twelve depending on the assumptions on the key-schedule). In this paper, we extend this line of work by considering the resistance of the iterated Even-Mansour cipher to xor-induced related-key attacks (i.e., related-key attacks where the adversary is allowed to xor any constant of its choice to the secret key) and to chosen-key attacks. For xor-induced related-key attacks, we first provide a distinguishing attack for two rounds, assuming the key-schedule is linear. We then prove that for a linear key-schedule, three rounds yield a cipher which is secure against xor-induced related-key attacks up to $O(2^{\frac{n}{2}})$ queries of the adversary, whereas for a nonlinear key-schedule, one round is sufficient to obtain a similar security bound. We also show that the iterated Even-Mansour cipher with four rounds offers some form of provable resistance to chosen-key attacks, which is the minimal number of rounds to achieve this property. The main technical tool that we use to prove this result is \emph{sequential indifferentiability}, a weakened variant of (full) indifferentiability introduced by Mandal \emph{et al.} (TCC~2010).

Slide attacks use pairs of encryption operations which are slid against each other. Slide with a twist attacks are more sophisticated variants of slide attacks which slide an encryption operation against a decryption operation. Designed by Biryukov and Wagner in 2000, these attacks were used against several cryptosystems, including DESX, the Even-Mansour construction, and Feistel structures with four-round self-similarity. They were further extended in 2012 to the mirror slidex framework, which was used to attack the 20-round GOST block cipher and several additional variants of the Even-Mansour construction. In this paper, we revisit all the previously published applications of these techniques and show that in almost all cases, the same or better results can be achieved by a simpler attack which is based on the seemingly unrelated idea of exploiting internal fixed points. The observation that such fixed points can be useful in cryptanalysis of block ciphers is known for decades and is the basis of the reflection attack presented by Kara in 2007. However, all the examples to which reflection attacks were applied were based on particular constructions such as Feistel structures or GOST key schedules in which it was easy to explicitly list and count the fixed points. In this paper, we generalize Kara’s reflection attack by using the combinatorial result that random involutions on 2^n values are expected to have a surprisingly large number of O(2^n/2) fixed points (whereas random permutations are expected to have only O(1) fixed points). This makes it possible to reduce the complexity of the best known attack on additional cryptographic schemes in which it is difficult to explicitly characterize and count the internal fixed points.

Lightweight cryptography is a rapidly evolving area of research and it has great impact especially on the new computing environment called the Internet of Things (IoT) or the Smart Object networks (Holler et al., 2014), where lots of constrained devices are connected on the Internet and exchange information on a daily basis. Every year there are many new submissions of cryptographic primitives which are optimized towards both software and hardware implementation so that they can operate in devices which have limited resources of hardware and are subject to both power and energy consumption constraints. In 2013, two families of ultra-lightweight block ciphers were proposed, SIMON and SPECK, which come in a variety of block and key sizes and were designed to be optimized in hardware and software implementation respectively (Beaulieu et al., 2013). In this paper, we study the security of the 64-bit SIMON with 128-bit key against advanced forms of differential cryptanalysis using truncated differentials (Knudsen, 1995; Courtois et al., 2014a). We follow similar method as the one proposed in SECRYPT 2013 (Courtois and Mourouzis, 2013) in order to heuristically discover sets of differences that propagate with sufficiently good probability and allow us to combine them efficiently in order to construct large-round statistical distinguishers. We present a 22-round distinguisher which we use it in a depth-first key search approach to develop an attack against 24 and 26 rounds with complexity 2^{124.5} and 2^{126} SIMON encryptions respectively. Our methodology provides a framework for extending distinguishers to attacks to a larger number of rounds assuming truncated differential properties of relatively high probability were discovered.

Block cipher is in vogue due to its requirement for integrity, confidentiality and authentication. Differential and Linear cryptanalysis are the basic techniques on block cipher and till today many cryptanalytic attacks are developed based on these. Each variant of these have different methods to find distinguisher and based on the distinguisher, the method to recover key. This paper illustrates the steps to find distinguisher and steps to recover key of all variants of differential and linear attacks developed till today. This is advantageous to cryptanalyst and cryptographer to apply various attacks simultaneously on any crypto algorithm.

Many modern block ciphers use maximum distance separate (MDS) matrices as their diffusion layers. In this paper, we propose a new method to verify a sort of MDS diffusion block matrices whose blocks are all polynomials in a certain primitive block over the finite field $\mathbb F_2$. And then we discover a new kind of transformations that can retain MDS property of diffusion matrices and generate a series of new MDS matrices from a given one. Moreover, we get an equivalence relation from this kind of transformation. And MDS property is an invariant with respect to this equivalence relation which can greatly reduce the amount of computation when we search for MDS matrices. The minimal polynomials of matrices play an important role in our strategy. To avoid being too theoretical, we list a series of MDS diffusion matrices obtained from our method for some specific parameters. Furthermore, we talk about MDS recursive diffusion layers with our method and extend the corresponding work of M. Sajadieh et al. published on FSE 2012 and the work of S. Wu published on SAC 2012.

While the symmetric-key cryptography community has now a good experience on how to build a secure and efficient fixed permutation, it remains an open problem how to design a key-schedule for block ciphers, as shown by the numerous candidates broken in the related-key model or in a hash function setting. Provable security against differential and linear cryptanalysis in the related-key scenario is an important step towards a better understanding of its construction. Using a structural analysis, we show that the full AES-128 cannot be proven secure unless the exact coefficients of the MDS matrix and the S-Box differential properties are taken into account since its structure is vulnerable to a related-key differential attack. We then exhibit a chosen-key distinguisher for AES-128 reduced to 9 rounds, which solves an open problem of the symmetric community. We obtain these results by revisiting algorithmic theory and graph-based ideas to compute all the best differential characteristics in SPN ciphers, with a special focus on AES-like ciphers subject to related-keys. We use a variant of Dijkstra's algorithm to efficiently find the most efficient related-key attacks on SPN ciphers with an algorithm linear in the number of rounds.

Side-channel cube attacks are a class of leakage attacks on block ciphers in which the attacker is assumed to have access to some leaked information on the internal state of the cipher as well as the plaintext/ciphertext pairs. The known Dinur-Shamir model and its variants require error-free data for at least part of the measurements. In this paper, we consider a new and more realistic model which can deal with the case when \textit{all} the leaked bits are noisy. In this model, the key recovery problem is converted to the problem of decoding a binary linear code over a binary symmetric channel with the crossover probability which is determined by the measurement quality and the cube size. We use the maximum likelihood decoding method to recover the key. As a case study, we demonstrate efficient key recovery attacks on PRESENT. We show that the full $80$-bit key can be restored with $2^{10.2}$ measurements with an error probability of $19.4\%$ for each measurement.

In FSE 2007, Ristenpart and Rogaway had described a generic method XLS to construct a length-preserving strong pseudorandom per- mutation (SPRP) over bit-strings of size at least n. It requires a length-preserving permutation E over all bits of size multiple of n and a blockcipher E with block size n. The SPRP security of XLS was proved from the SPRP assumptions of both E and E. In this paper we disprove the claim by demonstrating a SPRP distinguisher of XLS which makes only three queries and has distinguishing advantage about 1/2. XLS uses a multi-permutation linear function, called mix2. In this paper, we also show that if we replace mix2 by any invertible linear functions, the construction XLS still remains insecure. Thus the mode has inherit weakness.

