Two recent works [Lin, EUROCRYPT 2016, Lin and Vaikuntanathan, FOCS 2016] showed how to construct Indistinguishability Obfuscation (IO) from constant degree multilinear maps. However, the concrete degrees of multilinear maps used in their constructions exceed 30. In this work, we reduce the degree of multilinear maps needed to 5, by giving a new construction of IO from asymmetric $L$-linear maps and a pseudo-random generator (PRG) with output locality $L$ and polynomial stretch. When plugging in a candidate PRG with locality-$5$ (\eg, [Goldreich, ECCC 2010, Mossel, Shpilka, and Trevisan, FOCS 2013, O'Donnald and Wither, CCC 2014]), we obtain a construction of IO from 5-linear maps. Our construction improves the state-of-the-art at two other fronts: First, it relies on ``classical'' multilinear maps, instead of their powerful generalization of graded encodings. Second, it comes with a security reduction to i) the SXDH assumption on algebraic multilinear maps [Boneh and Silverberg, Contemporary Mathematics, Rothblum, TCC 2013], ii) the security of PRG, and iii) sub-exponential LWE, all with sub-exponential hardness. The SXDH assumption is weaker and/or simpler than assumptions on multilinear maps underlying previous IO constructions. When noisy multilinear maps [Garg, Gentry, and Halivi, EUROCRYPT 2013] are used instead, security is based on a family of more complex assumptions that hold in the generic model.

From the proposal of key-recovery algorithms for RSA secret key from its noisy version at Crypto2009, there have been considerable researches on RSA key recovery from discrete noise. At CHES2014, two efficient algorithms for recovering secret keys are proposed from noisy analog data obtained through physical attacks such as side channel attacks. One of the algorithms works even if the noise distributions are unknown. However, the algorithm is not optimal especially if the noise distribution is imbalanced. To overcome this problem, we propose new algorithms to recover from such an imbalanced analog noise. We first present a generalized algorithm and show its success condition. We then construct the algorithm suitable for imbalanced noise under the condition that the variances of noise distributions are a priori known. Our algorithm succeeds in recovering the secret key from much more noise. We present the success condition in the explicit form and verify that our algorithm is superior to the previous results. We then show its optimality. Note that the proposed algorithm has the same performance as the previous one in the balanced noise. We next propose a key recovery algorithm that does not use the values of the variances. The algorithm first estimates the variance of noise distributions from the observed data with help of the EM algorithm and then recover the secret key by the first algorithm with their estimated variances. The whole algorithm works well even if the values of the variance is unknown in advance. We examine that our proposed algorithm succeeds in recovering the secret key from much more noise than the previous algorithm.

Revoking corrupted users is a desirable functionality for cryptosystems. Since Boldyreva, Goyal, and Kumar (ACM CCS 2008) proposed a notable result for scalable revocation method in identity-based encryption (IBE), several works have improved either the security or the efficiency of revocable IBE (RIBE). Currently, all existing scalable RIBE schemes that achieve adaptively security against decryption key exposure resistance (DKER) can be categorized into two groups; either with long public parameters or over composite-order bilinear groups. From both practical and theoretical points of views, it would be interesting to construct adaptively secure RIBE scheme with DKER and short public parameters in prime-order bilinear groups. In this paper, we address this goal by using Seo and Emura's technique (PKC 2013), which transforms the Waters IBE to the corresponding RIBE. First, we identify necessary requirements for the input IBE of their transforming technique. Next, we propose a new IBE scheme having several desirable properties; satisfying all the requirements for the Seo-Emura technique, constant-size public parameters, and using prime-order bilinear groups. Finally, by applying the Seo-Emura technique, we obtain the first adaptively secure RIBE scheme with DKER and constant-size public parameters in prime-order bilinear groups. We also discuss some extensions of the proposed RIBE scheme.

Energy consumption of block ciphers is critical in resource constrained devices. Unrolling has been explored in literature as a technique to increase efficiency by eliminating energy spent in loop control elements such as registers and multiplexers. However these savings are minimal and are offset by the increase in glitching power that comes with unrolling. We propose an efficient latch-based glitch filter for unrolled designs that reduces energy per encryption by an order of magnitude over a straightforward implementation, and by 28-32% over the best existing glitch filtering schemes. We explore the optimal number of glitch filters that should be used in order to minimize total energy, and provide estimates of the area cost. Partially unrolled designs also benefit from using our scheme with energies competitive to fully serialized implementations. We demonstrate our approach on the SIMON-128 and AES-256 block ciphers.

We provide a new family of elliptic curves that results in a one to two percent performance improvement of the elliptic curve integer factorization method. The speedup is confirmed by extensive tests for factors ranging from 15 to 63 bits.

True random number generators (TRNGs) are essential for cryptographic systems, and they are usually evaluated by the concept of entropy. In general, the entropy of a TRNG is estimated from its stochastic model, and reflected in the statistical results of the generated raw bits. Oscillator-based TRNGs are widely used in practical cryptographic systems due to its elegant structure, and its stochastic model has been studied in different aspects. In this paper, we investigate the applicability of the different entropy estimation methods for oscillator-based TRNGs, including the bit-rate entropy, the lower bound and the approx imate entropy. Particularly, we firstly analyze the two existing stochastic models (one of which is phase-based and the other is time-based), and deduce consistent bit-rate entropy results from these two models. Then, we design an approximate entropy calculation method on the output raw bits of a simulated oscillator-based TRNG, and this statistical calculation result well matches the bit-rate entropy from stochastic models. In addition, we discuss the extreme case of tiny randomness where some methods are inapplicable, and provide the recommendations for these entropy evaluation methods. Finally, we design a hardware verification method in a real oscillator-based TRNG, and validate these estimation methods in the hardware platform.

Online ciphers, in spite of being insecure against an sprp adversary, can be desirable at places because of their ease of implementation and speed. Here we propose a single-keyed inverse-free construction that achieves online sprp security with an optimal number of blockcipher calls. We also include a partial block construction, without requiring any extra key.

Attribute-Based Encryption (ABE) allows to target the recipients of a message according to a policy expressed as a predicate among some attributes. Ciphertext-policy ABE schemes can choose the policy at the encryption time. In this paper, we define a new property for ABE: homomorphic-policy. A combiner is able to (publicly) combine ciphertexts under different policies into a ciphertext under a combined policy (AND or OR). More precisely, using linear secret sharing schemes, we design Attribute-Based Key Encapsulation Mechanisms (ABKEM) with the Homomorphic-Policy property: given several encapsulations of the same keys under various policies, anyone can derive an encapsulation of the same key under any combination of the policies. As an application, in Pay-TV, this allows to separate the content providers that can generate the encapsulations of a session key under every attributes, this key being used to encrypt the payload, and the service providers that build the decryption policies according to the subscriptions. The advantage is that the aggregation of the encapsulations by the service providers does not contain any secret information.

We device a general secret sharing scheme for evolving access structures (following [KNY16]). Our scheme has (sub)exponentially smaller share complexity (share of $i$'th party) for certain access structures compared to the general scheme in ~\cite{KNY16}. We stress that unlike ~\cite{KNY16}'s scheme, our scheme requires that the entire evolving access structure is known in advance. Revising, ~\cite{KNY16}'s scheme (in its most optimized form) is based on a representation of the access structure by an ordered (possibly infinite) oblivious, read once decision tree. Each node is associated with an output of the function (0 or 1). The tree is augmented to cut paths that reach a node where $f$ evaluates to 1 at that node (works for evolving access structures, in which the descendants of all 1-nodes must be 1). Each party $P_i$ receives a (single-bit) share for each edge exiting a node labeled by $x_i$. Generally, the scheme of ~\cite{KNY16} has share complexity $O(w_T(i))$, where $w_T(i)$ is the width of layer $i$ relevant decision tree. In general, this width can reach $\Omega(2^i)$. To get non trivial share complexity, $e^{n^{o(1)}}$, a \emph{tree} of width $e^{n^{o(1)}}$ is required. Our scheme is based on a generalized (infinite) tree representation of the access structure. The main difference is that vertices are labeled with sequences of variables, rather than a single variable. As a result, we often get smaller trees, and the edges $e$ are labeled by more complex (non-evloving) monotone functions $g_e$ of the variables in the sequence. The share associated with the edge is shared (among the parties in the relevant sequence). As a result, the tree is smaller, while the shares received for every edge in it are bigger. Still, the tradeoff is often on our side. Namely, for access structures with ordered read-once \emph{branching programs} with relatively small width, $e^{O(i^c)}$ for $c<0.25$, share complexity of $e^{n^{o(1)}}$ is achieved. More specifically, the resulting share complexity is $(iw_{BP}(i^2))^{O(\log{i} + \log{w_{BP}(i^2)})}$. In particular, for $w=\Omega(i)$, we get share complexity of $w_{BP}(i^2)^{O(\log{w_{BP}(i^2)})}$. Finally, a further improved variant of our scheme for a special class of ``counting'' access structures yields polynomial share complexity. In particular, we obtain an evolving secret sharing scheme for \emph{evolving majority} with share complexity $\tilde{O}(n^6)$, answering an open question of~\cite{KNY16}.

At FSE 2006, Iwata introduced the CENC encryption mode and proved its security up to 2^{2n/3} plaintext blocks processed in total. He conjectured optimal security up to a constant. In this brief note, we confirm this conjecture. Rather than proving it ourselves, we point out that the conjecture's proof follows as a corollary of Patarin's ``Theorem P_i xor P_j for any xi_max'' from 2010. This connection appears to have remained unnoticed, and the sole purpose of this brief note is to make the connection explicit.

In broadcast encryption schemes, a distribution center broadcasts an encrypted message to a subset $ S $ chosen from a universe of receivers and only the intended users are able to decrypt the message. Most broadcast encryption schemes do not provide anonymity and the identities of target receivers are sent in plaintext. However, in several applications, the authorized users' identities has the same sensitivity as the message itself. YRL, is an anonymous attribute-based broadcast encryption scheme with linear computation, communication and storage overheads in the number of attributes. In this paper, we first propose an attack on the YRL scheme and show that unfortunately the unauthorized receivers can also decrypt the broadcasted message. Next, we propose the Improved-YRL scheme and prove that it achieves anonymity and semantic security under adaptive corruptions in the chosen ciphertext setting. The proof is provided using the dual system encryption technique and is based on three complexity assumptions in composite order bilinear maps. The Improved-YRL scheme is a step forward in solving the long-standing problem of secure and low overhead anonymous broadcast encryption.

We propose practically efficient signature schemes which feature several attractive properties: (a) they only rely on the security of symmetric-key primitives (block ciphers, hash functions), and are therefore a viable candidate for post-quantum security, (b) they have extremely small signing keys, essentially the smallest possible, and, (c) they are highly parametrizable. For this result we take advantage of advances in two very distinct areas of cryptography. The first is the area of primitives in symmetric cryptography, where recent developments led to designs which exhibit an especially low number of multiplications. The second is the area of zero-knowledge proof systems, where significant progress for efficiently proving statements over general circuits was recently made. We follow two different directions, one of them yielding the first practical instantiation of a design paradigm due to Bellare and Goldwasser without relying on structured hardness assumptions. For both our schemes we explore the whole design spectrum to obtain optimal parameter choices for different settings. Within limits, in all cases our schemes allow to trade-off computational effort with signature sizes. We also demonstrate that our schemes are parallelizable to the extent that they can practically take advantage of several cores on a CPU.