Ristenpart and Rogaway proposed XLS in 2007 which is a generic method to encrypt messages with incomplete last blocks. Later Andreeva et al., in 2013 proposed an authenticated encryption COPA which uses XLS while processing incomplete message blocks. Following the design of COPA, several other CAESAR candidates used the similar approach. Surprisingly in 2014, Nandi showed a three-query distinguisher against XLS which violates the security claim of XLS and puts a question mark on all schemes using XLS. However, due to the interleaved nature of encryption and decryption queries of the distinguisher, it was not clear whether the security claims of COPA remains true or not. This paper revisits XLS and COPA both in the direction of cryptanalysis and provable security. Our contribution of the paper can be summarized into following two parts: 1. Cryptanalysis: We describe two attacks - (i) a new distinguisher against XLS and extending this attack to obtain (ii) a forging algo- rithm with query complexity about 2^n/3 against COPA where n is the block size of the underlying blockcipher. 2. Security Proof: Due to the above attacks the main claims of XLS (already known before) and COPA are wrong. So we revise the security analysis of both and show that (i) both XLS and COPA are pseudorandom function or PRF up to 2^n/2 queries and (ii) COPA is integrity-secure up to 2^n/3 queries (matching the query complexity of our forging algorithm).

Boolean functions used in stream ciphers should have many cryptographic properties in order to help resist different kinds of cryptanalytic attacks. The resistance of Boolean functions against fast algebraic attacks is an important cryptographic property. Deciding the resistance of an n-variable Boolean function against fast algebraic attacks needs to determine the rank of a square matrix over finite field GF(2). In this paper, for rotation symmetric Boolean functions in prime n variables, exploiting the properties of partitioned matrices and circulant matrices, we show that the rank of such a matrix can be obtained by determining the rank of a reduced square matrix with smaller size over GF(2), so that the computational complexity decreases by a factor of n to the power omega for large n, where omega is approximately equal to 2.38 and is known as the exponent of the problem of computing the rank of matrices.

The (fast) algebraic immunity, including (standard) algebraic immunity and the resistance against fast algebraic attacks, has been considered as an important cryptographic property for Boolean functions used in stream ciphers. This paper is on the determination of the (fast) algebraic immunity of a special class of Boolean functions, called Boolean power functions. An n-variable Boolean power function f can be represented as a monomial trace function over finite field GF(2^n). To determine the (fast) algebraic immunity of Boolean power functions one may need the arithmetic in GF(2^n), which may be not computationally efficient compared with the operations over GF(2). We provide two sufficient conditions for Boolean power functions such that their immunities can determined only by the computations in GF(2). We show that Niho functions and a number of odd variables Kasami functions can satisfy the conditions.

In this paper, we present a new classification of 4-bit optimal S-boxes. All optimal 4-bit S-boxes can be classified into 183 different categories, among which we specify 3 platinum categories. Under the design criteria of the PRESENT (or SPONGENT) S-box, there are 8064 different S-boxes up to adding constants before and after an S-box. The 8064 S-boxes belong to 3 different categories, we show that the S-box should be chosen from one out of the 3 categories or other categories for better resistance against linear cryptanalysis. Furthermore, we study in detail how the S-boxes in the 3 platinum categories influence the security of PRESENT, RECTANGLE and SPONGENT88 against differential and linear cryptanalysis. Our results show that the S-box selection has a great influence on the security of the schemes. For block ciphers or hash functions with 4-bit S-boxes as confusion layers and bit permutations as diffusion layers, designers can extend the range of S-box selection to the 3 platinum categories and select their S-box very carefully. For PRESENT, RECTANGLE and SPONGENT88 respectively, we get a set of potentially best/better S-box candidates from the 3 platinum categories. These potentially best/better S-boxes can be further investigated to see if they can be used to improve the security-performance tradeoff of the 3 cryptographic algorithms.

Dickson polynomials which are permutations are interesting combinatorial objects and well studied. In this paper, we describe Dickson polynomials of the first kind in $\mathbb{F}_2[x]$ that are involutions over finite fields of characteristic $2$. Such description is obtained using modular arithmetic's tools. We give results related to the cardinality and the number of fixed points (in the context of cryptographic application) of this corpus. We also present a class of Dickson involutions with high degree.

In this paper we present known-plaintext single-key and chosen-key attacks on round-reduced LED-64 and LED-128. We show that with an application of the recently proposed slidex attacks, one immediately improves the complexity of the previous single-key 4-step attack on LED-128. Further, we explore the possibility of multicollisions and show single-key attacks on 6 steps of LED-128. A generalization of our multicollision attack leads to the statement that no 6-round cipher with two subkeys that alternate, or 2-round cipher with linearly dependent subkeys, is secure in the single-key model. Next, we exploit the possibility of finding pairs of inputs that follow a certain differential rather than a differential characteristic, and obtain chosen-key differential distinguishers for 5-step LED-64, as well as 8-step and 9-step LED-128. We provide examples of inputs that follow the 8-step differential, i.e. we are able to practically confirm our results on 2/3 of the steps of LED-128. We introduce a new type of chosen-key differential distinguisher, called random-difference distinguisher, and successfully penetrate 10 of the total 12 steps of LED-128. We show that this type of attack is generic in the chosen-key model, and can be applied to any 10-round cipher with two alternating subkeys.

In this paper, we propose related-key differential distinguishers based on the complementation property of Feistel ciphers. We show that with relaxed requirements on the complementation, i.e. the property does not have to hold for all keys and the complementation does not have to be on all bits, one can obtain a variety of distinguishers. We formulate criteria sufficient for attacks based on the complementation property. To stress the importance of our findings we provide analysis of the \textit{full-round} primitives: * For the hash mode of \camo without $FL,FL^{-1}$ layers, differential multicollisions with $2^{112}$ time * For GOST, practical recovery of the full key with 31 related keys and $2^{38}$ time/data

In this paper, we present a novel lightweight authenticated cipher optimized for hardware implementations called FIDES. It is an online nonce-based authenticated encryption scheme with authenticated data whose area requirements are as low as 793 GE and 1001 GE for 80-bit and 96-bit security, respectively. This is at least two times smaller than its closest competitors Hummingbird-2 and Grain-128a. While being extremely compact, Fides is both throughput and latency efficient, even in its most serial implementations. This is attained by our novel sponge-like design approach. Moreover, cryptographically optimal 5-bit and 6-bit S-boxes are used as basic nonlinear components while paying a special attention on the simplicity of providing first order side-channel resistance with threshold implementation.

LowMC is a collection of block cipher families introduced at Eurocrypt 2015 by Albrecht et al. Its design is optimized for instantiations of multi-party computation, fully homomorphic encryption, and zero-knowledge proofs. A unique feature of LowMC is that its internal affine layers are chosen at random, and thus each block cipher family contains a huge number of instances. The Eurocrypt paper proposed two specific block cipher families of LowMC, having 80-bit and 128-bit keys. In this paper, we mount interpolation attacks (algebraic attacks introduced by Jakobsen and Knudsen) on LowMC, and show that a practically significant fraction of $2^{-38}$ of its 80-bit key instances could be broken $2^{23}$ times faster than exhaustive search. Moreover, essentially all instances that are claimed to provide 128-bit security could be broken about $1000$ times faster. In order to obtain these results, we had to develop novel techniques and optimize the original interpolation attack in new ways. While some of our new techniques exploit specific internal properties of LowMC, others are more generic and could be applied, in principle, to any block cipher.

We revisit the security (as a pseudorandom permutation) of cascading-based constructions for block-cipher key-length extension. Previous works typically considered the extreme case where the adversary is given the entire codebook of the construction, the only complexity measure being the number $q_e$ of queries to the underlying ideal block cipher, representing adversary's secret-key-independent computation. Here, we initiate a systematic study of the more natural case of an adversary restricted to adaptively learning a number $q_c$ of plaintext/ciphertext pairs that is less than the entire codebook. For any such $q_c$, we aim to determine the highest number of block-cipher queries $q_e$ the adversary can issue without being able to successfully distinguish the construction (under a secret key) from a random permutation. More concretely, we show the following results for key-length extension schemes using a block cipher with $n$-bit blocks and $\kappa$-bit keys: - Plain cascades of length $\ell = 2r+1$ are secure whenever $q_c q_e^r \ll 2^{r(\kappa+n)}$, $q_c \ll 2^\ka$ and $q_e \ll 2^{2\ka}$. The bound for $r = 1$ also applies to two-key triple encryption (as used within Triple DES). - The $r$-round XOR-cascade is secure as long as $q_c q_e^r \ll 2^{r(\kappa+n)}$, matching an attack by Gazi (CRYPTO 2013). - We fully characterize the security of Gazi and Tessaro's two-call 2XOR construction (EUROCRYPT 2012) for all values of $q_c$, and note that the addition of a third whitening step strictly increases security for $2^{n/4} \le q_c \le 2^{3/4n}$. We also propose a variant of this construction without re-keying and achieving comparable security levels.

The decorrelation theory provides a different point of view on the security of block cipher primitives. Results on some statistical attacks obtained in this context can support or provide new insight on the security of symmetric cryptographic primitives. In this paper, we study, for the first time, the multidimensional linear attacks as well as the truncated differential attacks in this context. We show that the cipher should be decorrelated of order two to be resistant against some multidimensional linear and truncated differential attacks. Previous results obtained with this theory for linear, differential, differential-linear and boomerang attacks are also resumed and improved in this paper.

In this article, we provide the first third-party security analysis of the PRINCE lightweight block cipher, and the underlying PRINCE_core. First, while no claim was made by the authors regarding related-key attacks, we show that one can attack the full cipher with only a single pair of related keys, and then reuse the same idea to derive an attack in the single-key model for the full PRINCE_core for several instances of the $\alpha$ parameter (yet not the one randomly chosen by the designers). We also show how to exploit the structural linear relations that exist for PRINCE in order to obtain a key recovery attack that slightly breaks the security claims for the full cipher. We analyze the application of integral attacks to get the best known key-recovery attack on a reduced version of the PRINCE cipher. Finally, we provide time-memory-data tradeoffs, that require only known plaintext-ciphertext data, and that can be applied to full PRINCE.

In this paper, we consider the cycle structures of feedback shift registers (FSRs). At the beginning, the cycle structures of two special classes of FSRs, pure circulating registers (PCRs) and pure summing registers (PSRs), are studied and it is proved that there are no other FSRs have the same cycle structure of an PCR (or PSR). Then, we regard $n$-stage FSRs as permutations over $2^n$ elements. According to the group theory, two permutations have the same cycle structure if and only if they are conjugate with each other. Since a conjugate of an FSR may no longer an FSR, it is interesting to consider the permutations that always transfer an FSR to an FSR. It is proved that there are exactly two such permutations, the identity mapping and the mapping that map every state to its dual. Furthermore, we prove that they are just the two permutations that transfer any maximum length FSR to an maximum length FSR.

In this paper, we focus on the construction of semi-free-start collisions for SHA-256, and show how to turn them into collisions. We present a collision attack on 28 steps of the hash function with practical complexity. Using a two-block approach we are able to turn a semi-free-start collision into a collision for 31 steps with a complexity of at most $2^{65.5}$. The main improvement of our work is to extend the size of the local collisions used in these attacks. To construct differential characteristics and confirming message pairs for longer local collisions, we had to improve the search strategy of our automated search tool. To test the limits of our techniques we present a semi-free-start collision for 38 steps.

Kuznyechik is an SPN block cipher that has been chosen recently to be standardized by the Russian federation as a new GOST cipher. In this paper, we present two fault analysis attacks on two different settings of the cipher. The first attack is a differential fault attack which employs the random byte fault model, where the attacker is assumed to be able to fault a random byte in rounds seven and eight. Using this fault model enables the attacker to recover the master key using an average of four faults. The second attack considers the cipher with a secret sbox. By utilizing an ineffective fault analysis in the byte stuck-at-zero fault model, we present a four stage attack to recover both the master key and the secret sbox parameters. Our second attack is motivated by the fact that, similar to GOST 28147-89, Kuznyechik is expected to include the option of using secret sbox based on the user supplied key to increase its security margin. Both the presented attacks have practical complexities and aim to demonstrate the importance of protecting the hardware and software implementations of the new standard even if its sbox is kept secret.

In Asiacrypt 2010, Knellwolf, Meier and Naya-Plasencia proposed distinguishing attacks on Grain v1 when (i) Key Scheduling process is reduced to 97 rounds using $2^{27}$ chosen IVs and (ii) Key Scheduling process is reduced to 104 rounds using $2^{35}$ chosen IVs. Using similar idea, Banik obtained a new distinguisher for 105 rounds. In this paper, we show similar approach can work for 106 rounds. We present a new distinguisher on Grain v1 for 106 rounds with success probability 63\%.

Kuznyechik is an SPN block cipher that has been recently chosen to be standardized by the Russian federation as a new GOST cipher. The algorithm updates a 128-bit state for nine rounds using a 256-bit key. In this paper, we present a meet-in-the-middle attack on the 5-round reduced cipher. Our attack is based on the differential enumeration approach, where we propose a distinguisher for the middle rounds and match a sequence of state differences at its output. However, the application of the exact approach is not successful on Kuznyechik due to its optimal round diffusion properties. Accordingly, we adopt an equivalent representation for the last round where we can efficiently filter ciphertext pairs and launch the attack in the chosen ciphertext setting. We also utilize partial sequence matching which further reduces the memory and time complexities through relaxing the error probability. The adopted partial sequence matching approach enables successful key recovery by matching parts of the generated sequence instead of the full sequence matching used in the traditional settings of this attack. For the 5-round reduced cipher, the 256-bit master key is recovered with a time complexity of 2^{140.3}, a memory complexity of 2^{153.3}, and a data complexity of 2^{113}.

Authenticated encryption algorithms protect both the confidentiality and integrity of messages in a single processing pass. In this note we show how to utilize the $L \circ P \circ S$ transform of the Russian GOST R 34.11-2012 standard hash ``Streebog'' to build an efficient, lightweight algorithm for Authenticated Encryption with Associated Data (AEAD) via the Sponge construction and BLNK padding. The proposed algorithm ``StriBob'' has attractive security properties, is faster than the Streebog hash alone, twice as fast as the GOST 28147-89 encryption algorithm, and requires only a modest amount of running-time memory. StriBob is a Round 1 candidate in the CAESAR competition.

Dinur and Shamir have described cube attacks at EUROCRYPT ’09 and they have shown how efficient they are on the stream cipher Trivium up to 767 rounds. These attacks have been extended to distinguishers but since this seminal work, no better results on the complexity of key recovery attacks on Trivium have been presented. It appears that the time complexity to compute cubes is expensive and the discovery of linear superpoly also requires the computation of many cubes. In this paper, we increase the number of attacked initialization rounds by improving the time complexity of computing cube and we show attacks that go beyond this bound. We were able to find linear superpoly up to 784 rounds, which leads to an attack requiring $2^{39}$ queries. Using quadratic superpoly, we were also able to provide another attack up to 799 rounds which complexity is $2^{40}$ queries and $2^{62}$ for the exhaustive search part. To achieve such results, we find a way to reduce the density of the polynomials, we look for quadratic relations and we extensively use the Moebius transform to speed up computations for various purposes.