An Oblivious Parallel RAM (OPRAM) provides a general method to simulate any Parallel RAM (PRAM) program, such that the resulting memory access patterns leak nothing about secret inputs. OPRAM was originally proposed by Boyle et al. as the natural parallel counterpart of Oblivious RAM (ORAM), which was shown to have broad applications, e.g., in cloud outsourcing, secure processor design, and secure multi-party computation. Since parallelism is common in modern computing architectures such as multi-core processors or cluster computing, OPRAM is naturally a powerful and desirable building block as much as its sequential counterpart ORAM is. Although earlier works have shown how to construct OPRAM schemes with polylogarithmic simulation overhead, in comparison with best known sequential ORAM constructions, all existing OPRAM schemes are (poly-)logarithmic factors more expensive. In this paper, we present a new framework in which we construct both statistically secure and computationally secure OPRAM schemes whose asymptotical performance matches the best known ORAM schemes in each setting. Since an OPRAM scheme with simulation overhead X directly implies an ORAM scheme with simulation overhead X, our result can be regarded as providing a unifying framework in which we can subsume all known results on statistically and computationally secure ORAMs and OPRAMs alike. Particularly for the case of OPRAMs, we also improve the state-of-the-art scheme by superlogarithmic factors. To achieve the aforementioned results requires us to combine a variety of techniques involving 1) efficient parallel oblivious algorithm design; and 2) designing tight randomized algorithms and proving measure concentration bounds about the rather involved stochastic process induced by the OPRAM algorithm.

In this paper we study public key encryption schemes of indistinguishability security against receiver selective opening (IND-RSO) attacks, where the attacker can corrupt some receivers and get the corresponding secret keys in the multi-party setting. Concretely: -We present a general construction of RSO security against chosen ciphertext attacks (RSO-CCA) by combining any RSO secure scheme against chosen plaintext attacks (RSO-CPA) with any regular CCA secure scheme, along with an appropriate non-interactive zero-knowledge proof. -We show that the leakage-resistant construction given by Hazay \emph{et al.} in Eurocrypt 2013 from weak hash proof system (wHPS) is RSO-CPA secure. -We further show that the CCA secure construction given by Cramer and Shoup in Eurocrypt 2002 based on the universal HPS is RSO-CCA secure, hence obtain a more efficient paradigm for RSO-CCA security.

In side channel attack (SCA) studies, it is widely believed that unprotected implementations leak information about the intermediate states of the internal cryptographic process. However, directly recovering the intermediate states is not common practice in today's SCA study. Instead, most SCAs exploit the leakages in a "guess-and-determine" way, where they take a partial key guess, compute the corresponding intermediate states, then try to identify which one fits the observed leakages better. In this paper, we ask whether it is possible to take the other way around---directly learning the intermediate states from the side channel leakages. Under certain circumstances, we find that the intermediate states can be efficiently recovered with the well-studied Independent Component Analysis (ICA). Specifically, we propose several methods to convert the side channel leakages into effective ICA observations. For more robust recovery, we also present a specialized ICA algorithm which exploits the specific features of circuit signals. Experiments confirm the validity of our analysis in various circumstances, where most intermediate states can be correctly recovered with only a few hundred traces. To our knowledge, this is the first attempt to directly recover the intermediate states in a completely non-profiled setting. Our approach brings new possibilities to the current SCA study, including building an alternative SCA distinguisher, directly attacking the middle encryption rounds and reverse engineering with fewer restrictions. Considering its potential in more advanced applications, we believe our ICA-based SCA deserves more research attention in the future study.

In this paper, we describe several attacks to the protocol by Nguyen et al. presented at ESORICS 2016, an authenticated key agreement protocol mediated by a proxy entity, restricted to only symmetric encryption primitives and intended for IoT environments. This protocol uses long-term weak secrets as intermediate values during encryption and decryption procedures, which implies that these can be used to encrypt and decrypt messages without knowing the corresponding secret keys. In our work, we show how access to weak secrets can break forward security and lead to key compromise impersonation attacks. Moreover, we demonstrate that this problem cannot be solved even if the affected user revokes his previous secret key and updates it to a new one. In addition, we explain how the choice of a keyed hash as part of the protocol makes it potentially vulnerable to length-extension attacks, depending on the choice of hash function. We illustrate this latter problem experimentally. Finally, we show how a combination of these exploits can be used to set up elaborate attack scenarios.

Masking schemes achieve provable security against side-channel analysis by using secret sharing to decorrelate key-dependent intermediate values of the cryptographic algorithm and side-channel information. Masking schemes make assumptions on how the underlying leakage mechanisms of hardware or software behave to account for various physical effects. In this paper, we investigate the effect of the physical placement on the security using leakage assessment on power measurements collected from an FPGA. In order to differentiate other masking failures, we use threshold implementations as masking scheme in conjunction with a high-entropy pseudorandom number generator. We show that we can observe differences in---possibly---exploitable leakage by placing functions corresponding to different shares of a cryptographic implementation in close proximity.

As recently been emphasized by NSA and NIST, there is an increasing need for cryptographic schemes being secure against quantum computer attacks. Especially in the area of digital signature schemes, multivariate cryptography is one of the main candidates for this. At Inscrypt 2015, Nie et al. proposed a new multivariate signature scheme called CUOV, whose public key consists both of quadratic and cubic polynomials. However, the scheme was broken by an attack of Hashimoto. In this paper we take a closer look on the CUOV scheme and its attack and propose two new multivariate signature schemes called CSSv and SVSv2, which are secure against Hashimoto's attack and all other known attacks on multivariate schemes. Especially our schemes are more efficient than CUOV and UOV and highly comparable to Rainbow.

In this paper we consider the maximum absolute value $\Delta_f$ in the autocorrelation spectrum (not considering the zero point) of a function $f$. In even number of variables $n$, bent functions possess the highest nonlinearity with $\Delta_f = 0$. The long standing open question (for two decades) in this area is to obtain a theoretical construction of balanced functions with $\Delta_f < 2^{\frac n2}$. So far there are only a few examples of such functions for $n = 10, 14$, but no general construction technique is known. In this paper, we mathematically construct an infinite class of balanced Boolean functions on $n$ variables having absolute indicator strictly lesser than $\delta_n = 2^{\frac{n}{2}}-2^{\frac{n+6}{4}}$, nonlinearity strictly greater than $\rho_n = 2^{n-1} - 2^{\frac{n}{2}} + 2^{\frac n2-3} - 5\cdot2^{\frac{n-2}{4}}$ and algebraic degree $n-1$, where $n\equiv 2 \pmod 4$ and $n\geq 46$. While the bound $n \geq 46$ is required for proving the generic result, our construction starts from $n = 18$ and we could obtain balanced functions with $\Delta_f < 2^{\frac{n}{2}}$ and nonlinearity $> 2^{n-1} - 2^\frac{n}{2}$ for $n = 18, 22$ and $26$.

Since the development of tree-based Oblivious RAM by Shi et al. (Asiacrypt '11) it has become apparent that privacy preserving outsourced storage can be practical. Although most current constructions follow a client-server model, in many applications it is desirable to share data between different clients, in a way that hides the access patterns, not only from the server, but also between the clients. In this work, we introduce Blurry-ORAM, an extension of Path-ORAM that allows for oblivious sharing of data in the multi-client setting, so that accesses can be hidden from the server and other clients. Our construction follows the design of Path-ORAM as closely as possible in order to benefit from its performance as well as security. We prove our construction secure in a setting where the clients are semi-honest, do not trust each other but try to learn the access patterns of each other.

We show how to construct pseudorandom permutations (PRPs) that remain secure even if the adversary can query the permutation on a quantum superposition of inputs. Such PRPs are called \emph{quantum-secure}. Our construction combines a quantum-secure pseudorandom \emph{function} together with constructions of \emph{classical} format preserving encryption. By combining known results, we obtain the first quantum-secure PRP in this model whose security relies only on the existence of one-way functions. Previously, to the best of the author's knowledge, quantum security of PRPs had to be assumed, and there were no prior security reductions to simpler primitives, let alone one-way functions.

Recently, Tao et al. presented a new simple and efficient multivariate pubic key encryption scheme based on matrix multiplica- tion, which is called Simple Matrix Scheme or ABC. Using linearization method, we propose a polynomial time algorithm, which directly solves an equivalent private key from the public key of ABC. Furthermore, our attack can also be applied to the variants of ABC since these variants have the same algebraic structure as the ABC scheme. Therefore, the ABC cryptosystem and its variants are insecure.

Differential power analysis (DPA) is a powerful tool to extract the key of a cryptographic implementation from observing its power consumption during the en-/decryption of many different inputs. Therefore, cryptographic schemes based on frequent re-keying such as leakage-resilient encryption aim to inherently prevent DPA on the secret key by limiting the amount of data being processed under one key. However, the original asset of encryption, namely the plaintext, is disregarded. This paper builds on this observation and shows that the re-keying countermeasure does not only protect the secret key, but also induces another DPA vulnerability that allows for plaintext recovery. Namely, the frequent re-keying in leakage-resilient streaming modes causes constant plaintexts to be attackable through first-order DPA. Similarly, constant plaintexts can be revealed from re-keyed block ciphers using templates in a second-order DPA. Such plaintext recovery is particularly critical whenever long-term key material is encrypted and thus leaked. Besides leakage-resilient encryption, the presented attacks are also relevant for a wide range of other applications in practice that implicitly use re-keying, such as multi-party communication and memory encryption with random initialization for the key. Practical evaluations on both an FPGA and a microcontroller support the feasibility of the attacks and thus suggest the use of cryptographic implementations protected by mechanisms like masking in scenarios that require data encryption with multiple keys.

Group signature schemes (GSS) represent an important privacy-enhancing technology. However, their practical applicability is restricted due to inefficiencies of existing membership revocation mechanisms that often place a too large computational burden and communication overhead on the involved parties. Moreover, it seems that the general belief (or unwritten law) of avoiding online authorities by all means artificially and unnecessarily restricts the efficiency and practicality of revocation mechanisms in GSSs. While a mindset of preventing online authorities might have been appropriate more than 10 years ago, today the availability of highly reliable cloud computing infrastructures could be used to solve open challenges. More specifically, in order to overcome the inefficiencies of existing revocation mechanisms, we propose an alternative approach denoted as linking-based revocation (LBR) which is based on the concept of controllable linkability. The novelty of LBR is its transparency for signers and verifiers that spares additional computations as well as updates. We therefore introduce dedicated revocation authorities (RAs) that can be contacted for efficient (constant time) revocation checks. In order to protect these RAs and to reduce the trust in involved online authorities, we additionally introduce distributed controllable linkability. Using latter, RAs cooperate with multiple authorities to compute the required linking information, thus reducing the required trust. Besides efficiency, an appealing benefit of LBR is its generic applicability to pairing-based GSSs secure in the BSZ model as well as GSSs with controllable linkability. This includes the XSGS scheme, and the GSSs proposed by Hwang et al., one of which has been standardized in the recent ISO 20008-2 standard.

Asharov, Canetti, and Hazay (Eurocrypt 2011) studied how game-theoretic concepts can be used to capture the cryptographic properties of correctness, privacy, and fairness in two-party protocols for fail- stop adversaries. In this work, we further study the characterization of the cryptographic properties of specific two-party protocols, oblivious transfer (OT) and commitment, in terms of game theory. Specif- ically, for each protocol, OT and commitment, we define a two-party game between rational sender and receiver together with their utility functions. Then, we prove that a given protocol satisfies cryptographic properties if and only if the strategy of following the protocol is in a Nash equilibrium. Compared to the previous work of Asharov et al., our characterization has several advantages: The game is played by multiple rational parties; All the cryptographic properties of OT/commitment are characterized by a single game; Security for malicious adversaries is considered; Utility functions are specified in general forms based on the preferences of the parties; A solution concept employed is a plain Nash equilibrium. Based on the above equivalence between game-theoretic and cryptographic security, we introduce a new game-theoretic security by considering several unsatisfactory points in the utility functions of the game-theoretic framework. Then, we show that it is equivalent to the cryptographic security against risk- averse adversaries, who behave maliciously, but does not act in a way that can cause the other party’s successful attacks. Our results indicate that the security against risk-averse adversaries may be more natural from the perspective of game theory.

Functional encryption (FE) is an extremely powerful cryptographic mechanism that lets an authorized entity compute on encrypted data, and learn the results in the clear. However, all current cryptographic instantiations for general FE are too impractical to be implemented. We build Iron, a practical and usable FE system using Intel's recent Software Guard Extensions (SGX). We show that Iron can be applied to complex functionalities, and even for simple functions, outperforms the best known cryptographic schemes. We argue security by modeling FE in the context of hardware elements, and prove that Iron satisfies the security model.

We describe a defense against zeroizing attacks on indistinguishability obfuscation (iO) over the CLT13 multilinear map construction that only causes an additive blowup in the size of the branching program. This defense even applies to the most recent extension of the attack by Coron et al. (ePrint 2016), under which a much larger class of branching programs is vulnerable. To accomplish this, we describe an attack model for the current attacks on iO over CLT13 by distilling an essential common component of all previous attacks. This leads to the notion of a function being input partionable, meaning that the bits of the function’s input can be partitioned into somewhat independent subsets. We find a way to thwart these attacks by requiring a “stamp” to be added to the input of every function. The stamp is a function of the original input and eliminates the possibility of finding the independent subsets of the input necessary for a zeroizing attack. We give three different constructions of such “stamping functions” and prove formally that they each prevent any input partition. We also give details on how to instantiate one of the three functions efficiently in order to secure any branching program against this type of attack. The technique presented alters any branching program obfuscated over CLT13 to be secure against zeroizing attacks with only an additive blowup of the size of the branching program that is linear in the input size and security parameter. We can also apply our defense to a recent extension of annihilation attacks by Chen et al. (EUROCRYPT 2017) on obfuscation over the GGH13 multilinear map construction.

Secure two-party computation (S2PC) allows two parties to compute a function on their joint inputs while leaking only the output of the function. At TCC 2009 Orlandi and Nielsen proposed the LEGO protocol for maliciously secure 2PC based on cut-and-choose of Yao's garbled circuits at the gate level and showed that this is asymptotically more efficient than on the circuit level. Since then the LEGO approach has been improved upon in several theoretical works, but never implemented. In this paper we describe further concrete improvements and provide the first implementation of a protocol from the LEGO family. Our protocol is optimized for the offline/online setting and supports function-independent preprocessing using only a constant number of rounds. We have benchmarked our prototype and find that our protocol can compete with all existing implementations and that it is often more efficient. As an example, in a LAN setting we can evaluate an AES-128 with online latency down to 1.13 ms, while if evaluating 128 AES-128 in parallel the amortized cost is 0.09 ms per AES-128. This online performance does not come at the price of offline inefficiency as we achieve comparable performance to previous, less general protocols, and significantly better if we ignore the cost of the function-independent preprocessing. Also, as our protocol has an optimal 2-round online phase it is significantly more efficient than previous protocols' when considering a high latency network.

We show how short cycles in the state space of a cryptographic algorithm can be used to mount a fault attack on its implementation which results in a full secret key recovery. The attack is based on the assumption that an attacker can inject a transient fault at a precise location and time of his/her choice and more than once. We present an algorithm which uses a SAT-based bounded model checking for finding all short cycles of a given length. The existing Boolean Decision Diagram (BDD) based algorithms for finding cycles have limited capacity due to the excessive memory requirements of BDDs. The simulation-based algorithms can be applied to larger problem instances, however, they cannot guarantee the detection of all cycles of a given length. The same holds for general-purpose SAT-based model checkers. The presented algorithm can find all short cycles in cryptographic algorithms with very large state spaces. We evaluate it by analyzing Trivium, Bivium, Grain-80 and Grain-128 stream ciphers. The analysis shows these ciphers have short cycles whose existence, to our best knowledge, was previously unknown.

Bias-resistant public randomness is a critical component in many (distributed) protocols. Existing solutions do not scale to hundreds or thousands of participants, as is needed in many decentralized systems. We propose two large-scale distributed protocols, RandHound and RandHerd, which provide publicly-verifiable, unpredictable, and unbiasable randomness against Byzantine adversaries. RandHound relies on an untrusted client to divide a set of randomness servers into groups for scalability, and it depends on the pigeonhole principle to ensure output integrity, even for non-random, adversarial group choices. RandHerd implements an efficient, decentralized randomness beacon. RandHerd is structurally similar to a BFT protocol, but uses RandHound in a one-time setup to arrange participants into verifiably unbiased random secret-sharing groups, which then repeatedly produce random output at predefined intervals. Our prototype demonstrates that RandHound and RandHerd achieve good performance across hundreds of participants while retaining a low failure probability by properly selecting protocol parameters, such as a group size and secret-sharing threshold. For example, when sharding 512 nodes into groups of 32, our experiments show that RandHound can produce fresh random output after 240 seconds. RandHerd, after a setup phase of 260 seconds, is able to generate fresh random output in intervals of approximately 6 seconds. For this configuration, both protocols operate at a failure probability of at most 0.08% against a Byzantine adversary.

In the setting of secure multiparty computation, a set of parties with private inputs wish to compute some function of their inputs without revealing anything but their output. Over the last decade, the efficiency of secure \emph{two-party} computation has advanced in leaps and bounds, with speedups of some orders of magnitude, making it fast enough to be of use in practice. In contrast, progress on the case of multiparty computation (with more than two parties) has been much slower, with very little work being done. Currently, the only implemented efficient multiparty protocol has many rounds of communication (linear in the depth of the circuit being computed) and thus is not suited for Internet-like settings where latency is not very low. In this paper, we construct highly efficient \emph{constant-round} protocols for the setting of multiparty computation for semi-honest adversaries. Our protocols work by constructing a multiparty garbled circuit, as proposed in BMR (Beaver et al., STOC 1990). Our first protocol uses oblivious transfer and constitutes the \textit{first} concretely-efficient constant-round multiparty protocol for the case of no honest majority. Our second protocol uses BGW, and is significantly more efficient than the FairplayMP protocol (Ben-David et al., CCS 2008) that also uses BGW. We ran extensive experimentation comparing our different protocols with each other and with a highly-optimized implementation of semi-honest GMW. Due to our protocol being constant round, it significantly outperforms GMW in Internet-like settings. For example, with 13 parties situated in the Virginia and Ireland Amazon regions and the SHA256 circuit with 90,000 gates and of depth 4000, the overall running time of our protocol is 25 seconds compared to 335 seconds for GMW. Furthermore, our \emph{online time} is under half a second compared to 330 seconds for GMW.

ZHFE, proposed by Porras at el. at PQCrypto'14, is one of the very few existing multivariate encryption schemes and a very promising candidate for post-quantum cryptosystems. The only one drawback is its slow key generation. At PQCrypto'16, Baena et al. proposed an algorithm to construct the private ZHFE keys, which is much faster than the original algorithm, but still inefficient for practical parameters. Recently, Zhang and Tan proposed another private key generation algorithm, which is very fast but not necessarily able to generate all the private ZHFE keys. In this paper we propose a new efficient algorithm for the private key generation of the ZHFE scheme. Our algorithm reduces the complexity from $O(n^{2¥omega+1})$ by Baena et al. to $O(n^{¥omega+3})$, where $n$ is the number of variables and $2<¥omega<3$ is a linear algebra constant. We also estimate the number of possible keys generated by all existing private key generation algorithms for ZHFE. Our algorithm generates as many private ZHFE keys as the original and Baena et al.'s ones. This makes our algorithm is the best appropriate for the ZHFE scheme.

Redactable signature schemes allow to black out predefined parts of a signed message without affecting the validity of the signature, and are therefore an important building block in privacy-enhancing cryptography. However, a second look shows, that for many practical applications, they cannot be used in their vanilla form. On the one hand, already the identity of the signer may often reveal sensitive information to the receiver of a redacted message; on the other hand, if data leaks or is sold, everyone getting hold of (redacted versions of) a signed message will be convinced of its authenticity. We overcome these issues by providing a definitional framework and practically efficient instantiations of so called signer-anonymous designated-verifier redactable signatures (AD-RS). As a byproduct we also obtain the first group redactable signatures, which may be of independent interest. AD-RS are motivated by a real world use-case in the field of health care and complement existing health information sharing platforms with additional important privacy features. Moreover, our results are not limited to the proposed application, but can also be directly applied to various other contexts such as notary authorities or e-government services.

In the age of user-generated contents, the workloads imposed on information-security infrastructures become increasingly write-intensive. How- ever, existing security protocols, specifically authenticated data structures (ADSs), are historically designed based on update-in-place data structures and incur overhead when serving write-intensive workloads. In this work, we present LPAD (Log-structured Persistent Authenticated Directory), a new ADS protocol designed uniquely based on the log-structured merge trees (LSM trees) which recently gained popularity in the design of modern storage systems. On the write path, LPAD supports streaming, non-interactive updates with constant proof from trusted data owners. On the read path, LPAD supports point queries over the dynamic dataset with polynomial proof. The key to enable this efficiency is a verifiable reorganization operation, called verifiable merge, in LPAD. Verifiable merge is secured by the execution in an enclave of trusted execution environments (TEE). To minimize the trusted computing base (TCB), LPAD places the code related to verifiable merge in enclave, and nothing else. Our implementation of LPAD on Google LevelDB codebase and on Intel SGX shows that the TCB is reduced by 20 times: The enclave size of LPAD is one thousand code lines out of more than twenty thousands code lines of a vanilla LevelDB. Under the YCSB workloads, LPAD improves the performance by an order of magnitude compared with that of existing update-in-place ADSs.

We present Catena, an efficiently-verifiable Bitcoin witnessing scheme. Catena enables any number of thin clients, such as mobile phones, to efficiently agree on a log of application-specific statements managed by an adversarial server. Catena implements a log as an OP_RETURN transaction chain and prevents forks in the log by leveraging Bitcoin’s security against double spends. Specifically, if a log server wants to equivocate it has to double spend a Bitcoin transaction output. Thus, Catena logs are as hard to fork as the Bitcoin blockchain: an adversary without a large fraction of the network’s computational power cannot fork Bitcoin and thus cannot fork a Catena log either. However, different from previous Bitcoin-based work, Catena decreases the bandwidth requirements of log auditors from 90 GB to only tens of megabytes. More precisely, our clients only need to download all Bitcoin block headers (currently less than 35 MB) and a small, 600-byte proof for each statement in a block. We implement Catena in Java using the bitcoinj library and use it to extend CONIKS, a recent key transparency scheme, to witness its public-key directory in the Bitcoin blockchain where it can be efficiently verified by auditors. We show that Catena can secure many systems today, such as public-key directories, Tor directory servers and software transparency schemes.