The National Institute of Standards and Technology (NIST) specified three methods for format-preserving encryption (FPE) in Draft NIST Special Publication (SP) 800-38G, which was released for public comment in July, 2013. Each method was a mode of operation of the Advanced Encryption Standard (AES). One of the three modes, VAES3, was specified under the name FF2 in the NIST draft. This note describes a theoretical chosen-plaintext attack that shows the security strength of FF2 is less than 128 bits.

We propose \emph{pure} OMD (p-OMD) as a new variant of the Offset Merkle-Damgård (OMD) authenticated encryption scheme. Our new scheme inherits all desirable security features of OMD while having a more compact structure and providing higher efficiency. The original OMD scheme, as submitted to the CAESAR competition, couples a single pass of a variant of the Merkle-Damgård (MD) iteration with the counter-based XOR MAC algorithm to provide privacy and authenticity. Our improved p-OMD scheme dispenses with the XOR MAC algorithm and is \emph{purely} based on the MD iteration; hence, the name ``pure'' OMD. To process a message of $\ell$ blocks and associated data of $a$ blocks, OMD needs $\ell+a+2$ calls to the compression function while p-OMD only requires $\max\left\{\ell, a\right\}+2$ calls. Therefore, for a typical case where $\ell \geq a$, p-OMD makes just $\ell+2$ calls to the compression function; that is, associated data is processed almost freely compared to OMD. We prove the security of p-OMD under the same standard assumption (pseudo-randomness of the compression function) as made in OMD; moreover, the security bound for p-OMD is the same as that of OMD, showing that the modifications made to boost the performance are without any loss of security.

Impossible differential is a useful method for cryptanalysis. SIMON is a light weight block cipher that has attracted lots of attention ever since its publication in 2013. In this paper we propose impossible differential attack on five versions of SIMON, using bit conditions to minimize key bits guessed. We calculate keybits and give the exact attack results.

Simon is a family of block ciphers designed by the NSA and published in 2013. Due to their simple structure and the fact that the specification lacked security design rationale, the ciphers have been the subject of much cryptanalytic work, especially using differential and linear cryptanalysis. We improve previously published linear trail bias estimations by presenting a novel method to calculate the bias of short linear hulls in Simon and use them to construct longer linear approximations. By using these linear approximations we present key recovery attacks of up to 25 rounds for Simon64/128, 24 rounds for Simon32/64, Simon48/96, and Simon64/96, and 23 rounds for Simon48/72. The attacks on Simon32 and Simon48 are currently the best attacks on these versions. The attacks on Simon64 do not cover as many rounds as attacks using differential cryptanalysis but they work in the more natural setting of known plaintexts rather than chosen plaintexts.

AES-based functions have attracted of a lot of analysis in the recent years, mainly due to the SHA-3 hash function competition. In particular, the rebound attack allowed to break several proposals and many improvements/variants of this method have been published. Yet, it remained an open question whether it was possible to reach one more round with this type of technique compared to the state-of-the-art. In this article, we close this open problem by providing a further improvement over the original rebound attack and its variants, that allows the attacker to control one more round in the middle of a differential path for an AES-like permutation. Our algorithm is based on lists merging as defined by Naya-Plasencia at CRYPTO 2011, and we generalized the concept to non-full active truncated differential paths proposed by Sasaki et al. at ASIACRYPT 2010. As an illustration, we applied our method to the internal permutations used in Grostl, one of the five finalist hash functions of the SHA-3 competition. When entering this final phase, the designers tweaked the function so as to thwart attacks proposed by Peyrin at CRYPTO 2010 that exploited relations between the internal permutations. Until our results, no analysis was published on Grostl and the best results reached 8 and 7 rounds for the 256-bit and 512-bit version respectively. By applying our algorithm, we present new internal permutation distinguishers on 9 and 10 rounds respectively.

The fundamental problem of differential cryptanalysis is to find the highest entries in the Difference Distribution Table (DDT) of a given mapping F over n-bit values, and in particular to find the highest diagonal entries which correspond to the best iterative characteristics of $F$. The standard bottom-up approach to this problem is to consider all the internal components of the mapping along some differential characteristic, and to multiply their transition probabilities. However, this can provide seriously distorted estimates since the various events can be dependent, and there can be a huge number of low probability characteristics contributing to the same high probability entry. In this paper we use a top-down approach which considers the given mapping as a black box, and uses only its input/output relations in order to obtain direct experimental estimates for its DDT entries which are likely to be much more accurate. In particular, we describe three new techniques which reduce the time complexity of three crucial aspects of this problem: Finding the exact values of all the diagonal entries in the DDT for small values of n, approximating all the diagonal entries which correspond to low Hamming weight differences for large values of $n$, and finding an accurate approximation for any $DDT$ entry whose large value is obtained from many small contributions. To demonstrate the potential contribution of our new techniques, we apply them to the SIMON family of block ciphers, show experimentally that most of the previously published bottom-up estimates of the probabilities of various differentials are off by a significant factor, and describe new differential properties which can cover more rounds with roughly the same probability for several of its members. In addition, we show how to use our new techniques to attack a 1-key version of the iterated Even-Mansour scheme in the related key setting, obtaining the first generic attack on 4 rounds of this well-studied construction.

In this paper, we revisit Demirci and Selçuk meet-in-the-middle attacks on AES. We find a way to automatically model SPN block cipher and meet-in-the-middle attacks that allows to perform exhaustive search of this kind of attacks. This search uses the tool developed by Bouillaguet, Derbez and Fouque at CRYPTO 2011 as a subroutine to solve specific systems. We also take into account ideas introduced by Dunkelman, Keller and Shamir at ASIACRYPT 2010 which can be seen as a new tradeoff of the classical time/memory tradeoff used by Demirci and Selçuk. As a result, we automatically recover all the recent improved attacks of Derbez, Fouque and Jean on AES and we show new improved attacks against 8-rounds of AES-192 and AES-256.

We propose Chaskey: a very efficient Message Authentication Code (MAC) algorithm for 32-bit microcontrollers. It is intended for applications that require 128-bit security, yet cannot implement standard MAC algorithms because of stringent requirements on speed, energy consumption, or code size. Chaskey is a permutation-based MAC algorithm that uses the Addition-Rotation-XOR (ARX) design methodology. We formally prove that Chaskey is secure in the standard model, based on the security of an underlying Even-Mansour block cipher. Chaskey is designed to perform well on a wide range of 32-bit microcontrollers. Our benchmarks show that on the ARM Cortex-M3/M4, our Chaskey implementation reaches a speed of 7.0 cycles/byte, compared to 89.4 cycles/byte for AES-128-CMAC. For the ARM Cortex-M0, our benchmark results give 16.9 cycles/byte and 136.5 cycles/byte for Chaskey and AES-128-CMAC respectively.

A searchable symmetric encryption (SSE) scheme allows a client to store a set of encrypted files on an untrusted server in such a way that he can efficiently retrieve some of the encrypted files containing (or indexed by) specific keywords keeping the keywords and the files secret. In this paper, we first extend the model of SSE schemes to that of verifiable SSE schemes, and formulate the UC security. We then prove its weak equivalence with privacy and reliability. Finally we show an efficient verifiable SSE scheme which is UC-secure.