Since they were first proposed as a countermeasure against differential power analysis (DPA) in 2006, threshold schemes have attracted a lot of attention from the community concentrating on cryptographic implementations. What makes threshold schemes so attractive from an academic point of view is that they come with an information-theoretic proof of resistance against a specific subset of side-channel attacks: first-order DPA. From an industrial point of view they are attractive as a careful threshold implementation forces adversaries to DPA of higher order, with all its problems such a noise amplification. A threshold scheme that offers the mentioned provable security must exhibit three properties: correctness, incompleteness and uniformity. A threshold scheme becomes more expensive with the number of shares that must be implemented and the required number of shares is lower bound by the algebraic degree of the function being shared plus 1. Defining a correct and incomplete sharing of a function of degree d in d+1 shares is straightforward. However, up to now there is no generic method to achieve uniformity and finding uniform sharings of degree-d functions with d+1 shares is an active research area. In this paper we present a simple and relatively cheap method to find a correct, incomplete and uniform d+1-share threshold scheme for any S-box layer consisting of degree-d invertible S-boxes. The uniformity is not implemented in the sharings of the individual S-boxes but rather at the S-box layer level by the use of feed-forward and some expansion of shares. When applied to the Keccak-p nonlinear step Chi, its cost is very small.

Fault attacks pose a serious threat to cryptographic algorithm implementations. It is a non-trivial task to design a code that minimizes the risk of exploiting the incorrect output that was produced by inducing faults in the algorithm execution process. In this paper we propose a design of an instruction set simulator capable of analyzing the code behavior under fault attack conditions. Our simulator is easy to use and provides a valuable insights for the designers that could help to harden the code they implement.

OCB is neither integrity under releasing unvieried plaintext (INT-RUP) nor nonce-misuse resistant. The tag of OCB is generated by encrypting plaintext checksum, which is vulnerable in the INT-RUP security model. This paper focuses on the weakness of the checksum processing in OCB. We describe a new notion, called plaintext or ciphertext checksum (PCC), which is a generalization of plaintext checksum, and prove that all authenticated encryption schemes with PCC are insecure in the INT-RUP security model. Then we x the weakness of PCC, and describe a new approach called intermediate (parity) checksum (I(P)C for short). Based on the I(P)C approach, we provide two modied schemes OCB-IC and OCB-IPC to settle the INT-RUP of OCB in the nonce-misuse setting. OCB-IC and OCB-IPC are proven INT-RUP up to the birthday bound in the nonce-misuse setting if the underlying tweakable blockcipher is a secure mixed tweakable pseudorandom permutation (MTPRP). The security bound of OCB-IPC is tighter than OCB-IC. To improve their speed, we utilize a \prove-then-prune" approach: prove security and instantiate with a scaled-down primitive (e.g., reducing rounds for the underlying primitive invocations).

Some lattice-based public key cryptosystems allow one to transform ciphertext from one lattice or ring representation to another efficiently and without knowledge of public and private keys. In this work we explore this lattice transformation property from cryptographic engineering viewpoint. We apply ciphertext transformation to compress Ring-LWE ciphertexts and to enable efficient decryption on an ultra-lightweight implementation targets such as Internet of Things, Smart Cards, and RFID applications. Significantly, this can be done without modifying the original encryption procedure or its security parameters. Such flexibility is unique to lattice-based cryptography and may find additional, unique real-life applications. Ciphertext compression can significantly increase the probability of decryption errors. We show that the frequency of such errors can be analyzed, measured and used to derive precise failure bounds for $n$-bit error correction. We introduce XECC, a fast multi-error correcting code that allows constant time implementation in software. We use these tools to construct and explore TRUNC8, a concrete Ring-LWE encryption and authentication system. We analyze its implementation, security, and performance. We show that our lattice compression technique reduces ciphertext size by more than 40% at equivalent security level, while also enabling public key cryptography on previously unreachable ultra-lightweight platforms. The experimental public key encryption and authentication system has been implemented on an 8-bit AVR target, where it easily outperforms elliptic curve and RSA-based proposals at similar security level. Similar results have been obtained with a Cortex M0 implementation. The new decryption code requires only a fraction of the software footprint of previous Ring-LWE implementations with the same encryption parameters, and is well suited for hardware implementation.

Isolated Execution Environments (IEE) offered by novel commodity hardware such as Intel’s SGX deployed in Skylake processors permit executing software in a protected environment that shields it from a malicious operating system; it also permits a remote user to obtain strong interactive attestation guarantees on both the code running in an IEE and its input/output behaviour. In this paper we show how IEEs provide a new path to constructing general secure multiparty computation (MPC) protocols. Our protocol is intuitive and elegant: it uses code within an IEE to play the role of a trusted third party (TTP), and the attestation guarantees of SGX to bootstrap secure communications between participants and the TTP. In our protocol the load of communications and computations on participants only depends on the size of each party’s inputs and outputs and is thus small and independent from the intricacy of the functionality to be computed. The remaining computational load– essentially that of computing the functionality – is moved to an untrusted party running an IEE-enabled machine, an appealing feature for Cloud-based scenarios. However, as often the case even with the simplest cryptographic protocols, we found that there is a large gap between this intuitively appealing solution and a protocol with rigorous security guarantees. We bridge this gap through a comprehensive set of results that include: i. a detailed construction of a protocol for secure computation for arbitrary functionalities; ii. formal security definitions for the security of the overall protocol and that of its components; and iii. a modular security analysis of our protocol that relies on a novel notion of labeled attested computation. We implemented and extensively evaluated our solution on SGX-enabled hardware, providing detailed measurements of our protocol as well as comparisons with software-only MPC solutions. Furthermore, we show the cost induced by using constant-time, i.e., timing side channel resilient, code in our implementation.

Thus far, partial key exposure attacks on RSA have been intensively studied using lattice based Coppersmith's methods. In the context, attackers are given partial information of a secret exponent and prime factors of (Multi-Prime) RSA where the partial information is exposed in various ways. Although these attack scenarios are worth studying, there are several known attacks whose constructions have similar flavor. In this paper, we try to formulate general attack scenarios to capture several existing ones and propose attacks for the scenarios. Our attacks contain all the state-of-the-art partial key exposure attacks, e.g., due to Ernst et al. (Eurocrypt'05) and Takayasu-Kunihiro (SAC'14, ICISC'14), as special cases. As a result, our attacks offer better results than previous best attacks in some special cases, e.g., Sarkar-Maitra's partial key exposure attacks on RSA with the most significant bits of a prime factor (ICISC'08) and Hinek's partial key exposure attacks on Multi-Prime RSA (J. Math. Cryptology '08). We claim that our contribution is not only generalizations or improvements of the existing results. Since our attacks capture general exposure scenarios, the results can be used as a tool kit; the security of some future variants of RSA can be examined without any knowledge of Coppersmith's methods.

The Learning with Errors (LWE) problem has been widely used as a hardness assumption to construct public-key primitives. In this paper, we propose an efficient instantiation of a PKE scheme based on LWE with a sparse secret, named as spLWE. We first construct an IND-CPA PKE and convert it to an IND-CCA scheme in the quantum random oracle model by applying a modified Fujisaki-Okamoto conversion of Unruh. In order to guarantee the security of our base problem suggested in this paper, we provide a polynomial time reduction from LWE with a uniformly chosen secret to spLWE. We modify the previous attacks for LWE to exploit the sparsity of a secret key and derive more suitable parameters. We can finally estimate performance of our scheme supporting 256-bit messages: our implementation shows that our IND-CCA scheme takes 313 micro seconds and 302 micro seconds respectively for encryption and decryption with the parameters that have 128-quantum bit security.

Credit networks model transitive trust (or credit) between users in a distributed environment and have recently seen a rapid increase of popularity due to their flexible design and robustness against intrusion. They serve today as a backbone of real-world IOweYou transaction settlement networks such as Ripple and Stellar, which are deployed by various banks worldwide, as well as several other systems, such as spam-resistant communication protocols and Sybil-tolerant social networks. Current solutions, however, raise serious privacy concerns, as the network topology as well as the credit value of the links are made public for apparent transparency purposes and any changes are logged. In payment scenarios, for instance, this means that all transactions have to be public and everybody knows who paid what to whom. In this work, we question the necessity of a privacy-invasive transaction ledger. In particular, we present SilentWhispers, the first distributed, privacy-preserving credit network that does not require any ledger to protect the integrity of transactions. Yet, SilentWhispers guarantees integrity and privacy of link values and transactions even in the presence of distrustful users and malicious neighbors, whose misbehavior in changing link values is detected and such users can be held accountable. We formalize these properties as ideal functionalities in the universal composability framework and present a secure realization based on a novel combination of secret-sharing-based multiparty computation and digital signature chains. SilentWhispers can handle network churn, and it is efficient as demonstrated with a prototype implementation evaluated using payments data extracted from the currently deployed Ripple payment system.

We investigate six authenticated encryption schemes (ACORN, ASCON-128a, Ketje Jr, ICEPOLE-128a, MORUS, and NORX-32) from the CAESAR competition. We aim at state recovery attacks using a SAT solver as a main tool. Our analysis reveals that these schemes, as submitted to CAESAR, provide strong resistance against SAT-based state recoveries. To shed a light on their security margins, we also analyse modified versions of these algorithms, including round-reduced variants and versions with higher security claims. Our attacks on such variants require only a few known plaintext-ciphertext pairs and small memory requirements (to run the SAT solver), whereas time complexity varies from very practical (few seconds on a desktop PC) to `theoretical' attacks.

Recently a novel family of braid based cryptographic hash function candidates was published, claiming to be suitable for use in low resource environments. It was shown that the new hash function family performed extremely well on a range of cryptographic test suites. In this paper we instantiate an instance of the hash family, called Hickory Hash, fix a set of parameters, implement it on a Texas Instruments MSP430 16-bit microcontroller, and compare its performance characteristics to SHA2. We show that the Hickory Hash can be a viable tool for low-power, constrained devices like those associated with the Internet of Things.

$\mathcal{F}$-Related-Key Attacks (RKA) on cryptographic systems consider adversaries who can observe the outcome of a system under not only the original key, say $k$, but also related keys $f(k)$, with $f$ adaptively chosen from $\mathcal{F}$ by the adversary. In this paper, we define new RKA security notions for several cryptographic primitives including message authentication code (MAC), public-key encryption (PKE) and symmetric encryption (SE). This new kind of RKA notions are called _super-strong_ RKA securities, which stipulate minimal restrictions on the adversary's forgery or oracle access, thus turn out to be the strongest ones among existing RKA security requirements. We present paradigms for constructing super-strong RKA secure MAC, PKE and SE from a common ingredient, namely _Tag-based Hash Proof System_ (THPS). We also present constructions for THPS based on the $k$-Linear and the DCR assumptions. When instantiating our paradigms with concrete THPS constructions, we obtain super-strong RKA secure MAC, PKE and SE schemes for the class of restricted affine functions $\mathcal{F}_{\text{raff}}$, of which the class of linear functions $\mathcal{F}_{\text{lin}}$ is a subset. To the best of our knowledge, our MACs, PKEs and SEs are the first ones possessing super-strong RKA securities for a non-claw-free function class $\mathcal{F}_{\text{raff}}$ in the standard model and under standard assumptions. Our constructions are free of pairing and are as efficient as those proposed in previous works. In particular, the keys, tags of MAC and ciphertexts of PKE & SE all consist of only a constant number of group elements.

Advancements in quantum computing have spurred the development of new asymmetric cryptographic primitives that are conjectured to be secure against quantum attackers. One promising class of these primitives is based on lattices, leading to encryption protocols based on the Learning With Errors (LWE) problem. Key exchange algorithms based on this problem are computationally efficient and enjoy on a strong worst-case hardness guarantee. However, despite recent improvements, the resulting handshake sizes are still significantly larger than those in use today. This thesis looks at the possibility of applying the Leech lattice code to one such scheme, with the goal of decreasing the size of the resulting handshake. We also look at the feasibility of a cryptographically safe implementation of a Leech lattice decoder (available at https://github.com/avanpo/leech-decoding), and the resulting impact on efficiency.

Conventionally, key-scheduling algorithm (KSA) of a cryptographic scheme runs for predefined number of steps. We suggest a different approach by utilization of randomized stopping rules to generate permutations which are indistinguishable from uniform ones. We explain that if the stopping time of such a shuffle is a Strong Stationary Time and bits of the secret key are not reused then these algorithms are immune against timing attacks. We also revisit the well known paper of Mironov~\cite{Mironov2002} which analyses a card shuffle which models KSA of RC4. Mironov states that expected time till reaching uniform distribution is $2n H_n - n$ while we prove that $n H_n+ n$ steps are enough (by finding a new strong stationary time for the shuffle). Nevertheless, both cases require $O(n \log^2 n)$ bits of randomness while one can replace the shuffle used in RC4 (and in Spritz) with a better shuffle which is optimal and needs only $O(n \log n)$ bits.

Bitcoin’s innovative and distributedly maintained blockchain data structure hinges on the adequate degree of difficulty of so-called “proofs of work,” which miners have to produce in order for transactions to be inserted. Importantly, these proofs of work have to be hard enough so that miners have an opportunity to unify their views in the presence of an adversary who interferes but has bounded computational power, but easy enough to be solvable regularly and enable the miners to make progress. As such, as the miners’ population evolves over time, so should the difficulty of these proofs. Bitcoin provides this adjustment mechanism, with empirical evidence of a constant block generation rate against such population changes. In this paper we provide the first (to our knowledge) formal analysis of Bitcoin’s target (re)calculation function in the cryptographic setting, i.e., against all possible adversaries aiming to subvert the protocol’s properties. We extend the q-bounded synchronous model of the Bitcoin backbone protocol [Eurocrypt 2015], which posed the basic properties of Bitcoin’s underlying blockchain data structure and shows how a robust public transaction ledger can be built on top of them, to environments that may introduce or suspend parties in each round. We provide a set of necessary conditions with respect to the way the population evolves under which the “Bitcoin backbone with chains of variable difficulty” provides a robust transaction ledger in the presence of an actively malicious adversary controlling a fraction of the miners strictly below 50% in each instant of the execution. Our work introduces new analysis techniques and tools to the area of blockchain systems that may prove useful in analyzing other blockchain protocols.

Within the next few years, billions of IoT devices will densely populate our cities. In this paper we describe a new type of threat in which adjacent IoT devices will infect each other with a worm that will spread explosively over large areas in a kind of nuclear chain reaction, provided that the density of compatible IoT devices exceeds a certain critical mass. In particular, we developed and verified such an infection using the popular Philips Hue smart lamps as a platform. The worm spreads by jumping directly from one lamp to its neighbors, using only their built-in ZigBee wireless connectivity and their physical proximity. The attack can start by plugging in a single infected bulb anywhere in the city, and then catastrophically spread everywhere within minutes, enabling the attacker to turn all the city lights on or off, permanently brick them, or exploit them in a massive DDOS attack. To demonstrate the risks involved, we use results from percolation theory to estimate the critical mass of installed devices for a typical city such as Paris whose area is about 105 square kilometers: The chain reaction will fizzle if there are fewer than about 15,000 randomly located smart lights in the whole city, but will spread everywhere when the number exceeds this critical mass (which had almost certainly been surpassed already). To make such an attack possible, we had to find a way to remotely yank already installed lamps from their current networks, and to perform over-the-air firmware updates. We overcame the first problem by discovering and exploiting a major bug in the implementation of the Touchlink part of the ZigBee Light Link protocol, which is supposed to stop such attempts with a proximity test. To solve the second problem, we developed a new version of a side channel attack to extract the global AES-CCM key (for each device type) that Philips uses to encrypt and authenticate new firmware. We used only readily available equipment costing a few hundred dollars, and managed to find this key without seeing any actual updates. This demonstrates once again how difficult it is to get security right even for a large company that uses standard cryptographic techniques to protect a major product.

Isogeny based post-quantum cryptography is one of the most recent addition to the family of quantum resistant cryptosystems. In this paper, we propose an efficient modular multiplication algorithm for primes of the form $p = 2 \cdot 2^a \cdot 3^b - 1$ with b even, typically used in such cryptosystem. Our modular multiplication algorithm exploits the special structure present in such primes. We compare the efficiency of our technique with Barrett reduction and Montgomery multiplication. Our C implementation shows that our algorithm is approximately 3 times faster than the normal Barrett reduction.

Addition chain calculations play a critical role in determining the efficiency of cryptosystems based on isogenies on elliptic curves. However, finding a minimal length addition chain is not easy; a generalized version of the problem, in which one must find a chain that simultaneously forms each of a sequence of values, is NP-complete. For the special primes used in such cryptosystems, finding fast addition chains for finite field arithmetic such as inversion and square root is also not easy. In this paper, we investigate the shape of smooth isogeny primes and propose new methods to calculate fast addition chains. Further, we also provide techniques to reduce the temporary register consumption of these large exponentials, applicable to both software and hardware implementations utilizing addition chains. Lastly, we utilize our procedures to compare multiple isogeny primes by the complexity of the addition chains.

In this paper, we present a constant-time hardware implementation that achieves new speed records for the supersingular isogeny Diffie-Hellman (SIDH), even when compared to highly optimized Haswell computer architectures. We employ inversion-free projective isogeny formulas presented by Costello et al. at CRYPTO 2016 on an FPGA. Modern FPGA's can take advantage of heavily parallelized arithmetic in $\mathbb{F}_{p^{2}}$, which lies at the foundation of supersingular isogeny arithmetic. Further, by utilizing many arithmetic units, we parallelize isogeny evaluations to accelerate the computations of large-degree isogenies by approximately 57\%. On a constant-time implementation of 124-bit quantum security SIDH on a Virtex-7, we generate ephemeral public keys in 10.6 and 11.6 ms and generate the shared secret key in 9.5 and 10.8 ms for Alice and Bob, respectively. This improves upon the previous best time in the literature for 768-bit implementations by a factor of 1.48. Our 83-bit quantum security implementation improves upon the only other implementation in the literature by a speedup of 1.74 featuring fewer resources and constant-time.

We propose a new framework for concurrently composable security that relaxes the security notion of UC security. As in previous frameworks, our notion is based on the idea of providing the simulator with super-polynomial resources. However, in our new framework simulators are only given restricted access to the results computed in super-polynomial time. This is done by modeling the super-polynomial resource as a stateful oracle that may directly interact with a functionality without the simulator seeing the communication. We call these oracles shielded oracles. Our notion is fully compatible with the UC framework, i.e., protocols proven secure in the UC framework remain secure in our framework. Furthermore, our notion lies strictly between SPS and Angel-based security, while being closed under protocol composition. Shielding away super-polynomial resources allows us to apply new proof techniques where we can replace super-polynomial entities by indistinguishable polynomially bounded entities. This allows us to construct secure protocols in the plain model using weaker primitives than in previous composable frameworks involving simulators with super-poly resources. In particular, we only use non-adaptive-CCA-secure commitments as a building block in our constructions. As a feasibility result, we present a constant-round general MPC protocol in the plain model based on standard assumptions that is secure in our framework.

One-time signatures (OTS) are called one-time, because the accompanying reductions only guarantee security under single-message attacks. However, this does not imply that efficient attacks are possible under two-message attacks. Especially in the context of hash-based OTS (which are basic building blocks of recent standardization proposals) this leads to the question if accidental reuse of a one-time key pair leads to immediate loss of security or to graceful degradation. In this work we analyze the security of the most prominent hash-based OTS, Lamport's scheme, its optimized variant, and WOTS, under different kinds of two-message attacks. Interestingly, it turns out that the schemes are still secure under two message attacks, asymptotically. However, this does not imply anything for typical parameters. Our results show that for Lamport's scheme, security only slowly degrades in the relevant attack scenarios and typical parameters are still somewhat secure, even in case of a two-message attack. As we move on to optimized Lamport and its generalization WOTS, security degrades faster and faster, and typical parameters do not provide any reasonable level of security under two-message attacks.

Data deduplication, aiming to eliminate duplicate data, has been widely used in cloud storage to reduce the amount of storage space and save bandwidth. Unfortunately, as an increasing number of sensitive data are stored remotely, the encryption, the simplest way for data privacy, is not compatible with data deduplication. Though many research efforts have been devoted to securing deduplication, they all are subject to performance, security, and applicability limitations. Here, we propose two encrypted deduplication schemes, SDedup and XDedup, both based on Merkle puzzle. To the best of our knowledge, XDedup is the first brute-force resilient encrypted deduplication with only symmetrically cryptographic two-party interactions. The analysis and numerical simulations are conducted to demonstrate the performance and practicality of SDedup and XDedup.

It is widely understood that we are just human beings rather than being almighty; hence using ideally random numbers in practice, as supposed in usual theoretical designs of cryptographic protocols, is beyond our ability or at least too expensive. For this point, a standard solution in implementation is to use secure pseudorandom generators (PRGs); ordinary cryptographers' intuition tells that the security of cryptographic protocols should not be lost when applying a secure PRG though no general proof for this is known. In this paper, as opposed to the intuition, we give two examples (under certain, different computational assumptions) of a pair of a secure two-party computation protocol in the semi-honest model (one of which is essentially a practical protocol proposed in ACM CCS 2013, not just an artificially constructed one) and a secure PRG satisfying that the security is lost when the PRG is applied. This phenomenon comes mainly from the fact that, in the security model for two-party protocols the seed for a PRG will be visible by a corrupted party him/herself, while the security notion for PRGs assumes that the seed is not visible. On the other hand, as an affirmative result, we give a sufficient condition for a two-party protocol and a PRG to ensure that the security is preserved when the PRG is applied.

In the Micali-Shamir paper improving the efficiency of the original Fiat-Shamir protocol, the authors state that "(...) not all of the $v_i$'s will be quadratic residues mod $n$. We overcome this technical difficulty with an appropriate perturbation technique (...)" This perturbation technique is made more explicit in the associated patent application: "Each entity is allowed to modify the standard $v_j$ which are QNRs. A particularly simple way to achieve this is to pick a modulus $n=pq$ where $p=3 \bmod 8$ and $q=7 \bmod 8$, since then exactly one of $v_j,-v_j,2v_j,-2v_j$ is a QR mod $n$ for any $v_j$. The appropriate variant of each $v_j$ can be (...) deduced by the verifier himself during the verification of given signatures." In this short note we clarify the way in which the verifier can infer by himself the appropriate variant of each $v_j$ during verification.

Motivated by the recent searchable symmetric encryption protocol of Cash et al., we propose a new multi-client searchable encryption protocol in this work. By tactfully leveraging the RSA-function, our protocol avoids the per-query interaction between the data owner and the client, thus reducing the communication overhead significantly and eliminating the need of the data owner to provide the online services to clients at all times. Furthermore, our protocol manages to protect the query privacy of clients to some extent, meaning that our protocol hides the exact queries from the data owner. In terms of the leakage to server, it is exactly the same as Cash et al., thus achieving the same security against the adversarial server. In addition, by employing attribute-based encryption technique, our protocol also realizes the fine-grained access control on the stored data. To be compatible with our RSA-based approach, we also present a deterministic and memory-efficient `keyword to prime' hash function, which may be of independent interest.

We present security vulnerabilities in the remote voting system Helios. We propose Apollo, a modified version of Helios, which addresses these vulnerabilities and could improve the feasibility of internet voting. In particular, we note that Apollo does not possess Helios' major known vulnerability, where a dishonest voting terminal can change the vote after it obtains the voter's credential. With Apollo-lite, votes not authorized by the voter are detected by the public and prevented from being included in the tally. The full version of Apollo enables a voter to prove that her vote was changed. We also describe a very simple protocol for the voter to interact with any devices she employs to check on the voting system, to enable frequent and easy auditing of encryptions and checking of the bulletin board.