TWINE is a recent lightweight block cipher based on a Feistel structure. We first present two new attacks on TWINE-128 reduced to 25 rounds that have a slightly higher overall complexity than the 25-round attack presented by Wang and Wu at ACISP 2014, but a lower data complexity. Then, we introduce alternative representations of both the round function of this block cipher and of a sequence of 4 rounds. LBlock, another lightweight block cipher, turns out to exhibit the same behaviour. Then, we illustrate how this alternative representation can shed new light on the security of TWINE by deriving high probability iterated truncated differential trails covering 4 rounds with probability $2^{-16}$. The importance of these is shown by combining different truncated differential trails to attack 23-rounds TWINE-128 and by giving a tighter lower bound on the high probability of some differentials by clustering differential characteristics following one of these truncated trails. A comparison between these high probability differentials and those recently found in a variant of LBlock by Leurent highlights the importance of considering the whole distribution of the coefficients in the difference distribution table of a S-Box and not only their maximum value.

In this paper, we study stability and linearization of multi- valued nonlinear feedback shift registers which are considered as logic networks. First, the linearization of multi-valued nonlinear feedback shift registers (NFSRs) is discussed, which is to nd their state transition ma- trices by considering it as a logical network via a semi-tensor product ap- proach. For a multi-valued NFSR, the new state transition matrix which can be simply computed from the truth table of its feedback function is more explicit. Second, based on the linearization theory of multi-valued NFSRs, we investigate the stability of multi-valued NFSRs, and some suf- cient and necessary conditions are provided for globally (locally) stable multi-valued NFSRs. Finally, some examples are presented to show the eectiveness of the proposed results.

The Linearization of Nonlinear feedback shift registers (NFSRs) is to find their state transition matrices. In this paper, we investigate the linearization multi-valued NFSRs by considering it as a logical network via a semi-tensor product approach. A new state transition matrix is found for an multi-valued NFSR, which can be simply computed from the truth table of its feedback function, and the new state transition matrix is easier to compute and is more explicit. First, a linear representation of a multi-valued NFSR is given, based on which several necessary and sufficient conditions for the nonsingularity are given. Then, some properties of the state transition matrice are provided, which are helpful to theoretically analyze NFSRs. Finally, we give properties of a maximum length multi-valued NFSR and the linear representation of the general structure of an n-bit shift register with updating functions.

The PRINCE cipher is the result of a cooperation between the Technical University of Denmark (DTU), NXP Semiconductors and the Ruhr University Bochum. The cipher was designed to reach an extremely low-latency encryption and instant response time. PRINCE has already gained a lot of attention from the academic community, however, most of the attacks are theoretical, usually with very high time or data complexity. Our work helps to fill the gap in more practically oriented attacks, with more realistic scenarios and complexities. We present new attacks, up to 7 rounds, relying on integral and higher-order differential cryptanalysis.

We introduce internal differential boomerang distinguisher as a combination of internal differentials and classical boomerang distinguishers. The new boomerangs can be successful against cryptographic primitives having high-probability round-reduced internal differential characteristics. The internal differential technique, which follow the evolution of differences between parts of the state, is particularly meaningful for highly symmetric functions like the inner permutation Keccak-f of the hash functions defined in the future SHA-3 standard. We find internal differential and standard characteristics for three to four rounds of Keccak-f, and with the use of the new technique, enhanced with a strong message modification, show practical distinguishers for this permutation. Namely, we need $2^{12}$ queries to distinguish 7 rounds of the permutation starting from the first round, and approximately $2^{18}$ queries to distinguish 8 rounds starting from the fourth round. Due to the exceptionally low complexities, all of our results have been completely verified with a computer implementation of the analysis.

The demand for more efficient ciphers is a likely to sharpen with new generation of products and applications. Previous cipher designs typically focused on optimizing only one of the two parameters - hardware size or speed, for a given security level. In this paper, we present a methodology for designing a class of stream ciphers which takes into account both parameters simultaneously. We combine the advantage of the Galois configuration of NLFSRs, short propagation delay, with the advantage of the Fibonacci configuration of NLFSRs, which can be analyzed formally. According to our analysis, the presented stream cipher Espresso is the fastest among the ciphers below 1500 GE, including Grain-128 and Trivium.

While some recent publications have shown some strong relations between impossible differential and zero-correlation distinguishers as well as between zero-correlation and integral distinguishers, we analyze in this paper some relation between the underlying key-recovery attacks against Type-II Feistel networks. The results of this paper are build on the relation presented at ACNS 2013. In particular, using a matrix representation of the round function, we show that we can not only find impossible, integral and multidimensional zero-correlation distinguishers but also find the key-words involved in the underlined key-recovery attacks. Based on this representation, for matrix-method-derived strongly-related zero-correlation and impossible distinguishers, we show that the key-words involved in the zero-correlation attack is a subset of the key-words involved in the impossible differential attack. Other relations between the key-words involved in zero-correlation, impossible and integral attacks are also extracted. Also we show that in this context the data complexity of the multidimensional zero-correlation attack is larger than that of the other two attacks.

Abstract. Design of secure light-weight stream ciphers is an important area in cryptographic hardware & embedded systems and a very recent design by Armknecht and Mikhalev (FSE 2015) has received serious attention that uses shorter internal state and still claims to resist the time-memory-data-tradeoff (TMDTO) attacks. An instantiation of this design paradigm is the stream cipher named Sprout with 80-bit secret key. In this paper we cryptanalyze the cipher and refute various claims. The designers claim that the secret key of Sprout can not be recovered efficiently from the complete state information using a guess and determine attack. However, in this paper, we show that it is possible with a few hundred bits in practical time. More importantly, from around 850 key-stream bits, complete knowledge of NFSR (40 bits) and a partial knowledge of LFSR (around one third, i.e., 14 bits); we can obtain all the secret key bits. This cryptanalyzes Sprout with 2^{54} attempts (considering constant time complexity required by the SAT solver in each attempt, which is around 1 minute in a laptop). This is less than the exhaustive key search. Further, we show how related ideas can be employed to mount a fault attack against Sprout that requires around 120 faults in random locations (20 faults, if the locations are known), whereas the designers claim that such a fault attack may not be possible. Our cryptanalytic results raise quite a few questions about this design paradigm in general that should be revisited with greater care.

In this work, we apply the sliced biclique cryptanalysis technique to show 8-round collision attack on a hash function H based on 4-branch, Type-2 Generalized Feistel Network (Type-2 GFN). This attack is generic and works on 4-branch, Type-2 GFN with any parameters including the block size, type of round function, the number of S-boxes in each round and the number of SP layers inside the round function. We first construct a 8-round distinguisher on 4-branch, Type-2 GFN and then use this distinguisher to launch 8-round collision attack on compression functions based on Matyas-Meyer-Oseas (MMO) and Miyaguchi-Preneel (MP) modes. The complexity of the attack on 128-bit compression function is 2^56. The attack can be directly translated to collision attack on MP and MMO based hash functions and pseudo-collision attack on Davies-Meyer (DM) based hash functions. When the round function F is instantiated with double SP layer, we show the first 8-round collision attack on 4-branch, Type-2 GFN with double SP layer based compression function. The previous best attack on this structure was a 6-round near collision attack shown by Sasaki at Indocrypt'12. His attack cannot be used to generate full collisions on 6-rounds and hence our result can be regarded the best so far in literature on this structure.