As a core component of Substitution-Permutation Networks, diffusion layer is mainly introduced by matrices from maximum distance separable (MDS) codes. Surprisingly, up to now, most constructions of MDS matrices require to perform an equivalent or even exhaustive search. Especially, not many MDS proposals are known that obtain an excellent hardware efficiency and simultaneously guarantee a remarkable software implementation. In this paper, we study the cyclic structure of rotational-XOR diffusion layer, one of the commonly used linear layers over ${(\mathbb{F}_{\rm{2}}^b)^n}$, which consists of only rotation and XOR operations. First, we provide novel properties on this class of matrices, and prove the a lower bound on the number of rotations for $n \ge 4$ and show the tightness of the bound for $n=4$. Next, by precisely characterizing the relation among sub-matrices for each possible form, we can eliminate all the other non-optimal cases. Finally, we present a direct construction of such MDS matrices, which allows to generate $4 \times 4$ perfect instances for arbitrary $b \ge 4$. Every example contains the fewest possible rotations, so under this construction strategy, our proposal costs the minimum gate equivalents (resp. cyclic shift instructions) in the hardware (resp. software) implementation. To the best of our knowledge, it is the first time that rotational-XOR MDS diffusion layers have been constructed without any auxiliary search.

We revisit the problem of estimating Renyi Entropy from samples, focusing on the important case of collision entropy. With $n$ samples we approximate the collision entropy of $X$ within an additive factor of $O\left( 2^{2\Delta}\log^{\frac{1}{2}}(1/\epsilon) \right)$ with probability $1-\epsilon$, where $\Delta$ is a known (a priori) upper bound on the difference between Renyi entropies of $X$ of order 2 and 3 respectively. In particular, we simplify and improve the previous result on estimating collision entropy due to Acharya et al. (SODA'15) up to a factor exponential in the entropy gap. We also discuss applications of our bound in anomaly analysis, namely (a) detection of attacks against stateless sources in TRNGs, and (b) detection of DDoS attacks at network firewalls.

ChaCha and Salsa are two software oriented stream ciphers that have attracted serious attention in academic as well as commercial domain. The most important cryptanalysis of reduced versions of these ciphers was presented by Aumasson et al. in FSE 2008. One part of their attack was to apply input difference(s) to investigate biases after a few rounds. So far there have been certain kind of limited exhaustive searches to obtain such biases. For the first time, in this paper, we show how to theoretically choose the combinations of the output bits to obtain significantly improved biases. The main idea here is to consider the multi-bit differentials as extension of suitable single-bit differentials with linear approximations, which is essentially a differential-linear attack. As we consider combinations of many output bits (for example 19 for Salsa and 21 for ChaCha), exhaustive search is not possible here. By this method we obtain very high biases for linear combinations of bits in Salsa after 6 rounds and in ChaCha after 5 rounds. These are clearly two rounds of improvement for both the ciphers over the existing works. Using these biases we obtain several significantly improved cryptanalytic results for reduced round Salsa and ChaCha that could not be obtained earlier. In fact, with our results it is now possible to cryptanalyse 6-round Salsa and 5-round ChaCha in practical time.

Micropayments (payments worth a few pennies) have numerous potential applications. A challenge in achieving them is that payment networks charge fees that are high compared to “micro” sums of money. Wheeler (1996) and Rivest (1997) proposed probabilistic payments as a technique to achieve micropayments: a merchant receives a macro-value payment with a given probability so that, in expectation, he receives a micro-value payment. Despite much research and trial deployment, micropayment schemes have not seen adoption, partly because a trusted party is required to process payments and resolve disputes. The widespread adoption of decentralized currencies such as Bitcoin (2009) suggests that decentralized micropayment schemes are easier to deploy. Pass and Shelat (2015) proposed several micropayment schemes for Bitcoin, but their schemes provide no more privacy guarantees than Bitcoin itself, whose transactions are recorded in plaintext in a public ledger. We formulate and construct *decentralized anonymous micropayment* (DAM) schemes, which enable parties with access to a ledger to conduct offline probabilistic payments with one another, directly and privately. Our techniques extend those of Zerocash (2014) with a new probabilistic payment scheme; we further provide an efficient instantiation based on a new fractional message transfer protocol. Double spending in our setting cannot be prevented. Our second contribution is an economic analysis that bounds the additional utility gain of any cheating strategy, and applies to virtually any probabilistic payment scheme with offline validation. In our construction, this bound allows us to deter double spending by way of advance deposits that are revoked when cheating is detected.

Covert computation of general functions strengthens the notion of secure computation, so that the computation hides not only everything about the participants' inputs except for what is revealed by the function output, but it also hides the very fact that the computation is taking place, by ensuring that protocol participants are indistinguishable from random beacons, except when the function output explicitly reveals the fact that a computation took place. General covert computation protocols proposed before have non-constant round complexity [16,4] and their efficiency is orders of magnitude away from known non-covert secure computation protocols. Furthermore, [8] showed that constant-round covert computation of non-trivial functionalities with black-box simulation is impossible in the plain model. However, the lower-bound of [8] does not disallow constant-round covert computation given some relaxation in the computation model. Indeed, in this work we propose the first constant-round protocol for covert Two-Party Computation (2PC) of general functions, secure against malicious adversaries under concurrent composition, assuming the Common Reference String (CRS) model. Our protocol is a covert variant of a well-known paradigm in standard, i.e. non-covert, secure 2PC, using cut-and-choose technique over O(security parameter) copies of Yao's garbled circuit protocol, and its efficiency is only a constant factor away from non-covert secure 2PC protocols that use cut-and-choose over garbled circuits. An essential tool in the protocol is a concurrently secure covert simulation-sound Conditional KEM (CKEM) for arithmetic languages in prime-order groups. We show that the Implicit Zero-Knowledge arguments in the CRS model of Benhamouda et al. [2] provide covert CKEM's for all languages needed in our covert 2PC protocol. We also show that in the Random Oracle Model the covert CKEM's of [11] also satisfy concurrent security and simulation-soundness. The ROM-based covert CKEM's of [11] match the cost of ROM-based NIZK's for the same languages, while the CRS-model CKEM's of [2] are (only) 2-4 times more expensive.

Arbiter Physically Unclonable Function (APUF), while being relatively lightweight, is extremely vulnerable to modeling attacks. Hence, various compositions of APUFs such as XOR APUF and Lightweight Secure PUF have been proposed to be secure alternatives. Previous research has demonstrated that PUF compositions have two major challenges to overcome: vulnerability against modeling and statistical attacks, and lack of reliability. In this paper, we introduce a multiplexer based composition of APUFs, denoted as MPUF, to simultaneously overcome these challenges. In addition to the basic MPUF design, we propose two MPUF variants namely cMPUF and rMPUF to improve robustness against cryptanalysis and reliability based modeling attack, respectively. The rMPUF demonstrates enhanced robustness against reliability based modeling attack, while even the well-known XOR APUF, otherwise robust to machine learning based modeling attacks, has been modeled using the same technique with linear data and time complexities. The rMPUF can provide a good trade-off between security and hardware overhead while maintaining a significantly higher reliability level than any practical XOR APUF instance. Moreover, MPUF variants are the first APUF compositions, to the best of our knowledge, that can achieve Strict Avalanche Criterion without any additional hardware. Finally, we validate our theoretical findings using Matlab-based simulations of MPUFs.

Inner product encryption (IPE) is a new cryptographic primitive initially proposed by Abdalla et al. in 2015. IPE can be classified into public-key IPE and secret-key IPE. The currently proposed PK-IPE schemes can-not resist the following collusion attack: an invalid user that holds no private key can ”buy” a combined key generated from multiple collusion adversaries, and the user can use this private key to decrypt a ciphertext. Furthermore, the user should not let the collusion adversaries know the ciphertext, and the collusion adversaries should not let the user learn their private keys. We present a new PK-IPE to resist such collusion attack. Our PK-IPE is proven secure under the selective-vector chosen-plaintext attack model. We formalize a selective vector collusion attack model to prove that our scheme is secure under this model.

Attribute-Based Encryption (ABE) is a special type of public key encryption that allows users to share sensitive data efficiently through fine-grained access control. The security involved in existing ABE systems is currently insufficient. These systems are usually built on the Decisional Bilinear Diffie-Hellman (DBDH) assumption or the q-type DBDH assumption, which is stronger than the DBDH assumption. However, once the DBDH assumption is unsecure, all concerned ABEs become vulnerable to threats. To address this problem, the $k$-BDH assumption family proposed by Benson et al. is adopted. Any assumption in the $k$-BDH assumption family is associated with parameter $k$ and becomes strictly weaker as $k$ increased. We propose a framework to implement Ciphertext-Policy Attribute Based Encryption (CP-ABE) under the arbitrary assumption in the $k$-BDH assumption family. When the $k'$-BDH assumption in the $k$-BDH assumption family becomes unsecure, where $k'$-BDH is the assumption on which our ABE relies, the scheme can be shifted to rely on the $l'$-BDH assumption instead, where $l'>k'$. This condition guarantees security as the underlying assumption of our scheme becomes weaker. In addition, we define the formal security model of our schemes and prove the security of CP-ABE in the selective attribute model.

We aim to understand, formalize and provably achieve the goals underlying the core key-ratcheting technique of Borisov, Goldberg and Brewer, extensions of which are now used in secure messaging systems. We give syntax and security definitions for ratcheted encryption and key-exchange. We give a proven-secure protocol for ratcheted key exchange. We then show how to generically obtain ratcheted encryption from ratcheted key-exchange and standard encryption.

Realistic secure processors, including those built for academic and commercial purposes, commonly realize an “attested execution” abstraction. Despite being the de facto standard for modern secure processors, the “attested execution” abstraction has not received adequate formal treatment. We provide formal abstractions for “attested execution” secure processors and rigorously explore its expressive power. Our explorations show both the expected and the surprising. On one hand, we show that just like the common belief, attested execution is extremely powerful, and allows one to realize powerful cryptographic abstractions such as stateful obfuscation whose existence is otherwise impossible even when assuming virtual blackbox obfuscation and stateless hardware tokens. On the other hand, we show that surprisingly, realizing composable two-party computation with attested execution processors is not as straightforward as one might anticipate. Specifically, only when both parties are equipped with a secure processor can we realize composable two-party computation. If one of the parties does not have a secure processor, we show that composable two-party computation is impossible. In practice, however, it would be desirable to allow multiple legacy clients (without secure processors) to leverage a server’s secure processor to perform a multi-party computation task. We show how to introduce minimal additional setup assumptions to enable this. Finally, we show that fair multi-party computation for general functionalities is impossible if secure processors do not have trusted clocks. When secure processors have trusted clocks, we can realize fair two-party computation if both parties are equipped with a secure processor; but if only one party has a secure processor (with a trusted clock), then fairness is still impossible for general functionalities.

We present Tesla# (pronounced "Tesla Sharp"), a digital signature scheme based on the RLWE assumption that continues a recent line of proposals of lattice-based digital signature schemes originating in work by Lyubashevsky as well as by Bai and Galbraith. It improves upon all of its predecessors in that it attains much faster key pair generation, signing, and verification, outperforming most (conventional or lattice-based) signature schemes on modern processors. We propose a selection of concrete parameter sets, including a high-security instance that aims at achieving post-quantum security. Based on these parameters, we present a full-fledged software implementation protected against timing and cache attacks that supports two scheme variants: one providing 128 bits of classical security and another providing 128 bits of post-quantum security.

The linear complexity and $k$-error linear complexity of sequences are important measures of the strength of key-streams generated by stream ciphers. The counting function of a sequence complexity measure gives the number of sequences with given complexity measure value and it is useful to determine the expected value and variance of a given complexity measure of a family of sequences. Fu et al. studied the distribution of $2^n$-periodic binary sequences with 1-error linear complexity in their SETA 2006 paper and peoples have strenuously promoted the solving of this problem from $k=2$ to $k=4$ step by step. Unfortunately, it still remains difficult to obtain the solutions for larger $k$ and the counting functions become extremely complex when $k$ become large. In this paper, we define an equivalent relation on error sequences. We use a concept of \textit{cube fragment} as basic modules to construct classes of error sequences with specific structures. Error sequences with the same specific structures can be represented by a single \textit{symbolic representation}. We introduce concepts of \textit{trace}, \textit{weight trace} and \textit{orbit} of sets to build quantitative relations between different classes. Based on these quantitative relations, we propose an algorithm to automatically generate symbolic representations of classes of error sequences, calculate \textit{coefficients} from one class to another and compute \textit{multiplicity} of classes defined based on specific equivalence on error sequences. This algorithm can efficiently get the number of sequences with given $k$-error linear complexity. The time complexity of this algorithm is $O(2^{k\log k})$ in the worst case which does not depend on the period $2^n$.

Side-channel attacks put the security of the implementations of cryptographic algorithms under threat. Secret information can be recovered by analyzing the physical measurements acquired during the computations and using key recovery distinguishing functions to guess the best candidate. Several generic and model based distinguishers have been proposed in the literature. In this work we describe two contributions that lead to better performance of side-channel attacks in challenging scenarios. First, we describe how to transform the physical leakage traces into a new space where the noise reduction is near-optimal. Second, we propose a new generic distinguisher that is based upon minimal assumptions. It approaches a key distinguishing task as a problem of classification and ranks the key candidates according to the separation among the leakage traces. We also provide experiments and compare their results to those of the Correlation Power Analysis (CPA). Our results show that the proposed method can indeed reach better success rates even in the presence of significant amount of noise.

Converting a Boolean mask to an arithmetic mask, and vice versa, is often required in implementing side-channel resistant instances of cryptographic algorithms that mix Boolean and arithmetic operations. In this paper, we describe a method for converting a Boolean mask to an arithmetic mask that runs in constant time for a fixed order. We propose explicit algorithms for a second-order secure Boolean-to-arithmetic mask conversion that uses 31 instructions and for a third-order secure mask conversion that uses 74 instructions. We show that our solution is more efficient than previously proposed methods for any choice of masking-scheme order, typically by several orders of magnitude.

A covering system of congruences can be defined as a set of congruence relations of the form: $\{r_1 \pmod{m_1}, r_2 \pmod{m_2}, \dots, r_t \pmod{m_t}\}$ for $m_1, \dots, m_t \in \mathbb{N}$ satisfying the property that for every integer $k$ in $\mathbb{Z}$, there exists at least an index $i \in \{1, \dots, t\}$ such that $k \equiv r_i \pmod{m_i}$. First, we show that most existing scalar multiplication algorithms can be formulated in terms of covering systems of congruences. Then, using a special form of covering systems called exact \mbox{$n$-covers}, we present a novel uniformly randomized scalar multiplication algorithm with built-in protections against various types of side-channel attacks. This algorithm can be an alternative to Coron's scalar blinding technique for elliptic curves, in particular when the choice of a particular finite field tailored for speed compels to use a large random factor.

Smart metering, smart parking, health, environment monitoring, and other applications drive the deployment of the so-called Internet of Things (IoT). Whilst cost and energy efficiency are the main factors that con- tribute to the popularity of commercial devices in the IoT domain, secu- rity features are increasingly desired. Security features typically guarantee authenticity of devices and/or data, as well as confidentiality of data in transit. Our study finds that whilst cryptographic algorithms for confi- dentiality and authenticity are supported in hardware on a popular class of devices, there is no adequate support for random number generation available. We show how to passively manipulate the on-board source for randomness, and thereby we can completely undermine the security pro- vided by (otherwise) strong cryptographic algorithms, with devastating results.

For encryption schemes, key dependent message (KDM) security requires that ciphertexts preserve secrecy even when the messages to be encrypted depend on the secret keys. While KDM security has been extensively studied for public-key encryption (PKE), it receives much less attention in the setting of identity-based encryption (IBE). In this work, we focus on the KDM security for IBE. Our results are threefold. We first propose a generic approach to transfer the KDM security results (both positive and negative) from PKE to IBE. At the heart of our approach is a neat structure-mirroring PKE-to-IBE transformation based on indistinguishability obfuscation and puncturable PRFs, which establishes a connection between PKE and IBE in general. However, the obtained results are restricted to selective-identity sense. We then concentrate on results in adaptive-identity sense. On the positive side, we present two constructions that achieve KDM security in the adaptive-identity sense for the first time. One is built from identity-based hash proof system (IB-HPS) with homomorphic property, which indicates that the IBE schemes of Gentry (Eurocrypt 2006), Coron (DCC 2009), Chow et al. (CCS 2010) are actually KDM-secure in the single-key setting. The other is built from indistinguishability obfuscation and a new notion named puncturable unique signature, which is bounded KDM-secure in the single-key setting. On the negative side, we separate CPA/CCA security from $n$-circular security (which is a prototypical case of KDM security) for IBE by giving a counterexample based on differing-inputs obfuscation and a new notion named puncturable IBE. We further propose a general framework for generating $n$-circular security counterexamples in identity-based setting, which might be of independent interest.

We present a methodology to achieve low latency homomorphic operations on approximations to complex numbers, by encoding a complex number as an evaluation of a polynomial at a root of unity. We then use this encoding to evaluate a Discrete Fourier Transform (DFT) on data which has been encrypted using a Somewhat Homomorphic Encryption (SHE) scheme, with up to three orders of magnitude improvement in latency over previous methods. We are also able to deal with much larger input sizes than previous methods. Due to the fact that the entire DFT algorithm is an algebraic operation over the underlying ring of the SHE scheme (for a suitably chosen ring), our method for the DFT utilizes exact arithmetic over the complex numbers, as opposed to approximations.

Man-in-the-middle attacks in TLS due to compromised CAs have been mitigated by log-based PKI enhancements such as Certificate Transparency. However, these log-based schemes do not offer sufficient incentives to logs and monitors, and do not offer any actions that domains can take in response to CA misbehavior. We propose IKP, a blockchain-based PKI enhancement that offers automatic responses to CA misbehavior and incentives for those who help detect misbehavior. IKP’s decentralized nature and smart contract system allows open participation, offers incentives for vigilance over CAs, and enables financial recourse against misbehavior. We demonstrate through a game theoretic model and through an Ethereum prototype implementation that the incentives and increased deterrence offered by IKP are technically and economically viable.

Designing public key cryptosystems that resist attacks by quantum computers is an important area of current cryptographic research and standardization. To retain confidentiality of today's communications against future quantum computers, applications and protocols must begin exploring the use of quantum-resistant key exchange and encryption. In this paper, we explore post-quantum cryptography in general and key exchange specifically. We review two protocols for quantum-resistant key exchange based on lattice problems: BCNS15, based on the ring learning with errors problem, and Frodo, based on the learning with errors problem. We discuss their security and performance characteristics, both on their own and in the context of the Transport Layer Security (TLS) protocol. We introduce the Open Quantum Safe project, an open-source software project for prototyping quantum-resistant cryptography, which includes liboqs, a C library of quantum-resistant algorithms, and our integrations of liboqs into popular open-source applications and protocols, including the widely used OpenSSL library.

This paper presents highly efficient designs of double authentication preventing signatures (DAPS). In a DAPS, signing two messages with the same first part and differing second parts reveals the signing key. In the context of PKIs we suggest that CAs who use DAPS to create certificates have a court-convincing argument to deny big-brother requests to create rogue certificates, thus deterring certificate subversion. We give two general methods for obtaining DAPS. Both start from trapdoor identification schemes. We instantiate our transforms to obtain numerous specific DAPS that, in addition to being efficient, are proven with tight security reductions to standard assumptions. We implement our DAPS schemes to show that they are not only several orders of magnitude more efficient than prior DAPS but competitive with in-use signature schemes that lack the double authentication preventing property.

User convenience and strong security are often at odds, and most security applications need to find some sort of balance between these two (often opposing) goals. The Resource Public Key Infrastructure (RPKI) [8], a security infrastructure built on top of interdomain routing, is not exempt from this issue. The RPKI uses the maxLength attribute to reduce the amount of information that must be explicitly recorded in its cryptographic objects. MaxLength also allows operators to easily reconfigure their networks with- out modifying their RPKI objects. However, we argue that the maxLength attribute strikes the wrong balance between security and user convenience. In particular, we argue that maxLength is commonly configured in a manner that either obviates the security benefis provided by the RPKI or causes legitimate routes to appear invalid, without providing performance improvements. Therefore, we argue that the maxLength attribute should be eliminated from the RPKI.

In 2010, Resch and Plank proposed a computationally secure secret sharing scheme, called the AONT-RS scheme. We present a generalisation of their scheme and discuss two ways in which information is leaked if the scheme is used to distribute small ciphertexts. We then discuss how to prevent such leakage and provide a proof of computational privacy in the random oracle model. Next, we extend the scheme to be robust, ensuring the distributed data is recoverable even if a bounded number of players submit incorrect shares. We prove the robust AONT-RS scheme achieves computational privacy and recoverability in the random oracle model. Finally, we compare the security, share size and complexity of the robust AONT-RS scheme with a refined version of Krawczyk's robust scheme by Bellare and Rogaway.

The Signal protocol is a cryptographic messaging protocol that provides end-to-end encryption for instant messaging in WhatsApp, Wire, and Facebook Messenger among many others, serving well over 1 billion active users. Signal includes several uncommon security properties (such as "future secrecy" or "post-compromise security"), enabled by a novel technique called *ratcheting* in which session keys are updated with every message sent. We conduct a formal security analysis of Signal's initial extended triple Diffie-Hellman (X3DH) key agreement and Double Ratchet protocols as a multi-stage authenticated key exchange protocol. We extract from the implementation a formal description of the abstract protocol, and define a security model which can capture the ratcheting key update structure as a multi-stage model where there can be a tree of stages, rather than just a sequence. We then prove the security of Signal's key exchange core in our model, demonstrating several standard security properties. We have found no major flaws in the design, and hope that our presentation and results can serve as a foundation for other analyses of this widely adopted protocol.

Anonymous credential systems enable users to authenticate themselves in a privacy-preserving manner. At the conference ESORICS 2016, Kaaniche and Laurent presented an anonymous certification scheme based on a new attribute based signature. In this note, we provide several attacks on their scheme.

In this work, we describe a new polynomial-time attack on the multilinear maps of Coron, Lepoint, and Tibouchi (CLT13), when used in candidate iO schemes. More specifically, we show that given the obfuscation of the simple branching program that computes the always zero functionality previously considered by Miles, Sahai and Zhandry (Crypto 2016), one can recover the secret parameters of CLT13 in polynomial time via an extension of the zeroizing attack of Coron et al. (Crypto 2015). Our attack is generalizable to arbitrary oblivious branching programs for arbitrary functionality, and allows (1) to recover the secret parameters of CLT13, and then (2) to recover the randomized branching program entirely. Our analysis thus shows that several of the single-input variants of iO over CLT13 are insecure.