This paper discusses provable security of two types of cascade encryptions. The first construction $\CE^l$, called $l$-cascade encryption, is obtained by sequentially composing $l$ blockcipher calls with independent keys. The security of $\CE^l$ has been a longstanding open problem until Gaži and Maurer~\cite{GM09} proved its security up to $2^{\ka+\min\{\frac{n}{2},\ka\}}$ query complexity for large cascading length, where $\ka$ and $n$ denote the key size and the block size of the underlying blockcipher, respectively. We improve this limit by proving the security of $\CE^l$ up to $2^{\ka+\min\left\{\ka,n\right\}-\frac{16}{l}\left(\frac{n}{2}+2\right)}$ query complexity: this bound approaches $2^{\ka+\min\left\{\ka,n\right\}}$ with increasing cascade length $l$. The second construction $\XCE^l$ is a natural cascade version of the DESX scheme with intermediate keys xored between blockcipher calls. This can also be viewed as an extension of double XOR-cascade proposed by Gaži and Tessaro~\cite{GT12}. We prove that $\XCE^l$ is secure up to $2^{\ka+n-\frac{8}{l}\left(\frac{n}{2}+2\right)}$ query complexity. As cascade length $l$ increases, this bound approaches $2^{\ka+n}$. In the ideal cipher model, one can obtain all the evaluations of the underlying blockcipher by making $2^{\ka+n}$ queries, so the $(\ka+n)$-bit security becomes the maximum that key-length extension based on a single $\ka$-bit key $n$-bit blockcipher is able to achieve. Cascade encryptions $\CE^l$~(with $n\leq\ka$) and $\XCE^l$ provide almost optimal security with large cascade length.

In this paper we experiment with cube testers on reduced round Trivium that can act as a distinguisher. Using heuristics, we obtain several distinguishers for Trivium running more than 800 rounds (maximum 829) with cube sizes not exceeding 27. In the process, we also exploit state biases that has not been explored before. Further, we apply our techniques to analyse Trivia-SC, a stream cipher proposed by modifying the parameters of Trivium and used as a building block for TriviA-ck (an AEAD scheme, which is submitted to the ongoing CAESAR competition). We obtain distinguishers till 900 rounds of Trivia-SC with a cube size of 21 only and our results refute certain claims made by the designers. These are the best results reported so far, though our work does not affect the security claims for the ciphers with full initialization rounds, namely 1152.

Known-key distinguishers for block ciphers were proposed by Knudsen and Rijmen at ASIACRYPT 2007 and have been a major research topic in cryptanalysis since then. A formalization of known-key attacks in general is known to be difficult. In this paper, we tackle this problem for the case of block ciphers based on ideal components such as random permutations and random functions as well as propose new generic known-key attacks on generalized Feistel ciphers. We introduce the notion of known-key indifferentiability to capture the security of such block ciphers under a known key. To show its meaningfulness, we prove that the known-key attacks on block ciphers with ideal primitives to date violate security under known-key indifferentiability. On the other hand, to demonstrate its constructiveness, we prove the balanced Feistel cipher with random functions and the multiple Even-Mansour cipher with random permutations known-key indifferentiable for a sufficient number of rounds. We note that known-key indifferentiability is more quickly and tightly attained by multiple Even-Mansour which puts it forward as a construction provably secure against known-key attacks.

A pseudorandom function F : K x X -> Y is said to be key homomorphic if given F(k1, x) and F(k2, x) there is an efficient algorithm to compute F(k1 xor k2, x), where xor denotes a group operation on k1 and k2 such as xor. Key homomorphic PRFs are natural objects to study and have a number of interesting applications: they can simplify the process of rotating encryption keys for encrypted data stored in the cloud, they give one round distributed PRFs, and they can be the basis of a symmetric-key proxy re-encryption scheme. Until now all known constructions for key homomorphic PRFs were only proven secure in the random oracle model. We construct the first provably secure key homomorphic PRFs in the standard model. Our main construction is based on the learning with errors (LWE) problem. In the proof of security we need a variant of LWE where query points are non-uniform and we show that this variant is as hard as the standard LWE. We also construct key homomorphic PRFs based on the decision linear assumption in groups with an l-linear map. We leave as an open problem the question of constructing standard model key homomorphic PRFs from more general assumptions.

In this paper, we revisit some existing techniques in Salsa20 cryptanalysis, and provide some new ideas as well. As a new result, we explain how a valid initial state can be obtained from a Salsa20 state after one round. This helps in studying the non-randomness of Salsa20 after 5 rounds. In particular, it can be seen that the 5-round bias reported by Fischer et al. (Indocrypt 2006) is a special case of our analysis. Towards improving the existing results, we revisit the idea of Probabilistic Neutral Bit (PNB) and how a proper choice of certain parameters reduce the complexity of the existing attacks. For cryptanalysis against 8-round Salsa20, we could achieve the key search complexity of $2^{247.2}$ compared to $2^{251}$ (FSE 2008) and $2^{250}$ (ICISC 2012).

A constant of $2^{22}$ appears in the security bounds of the Galois/Counter Mode of Operation, GCM. In this paper, we first develop an algorithm to generate nonces that have a high counter-collision probability. We show concrete examples of nonces with the counter-collision probability of about $2^{20.75}/2^{128}$. This shows that the constant in the security bounds, $2^{22}$, cannot be made smaller than $2^{19.74}$ if the proof relies on ``the sum bound.'' We next show that it is possible to avoid using the sum bound, leading to improved security bounds of GCM. One of our improvements shows that the constant of $2^{22}$ can be reduced to 32.

In the paper, we study whether it is possible to construct an efficient leakage-resilient symmetric scheme using the AES block cipher. We aim at bridging the gap between the theoretical leakage-resilient symmetric primitives used to build encryption schemes and the practical schemes that do not have any security proof against side-channel adversaries. Our goal is to construct an as efficient as possible leakage-resilient encryption scheme, but we do not want to change the cryptographic schemes already implemented. The basic idea consists in adding a leakage-resilient re-keying scheme on top of the encryption scheme and has been already suggested by Kocher to thwart differential power analysis techniques. Indeed, in such analysis, the adversary queries the encryption box and from the knowledge of the plaintext/ciphertext, she can perform a divide-and-conquer key recovery attack. The method consisting in changing the key for each or after a small number of encryptions with the same key is known as re-keying. It prevents DPA adversaries but not SPA attacks which use one single leakage trace. Here, we prove that using a leakage-resilient re-keying scheme on top of a secure encryption scheme in the standard model, leads to a leakage-resilient encryption scheme. The main advantage of the AES block cipher is that its implementations are generally heuristically-secure against SPA adversaries. This assumption is used in many concrete instantiations of leakage-resilient symmetric primitives. Consequently, if we use it and change the key for each new message block, the adversary will not be able to recover any key if the re-keying scheme is leakage-resilient. There is mainly two different techniques for re-keying scheme, either parallel or sequential, but if we want to avoid the adversary having access to many inputs/outputs, only the sequential method is possible. However, the main drawback of the latter technique is that in case of de-synchronization, many useless computations are required. In our re-keying scheme, we use ideas from the skip-list data structure to efficiently recover a specific key.

Two general classes (constructions) of bent functions are derived from the notion of spread. The first class, ${\cal PS}$, gives a useful framework for designing bent functions which are constant (except maybe at 0) on each of the $m$-dimensional subspaces of ${\Bbb F}_{2^{2m}}$ belonging to a partial spread. Explicit expressions (which may be used for applications) of bent functions by means of the trace can be derived for subclasses corresponding to some partial spreads, for instance the ${\cal PS}_{ap}$ class. Many more can be. The second general class, $H$, later slightly modified into a class called ${\cal H}$ so as to relate it to the so-called Niho bent functions, is (up to addition of affine functions) the set of bent functions whose restrictions to the subspaces of the Desarguesian spread (the spread of all multiplicative cosets of ${\Bbb F}_{2^m}^*$, added with 0, in ${\Bbb F}_{2^{2m}}^*$) are linear. It has been observed that the functions in ${\cal H}$ are related to o-polynomials, and this has led to several classes of bent functions in bivariate trace form. In this paper, after briefly looking at the ${\cal PS}$ functions related to the André spreads, and giving the trace representation of the ${\cal PS}$ corresponding bent functions and of their duals, we show that it is easy to characterize those bent functions whose restrictions to the subspaces of a spread are linear, but that it leads to a notion extending that of o-polynomial, for which it seems a hard task to find examples. We illustrate this with the André spreads and also study three other cases of ${\cal H}$-like functions (related to other spreads).