The Resource Public Key Infrastructure (RPKI) binds IP address blocks to owners’ public keys. RPKI enables routers to perform Route Origin Validation (ROV), thus preventing devastating attacks such as IP prefix hijacking. Yet, despite extensive effort, RPKI’s deployment is frustratingly sluggish, leaving the Internet largely insecure. We tackle fundamental questions regarding today’s RPKI’s deployment and security: What is the adoption status of RPKI and ROV? What are the implications for global security of partial adoption? What are the root-causes for slow adoption? How can deployment be pushed forward? We address these questions through a combination of empirical analyses, a survey of over 100 network practitioners, and extensive simulations. Our main contributions include the following.We present the first study measuring ROV enforcement, revealing disappointingly low adoption at the core of the Internet. We show, in contrast, that without almost ubiquitous ROV adoption by large ISPs significant security benefits cannot be attained. We next expose a critical security vulnerability: about a third of RPKI authorizations issued for IP prefixes do not protect the prefix from hijacking attacks. We examine potential reasons for scarce adoption of RPKI and ROV, including human error in issuing RPKI certificates and inter-organization dependencies, and present recommendations for addressing these challenges.

In 2000, Canetti, Goldreich, Goldwasser and Micali (STOC'00) proposed the notion of resettable zero-knowledge, which considers the scenario where a malicious verifier can reset the prover and force it to reuse its random tape. They provided a construction that resists such attacks, and in the following, the notion of resettability was considered in various other scenarios. Starting with resettably-sound zero-knowledge, over general resettable computation with one resettable party, to protocols where all parties are resettable. Most of these results are only concerned with the feasibility of resettable computation, while efficiency is secondary. There is a considerable gap in the round- and communication-efficiency between actively secure protocols and resettably secure protocols. Following the work of Goyal and Sahai (EUROCRYPT'09), we study the round- and communication-efficiency of resettable two-party computation in the setting where one of the two parties is resettable, and close the gap between the two notions of security: - We construct a fully simulatable resettable CRS in the plain model that directly yields constant-round resettable zero-knowledge and constant-round resettable two-party computation protocols in the plain model. - We present a new resettability compiler that follows the approach of Ishai, Prabhakaran and Sahai (CRYPTO'08) and yields constant-rate resettable two-party computation.

Ownership Transfer Protocols for RFID allow transferring the rights over a tag from a current owner to a new owner in a secure and private way. Recently, Kapoor and Piramuthu have proposed two schemes which solve most of the security weaknesses detected in previously published protocols. However, this paper reviews this work and points out that such schemes still present some practical and security issues. We then propose some modifications in these protocols that overcome such problems.

Smart contracts are computer programs that can be correctly executed by a network of mutually distrusting nodes, without the need of an external trusted authority. Since smart contracts handle and transfer assets of considerable value, besides their correct execution it is also crucial that their implementation is secure against attacks which aim at stealing or tampering the assets. We study this problem in Ethereum, the most well-known and used framework for smart contracts so far. We analyse the security vulnerabilities of Ethereum smart contracts, providing a taxonomy of common programming pitfalls which may lead to vulnerabilities. We show a series of attacks which exploit these vulnerabilities, allowing an adversary to steal money or cause other damage.

For decades, the Network Time Protocol (NTP) has been used to synchronize computer clocks over untrusted network paths. This work takes a new look at the security of NTP's datagram protocol. We argue that NTP's datagram protocol in RFC5905 is both underspecified and flawed. The NTP specifications do not sufficiently respect (1) the conflicting security requirements of different NTP modes, and (2) the mechanism NTP uses to prevent off-path attacks. A further problem is that (3) NTP's control-query interface reveals sensitive information that can be exploited in off-path attacks. We exploit these problems in several attacks that remote attackers can use to maliciously alter a target's time. We use network scans to find millions of IPs that are vulnerable to our attacks. Finally, we move beyond identifying attacks by developing a cryptographic model and using it to prove the security of a new backwards-compatible client/server protocol for NTP.

Very recently, the {\sf Atomic AES} architecture that provides dual functionality of the AES encryption and decryption module was proposed. It was surprisingly compact and occupied only around 2605 GE of silicon area and took 226 cycles for both the encryption and decryption operations. In this work we further optimize the above architecture to provide the dual encryption/decryption functionality in only 2060 GE and latency of 246/326 cycles for the encryption and decryption operations respectively. We take advantage of clock gating techniques to achieve Shiftrow and Inverse Shiftrow operations in 3 cycles instead of 1. This helps us replace many of the scan flip-flops in the design with ordinary flip-flops. Furthermore we take advantage of the fact that the Inverse Mixcolumn matrix in AES is the cube of the forward Mixcolumn matrix. Thus by executing the forward Mixcolumn operation three times over the state, one can achieve the functionality of Inverse Mixcolumn. This saves some more gate area as one is no longer required to have a combined implementation of the Forward and Inverse Mixcolumn circuit.

Security against hardware trojans is currently becoming an essential ingredient to ensure trust in information systems. A variety of solutions have been introduced to reach this goal, ranging from reactive (i.e., detection-based) to preventive (i.e., trying to make the insertion of a trojan more difficult for the adversary). In this paper, we show how testing (which is a typical detection tool) can be used to state concrete security guarantees for preventive approaches to trojan-resilience. For this purpose, we build on and formalize two important previous works which introduced ``input scrambling" and ``split manufacturing" as countermeasures to hardware trojans. Using these ingredients, we present a generic compiler that can transform any circuit into a trojan-resilient one, for which we can state quantitative security guarantees on the number of correct executions of the circuit thanks to a new tool denoted as ``testing amplification". Compared to previous works, our threat model covers an extended range of hardware trojans while we stick with the goal of minimizing the number of honest elements in our transformed circuits. Since transformed circuits essentially correspond to redundant multiparty computations of the target functionality, they also allow reasonably efficient implementations, which can be further optimized if specialized to certain cryptographic primitives and security goals.

Annihilation attacks, introduced in the work of Miles, Sahai, and Zhandry (CRYPTO 2016), are a class of polynomial-time attacks against several candidate indistinguishability obfuscation ($i\mathcal{O}$) schemes, built from Garg, Gentry, and Halevi (EUROCRYPT 2013) multilinear maps. In this work, we provide a general efficiently-testable property of two branching programs, called ``partial inequivalence'', which we show is sufficient for our variant of annihilation attacks on several obfuscation constructions based on GGH13 multilinear maps. We give examples of pairs of natural $\mathsf{NC}^1$ circuits, which -- when processed via Barrington's Theorem -- yield pairs of branching programs that are partially inequivalent. As a consequence we are also able to show examples of ``bootstrapping circuits,'' used to obtain obfuscations for all circuits (given an obfuscator for $\mathsf{NC}^1$ circuits), in certain settings also yield partially inequivalent branching programs. Prior to our work, no attacks on any obfuscation constructions for these settings were known.

We describe an efficient and secure decryption protocol to the Norwegian Internet voting project. We first adapt Groth’s shuffle-decryption from 2010 to our purpose, and we prove all security properties in the random oracle model. We then describe the complete decryption algorithm, and prove that it maintains the security of the rest of the protocol.

If two different secret keys of a stream cipher yield the same internal state after the key scheduling algorithm (KSA) and hence generates the same sequence of keystream bits, they are called a colliding key pair. The number of possible internal states of RC4 stream cipher is very large (approximately $2^{1700}$), which makes finding key collision hard for practical key length (i.e., less than 30 bytes). Matsui [FSE 2009] for the first time reported a 24-byte colliding key pair and one 20-byte near-colliding key pair (i.e., for which the state arrays after the KSA differ in at most two positions) for RC4. Subsequently, Chen and Miyaji [ISC 2011] claimed to design a more efficient search algorithm using Matsui's collision pattern and reported a 22-byte colliding key pair which remains the only shortest known colliding key pair so far. In this paper, we show some limitations of both the above approaches and propose a faster collision search algorithm that overcomes these limitations. Using our algorithm, we are able to find three additional 22-byte colliding key pairs that are different from the one reported by Chen and Miyaji [ISC 2011]. We additionally give 12 new 20-byte near-colliding key pairs different from Matsui's [FSE 2009]. These results are significant, considering the argument by the experts [Biham and Dunkelman, 2007] that for shorter keys there might be no instances of collision at all.

In this paper we present two new attacks on cryptosystems based on principal ideal lattices. First, we show that, if there is one polynomially large entry in the transformation matrix from trapdoor basis to public basis, we can obtain the trapdoor basis with high probability. Our attack is quite simple, and rarely needs to use any lattice-reduction tools. The key point is that some class of matrices satisfies multiplication commutative law. We use multiplication commutative law to obtain a linear equation of integer variables, and find it not difficult to be solved as long as its rank is larger than half of its number of variables. Second, we show that, if each entry of the trapdoor basis is polynomially large, we can obtain the trapdoor basis with high probability. This attack is a modified version, and we don't care whether each entry of its transformation matrix is super-polynomially large. The key point is that we can obtain many vectors of the inverse ideal, and we can reduce each of these vectors into polynomially large multiple of its generator.

Software implementations of discrete logarithm based cryptosystems over finite fields typically make the assumption that any domain parameters they are presented with are trustworthy, i.e., the parameters implement cyclic groups where the discrete logarithm problem is assumed to be hard. An informal and widespread justification for this seemingly exists that says validating parameters at run time is too computationally expensive relative to the perceived risk of a server sabotaging the privacy of its own connection. In this paper we explore this trust assumption and examine situations where it may not always be justified. We conducted an investigation of discrete logarithm domain parameters in use across the Internet and discovered evidence of a multitude of potentially backdoored moduli of unknown order in TLS and STARTTLS spanning numerous countries, organizations, and protocols. Although our disclosures resulted in a number of organizations taking down suspicious parameters, we argue the potential for TLS backdoors is systematic and will persist until either until better parameter hygiene is taken up by the community, or finite field based cryptography is eliminated altogether.

We describe new cryptanalytic attacks on the candidate branching program obfuscator proposed by Garg, Gentry, Halevi, Raykova, Sahai and Waters (GGHRSW) using the GGH13 graded encoding, and its variant using the GGH15 graded encoding as specified by Gentry, Gorbunov and Halevi. All our attacks require very specific structure of the branching programs being obfuscated, which in particular must have some input-partitioning property. Common to all our attacks are techniques to extract information about the ``multiplicative bundling'' scalars that are used in the GGHRSW construction. For GGHRSW over GGH13, we show how to recover the ideal generating the plaintext space when the branching program has input partitioning. Combined with the information that we extract about the ``multiplicative bundling'' scalars, we get a distinguishing attack by an extension of the annihilation attack of Miles, Sahai and Zhandry. Alternatively, once we have the ideal we can solve the principle-ideal problem (PIP) in classical subexponential time or quantum polynomial time, hence obtaining a total break. For the variant over GGH15, we show how to use the left-kernel technique of Coron, Lee, Lepoint and Tibouchi to recover ratios of the bundling scalars. Once we have the ratios of the scalar products, we can use factoring and PIP solvers (in classical subexponential time or quantum polynomial time) to find the scalars themselves, then run mixed-input attacks to break the obfuscation.

We present a practical construction of an additively homomorphic commitment scheme based on structured lattice assumptions, together with a zero-knowledge proof of opening knowledge. Our scheme is a design improvement over the previous work of Benhamouda et al. in that it is not restricted to being statistically binding. While it is possible to instantiate our scheme to be statistically binding or statistically hiding, it is most efficient when both hiding and binding properties are only computational. This results in approximately a factor of 4 reduction in the size of the proof and a factor of 6 reduction in the size of the commitment over the aforementioned scheme.