In this paper, we analyse the higher order differential properties of NORX, an AEAD scheme submitted to CAESAR competition. NORX is a sponge based construction. Previous efforts, by the designers themselves, have focused on the first order differentials and rotational properties for a small number of steps of the NORX core permutation, which turn out to have quite low biases when extended to the full permutation. In our work, the higher order differential properties are identified that allow to come up with practical distinguishers of the 4-round full permutation for NORX64 and half round less than the full permutation (i.e., 3.5-round) for NORX32. These distinguishers are similar to zero-sum distinguishers but are probabilistic in nature rather than deterministic, and are of order as low as four. The distinguishers have very low complexities, and are significantly more efficient than the generic generalized birthday attack for the same configurations of zero-sums. While these distinguishers identify sharper non-randomness than what the designers identified, our results do not lend themselves for cryptanalysis of full-round NORX encryption or authentication.

The mere number of various apparently different statistical attacks on block ciphers has raised the question about their relationships which would allow to classify them and determine those that give essentially complementary information about the security of block ciphers. While mathematical links between some statistical attacks have been derived in the last couple of years, the important link between general truncated differential and multidimensional linear attacks has been missing. In this work we close this gap. The new link is then exploited to relate the complexities of chosen-plaintext and known-plaintext distinguishing attacks of differential and linear types, and further, to explore the relations between the key-recovery attacks. Our analysis shows that a statistical saturation attack is the same as a truncated differential attack, which allows us, for the first time, to provide a justifiable analysis of the complexity of the statistical saturation attack and discuss its validity on 24 rounds of the PRESENT block cipher. By studying the data, time and memory complexities of a multidimensional linear key-recovery attack and its relation with a truncated differential one, we also show that in most cases a known-plaintext attack can be transformed into a less costly chosen-plaintext attack. In particular, we show that there is a differential attack in the chosen-plaintext model on 26 rounds of PRESENT with less memory complexity than the best previous attack, which assumes known plaintext. The links between the statistical attacks discussed in this paper give further examples of attacks where the method used to sample the data required by the statistical test is more differentiating than the method used for finding the distinguishing property

Recently, a number of relations have been established among previously known statistical attacks on block ciphers. Leander showed in 2011 that statistical saturation distinguishers are on average equivalent to multidimensional linear distinguishers. Further relations between these two types of distinguishers and the integral and zero-correlation distinguishers were established by Bogdanov et al.. Knowledge about such relations is useful for classification of statistical attacks in order to determine those that give essentially complementary information about the security of block ciphers. The purpose of the work presented in this paper is to explore relations between differential and linear attacks. The mathematical link between linear and differential attacks was discovered by Chabaud and Vaudenay already in 1994, but it has never been used in practice. We will show how to use it for computing accurate estimatesof truncated differential probabilities from accurate estimates of correlations of linear approximations. We demonstrate this method in practice and give the first instantiation of multiple differential cryptanalysis using the LLR statistical test on PRESENT. On a more theoretical side,we establish equivalence between a multidimensional linear distinguisher and a truncated differential distinguisher, and show that certain zero-correlation linear distinguishers exist if and only if certain impossible differentials exist.

We consider tweakable blockciphers with beyond the birthday bound security. Landecker, Shrimpton, and Terashima (CRYPTO 2012) gave the first construction with security up to $\mathcal{O}(2^{2n/3})$ adversarial queries ($n$ denotes the block size in bits of the underlying blockcipher), and for which changing the tweak does not require changing the keys for blockcipher calls. In this paper, we extend this construction, which consists of two rounds of a previous proposal by Liskov, Rivest, and Wagner (CRYPTO 2002), by considering larger numbers of rounds $r>2$. We show that asymptotically, as $r$ increases, the resulting tweakable blockcipher approaches security up to the information bound, namely $\mathcal{O}(2^n)$ queries. Our analysis makes use of a coupling argument, and carries some similarities with the analysis of the iterated Even-Mansour cipher by Lampe, Patarin, and Seurin (ASIACRYPT 2012).

How does the security of the AES change when the S-box is replaced by a secret S-box, about which the adversary has no knowledge? Would it be safe to reduce the number of encryption rounds? In this paper, we demonstrate attacks based on integral cryptanalysis which allows to recover both the secret key and the secret S-box for respectively four, five, and six rounds of the AES. Despite the significantly larger amount of secret information which an adversary needs to recover, the attacks are very efficient with time/data complexities of $2^{17}/2^{16}$, $2^{38}/2^{40}$ and $2^{90}/2^{64}$, respectively. Another interesting aspect of our attack is that it works both as chosen plaintext and as chosen ciphertext attack. Surprisingly, the chosen ciphertext variant has a significantly lower time complexity in the attacks on four and five round, compared to the respective chosen plaintext attacks.

Pure OMD is an authenticated encryption mode that will be presented by Reyhanitabar et al. at FSE 2015. It is (among others) claimed to achieve authenticity against nonce-misusing adversaries. We show that this claim is incorrect, by presenting an adversary that makes 3 queries (including the forgery) of a total complexity 6.

A 25-gigabyte "point obfuscation" challenge "using security parameter 60" was announced at the Crypto 2015 rump session; "point obfuscation" is another name for password hashing. This paper shows that the particular matrix-multiplication hash function used in the challenge is much less secure than previous password-hashing functions are believed to be. This paper's attack algorithm broke the challenge in just 19 minutes using a cluster of 21 PCs.

In this paper, we present universal forgery and key recovery attacks on the most popular hash-based MAC constructions, e.g., HMAC and NMAC, instantiated with an AES-like hash function Whirlpool. These attacks work with Whirlpool reduced to 6 out of 10 rounds in single-key setting. To the best of our knowledge, this is the first result on ``original'' key recovery for HMAC (previous works only succeeded in recovering the equivalent keys). Interestingly, the number of attacked rounds is comparable with that for collision and preimage attacks on Whirlpool hash function itself. Lastly, we present a distinguishing-H attack against the full HMAC- and NMAC-Whirlpool.

Feistel structures are an extremely important and extensively researched type of cryptographic schemes. In this paper we describe improved attacks on Feistel structures with more than 4 rounds. We achieve this by a new attack that combines the main benefits of meet-in-the-middle attacks (which can reduce the time complexity by comparing only half blocks in the middle) and dissection attacks (which can reduce the memory complexity but have to guess full blocks in the middle in order to perform independent attacks above and below it). For example, for a 7-round Feistel structure on n-bit inputs with seven independent round keys of n/2 bits each), a MITM attack can use (2^1.5n ,2^1.5n) time and memory, while dissection requires (2^2n, 2^n) time and memory. Our new attack requires only (2^1.5n, 2^n) time and memory, using a few known plaintext/ciphertext pairs. When we are allowed to use more known plaintexts, we develop new techniques which rely on the existence of multicollisions and differential properties deep in the structure in order to further reduce the memory complexity. Our new attacks are not just theoretical generic constructions - in fact, we can use them to improve the best known attacks on several concrete cryptosystems such as CAST-128 (where we reduce the memory complexity from 2^111 to 2^64) and DEAL-256 (where we reduce the memory complexity from 2^200 to 2^144), without affecting their time and data complexities. An extension of our techniques applies even to some non-Feistel structures - for example, in the case of FOX, we reduce the memory complexity of all the best known attacks by a factor of 2^16.

Given (deterministic) ciphers $\calE$ and~$E$ that can encipher messages of $\el$ and $n$ bits, respectively, we construct a cipher~$\calE^*=XLS[\calE,E]$ that can encipher messages of $\el+s$ bits for any $s<n$. Enciphering such a string will take one call to~$\calE$ and two calls to~$E$. We prove that~$\calE^*$ is a strong pseudorandom permutation as long as~$\calE$ and~$E$ are. Our construction works even in the tweakable and VIL (variable-input-length) settings. It makes use of a multipermutation (a pair of orthogonal Latin squares), a combinatorial object not previously used to get a provable-security result.

We define the new notion of a multilinear pseudorandom function (PRF), and give a construction with a proof of security assuming the hardness of the decisional Diffie-Hellman problem. A direct application of our construction yields (non-multilinear) PRFs with aggregate security from the same assumption, resolving an open question of Cohen, Goldwasser, and Vaikuntanathan. Additionally, multilinear PRFs give a new way of viewing existing algebraic PRF constructions: our main theorem implies they too satisfy aggregate security.

Linear approximations of modular addition modulo a power of two was studied by Wallen in 2003. He presented an efficient algorithm for computing linear probabilities of modular addition. In 2013 Sculte-Geers investigated the problem from another viewpoint and derived a somewhat explicit for these probabilities. In this note we give a closed formula for linear probabilities of modular addition modulo a power of two, based on what Schlte-Geers presented: our closed formula gives a better insight on these probabilities and more information can be extracted from it.

We define ideal functionalities that are weaker than ideal functionalities traditionally used in realizing variable input length (VIL) random oracles (RO) in the indifferentiability or universal-Composability (UC) model. We also show realization of VIL-RO using these weaker ideal functionalities, with applications to proving Fugue and CubeHash hash functions to be VIL-RO. We argue that components of Fugue realize this weaker ideal functionality using techniques employed in proving resistance of Fugue to differential collision-attacks. This should be contrasted with other hash functions that are proven VIL-RO assuming the components are extremely ideal, e.g. random permutations.

Masking is a popular countermeasure against side channel attacks. Many practical works use Boolean masking because of its simplicity, ease of implementation and comparably low performance overhead. Some recent works have explored masking schemes with higher algebraic complexity and have shown that they provide more security than Boolean masking at the cost of higher overheads. In particular, masking based on the inner product was shown to be practical, albeit not efficient, for a small security parameter, and at the same time provable secure in the domain of leakage resilient cryptography for a large security parameter. In this work we explore a security versus efficiency tradeoff and provide an improved and tweaked inner product masking. Our practical security evaluation shows that it is less secure than the original inner product masking but more secure than Boolean masking. Our performance evaluation shows that our scheme is only four times slower than Boolean masking and more than two times faster than the original inner product masking. Besides the practical security analysis we prove the security of our scheme and its masked operations in the threshold probing model.

Rotational cryptanalysis is a probabilistic attack applicable to word oriented designs that use (almost) rotation-invariant constants. It is believed that the success probability of rotational cryptanalysis against ciphers and functions based on modular additions, rotations and XORs, can be computed only by counting the number of additions. We show that this simple formula is incorrect due to the invalid Markov cipher assumption used for computing the probability. More precisely, we show that chained modular additions used in ARX ciphers do not form a Markov chain with regards to rotational analysis, thus the rotational probability cannot be computed as a simple product of rotational probabilities of individual modular additions. We provide a precise value of the probability of such chains and give a new algorithm for computing the rotational probability of ARX ciphers. We use the algorithm to correct the rotational attacks on BLAKE2 and to provide valid rotational attacks against the simplified version of Skein.

We introduce new constructions of systematic authentication codes over finite fields and Galois rings. One code is built over finite fields using resilient functions and it provides optimal impersonation and substitution probabilities. Other two proposed codes are defined over Galois rings, one is based on resilient maps and it attains optimal probabilities as well, while the other uses maps whose Fourier transforms get higher values. Being the finite fields special cases of Galois rings, the first code introduced for Galois rings apply also at finite fields. For the special case of characteristic $p^2$, the maps used at the second case in Galois rings are bent indeed, and this case is subsumed by our current general construction of characteristic $p^s$, with $s\geq 2$.

A draft call for the CAESAR authenticated-encryption competition adopts an interface that is not aligned with existing definitions in the literature. It is the purpose of this brief note to formalize what we believe to be the intended definitions.

The FX-construction was proposed in 1996 by Kilian and Rogaway as a generalization of the DESX scheme. The construction increases the security of an $n$-bit core block cipher with a $\kappa$-bit key by using two additional $n$-bit masking keys. Recently, several concrete instances of the FX-construction were proposed, including PRINCE (proposed at Asiacrypt 2012) and PRIDE (proposed at CRYPTO 2014). These ciphers have $n=\kappa=64$, and are proven to guarantee about $127-d$ bits of security, assuming that their core ciphers are ideal, and the adversary can obtain at most $2^d$ data. In this paper, we devise new cryptanalytic time-memory-data tradeoff attacks on FX-constructions. While our attacks do not contradict the security proof of PRINCE and PRIDE, nor pose an immediate threat to their users, some specific choices of tradeoff parameters demonstrate that the security margin of the ciphers against practical attacks is smaller than expected. Our techniques combine a special form of time-memory-data tradeoffs, typically applied to stream ciphers, with recent analysis of FX-constructions by Fouque, Joux and Mavromati.

In recent years, a number of standardized symmetric encryption schemes have fallen foul of attacks exploiting the fact that in some real world scenarios ciphertexts can be delivered in a fragmented fashion. We initiate the first general and formal study of the security of symmetric encryption against such attacks. We extend the SSH-specific work of Paterson and Watson (Eurocrypt 2010) to develop security models for the fragmented setting. We also develop security models to formalize the additional desirable properties of ciphertext boundary hiding and robustness against Denial-of-Service (DoS) attacks for schemes in this setting. We illustrate the utility of each of our models via efficient constructions for schemes using only standard cryptographic components, including constructions that simultaneously achieve confidentiality, ciphertext boundary hiding and DoS robustness.

MAC striping has been suggested as a technique to authenticate encrypted payloads using short tags. For an idealized MAC scheme, the probability of a selective forgery has been estimated as $\binom{\ell+m}{m}^{-1}\cdot 2^{-m}$, when utilizing MAC striping with $\ell$-bit payloads and $m$-bit tags. We show that this estimate is too optimistic. For $m\le\ell$ and any payload, we achieve a selective forgery with probability $\ge \binom{\ell+m}{m}^{-1}$, and usually many orders of magnitude more than that.

This paper investigates the effect of affine transformations of the Sbox on the maximal expected differential probability MEDP and linear potential MELP over two rounds of a substitution-permutation network, when the diffusion layer is linear over the finite field defined by the Sbox alphabet. It is mainly motivated by the fact that the 2-round MEDP and MELP of the AES both increase when the AES Sbox is replaced by the inversion in $GF(2^8)$. Most notably, we give new upper bounds on these two quantities which are not invariant under affine equivalence. Moreover, within a given equivalence class, these new bounds are maximal when the considered Sbox is an involution. These results point out that different Sboxes within the same affine equivalence class may lead to different two-round MEDP and MELP. In particular, we exhibit some examples where the basis chosen for defining the isomorphism between $GF(2)^m$ and $GF(2^m)$ affects these values. For Sboxes with some particular properties, including all Sboxes of the form $A(x^s)$ as in the AES, we also derive some lower and upper bounds for the 2-round MEDP and MELP which hold for any MDS linear layer.