Leakage-resilient cryptography builds systems that withstand partial adversary knowledge of secret state. Ideally, leakage-resilient systems withstand current and future attacks; restoring confidence in the security of implemented cryptographic systems. Understanding the relation between classes of leakage functions is an important aspect. In this work, we consider the memory leakage model, where the leakage class contains functions over the system's entire secret state. Standard classes include functions with bounded output length, functions that retain (pseudo)~entropy in the secret, and functions that leave the secret computationally unpredictable. Standaert, Pereira, and Yu (Crypto, 2013) introduced a new class of leakage functions they call simulatable leakage. A leakage function is simulatable if a simulator can produce indistinguishable leakage without access to the true secret state. We extend their notion to general applications and consider two versions. For weak simulatability: the simulated leakage must be indistinguishable from the true leakage in the presence of public information. For strong simulatability, this requirement must also hold when the distinguisher has access to the true secret state. We show the following: * Weakly simulatable functions retain computational unpredictability. * Strongly simulatability functions retain pseudoentropy. * There are bounded length functions that are not weakly simulatable. * There are weakly simulatable functions that remove pseudoentropy. * There are leakage functions that retain computational unpredictability are not weakly simulatable.

GOST-R is a Russian Standard Cryptographic Hash function which was first introduced in 1994 by Russian Federal for information processing, information security and digital signature. In 2012, it was updated to GOST-R 34.11-2012 and replaced older one for all its applications from January 2013. GOST-R is based on modified Merkle-Damg\aa rd construction. Here, we present a modified version of GOST-R (MGR-hash). The modified design is based on wide pipe construction which is also a modified Merkle-Damg\aa rd construction. MGR is much more secure as well as three times faster than GOST-R. AES like block cipher has been used in designing the compression function of MGR because AES is one of the most efficient and secure block cipher and it has been evaluated for more than 12 years. We will also analyze the MGR hash function with respect to its security and efficiency.

Designing a keystream generator which utilizes Linear Feedback Shift Registers (LFSRs) against correlation, linear attacks is a highly challenging task. In this paper, a new framework for keystream gen- erators is proposed. It is comprised of a set of Linear Feedback Shift Registers (LFSRs), a Multiplicative Congruential Generator (MCG), a vector linear function and, a Boolean function which outputs the keystream. The framework is more generally discussed against corre- lation attacks, linear attacks and distinguishing (linear) attacks. It is shown that such attacks which are applicable to LFSR based keystream generators are not possible on the proposed framework.

The device-unique response of a physically unclonable function (PUF) can serve as the root of trust in an embedded cryptographic system. Fuzzy extractors transform this noisy non-uniformly distributed secret into a stable high-entropy key. The overall efficiency thereof, typically depending on error-correction with a binary [n,k,d] block code, is determined by the universal and well-known (n-k) bound on the min-entropy loss. We derive new considerably tighter bounds for PUF-induced distributions that suffer from, e.g., bias or spatial correlations. The bounds are easy-to-evaluate and apply to large non-trivial codes, e.g., BCH and Reed-Muller codes. Apart from an inherent reduction in implementation footprint, the newly developed theory also facilitates the analysis of state-of-the-art error-correction methods for PUFs. As such, we debunk the reusability claim of the reverse fuzzy extractor. Moreover, we provide proper quantitative motivation for debiasing schemes, as this was missing in the original proposals.

About three decades ago it was realized that implementing private channels between parties which can be adaptively corrupted requires an encryption scheme that is secure against selective opening attacks. Whether standard (IND-CPA) security implies security against selective opening attacks has been a major open question since. The only known reduction from selective opening to IND-CPA security loses an exponential factor. A polynomial reduction is only known for the very special case where the distribution considered in the selective opening security experiment is a product distribution, i.e., the messages are samples independent from each other. In this paper we give a reduction whose loss is quantified via the dependence graph (where message dependencies correspond to edges) of the underlying message distribution. In particular, for some concrete distributions including Markov distributions, our reduction is polynomial.

In this paper we consider a two party key-exchange protocol proposed by Grigoriev and Shpilrain which uses tropical matrix algebra as a platform. Our analysis shows that the scheme is not secure.

The iterated Even-Mansour construction defines a block cipher from a tuple of public $n$-bit permutations $(P_1,\ldots,P_r)$ by alternatively xoring some $n$-bit round key $k_i$, $i=0,\ldots,r$, and applying permutation $P_i$ to the state. The \emph{tweakable} Even-Mansour construction generalizes the conventional Even-Mansour construction by replacing the $n$-bit round keys by $n$-bit strings derived from a master key \emph{and a tweak}, thereby defining a tweakable block cipher. Constructions of this type have been previously analyzed, but they were either secure only up to the birthday bound, or they used a nonlinear mixing function of the key and the tweak (typically, multiplication of the key and the tweak seen as elements of some finite field) which might be costly to implement. In this paper, we tackle the question of whether it is possible to achieve beyond-birthday-bound security for such a construction by using only linear operations for mixing the key and the tweak into the state. We answer positively, describing a 4-round construction with a $2n$-bit master key and an $n$-bit tweak which is provably secure in the Random Permutation Model up to roughly $2^{2n/3}$ adversarial queries.

In Ciphertext-Policy Attribute-Based Encryption (CP-ABE), access policies associated with the ciphertexts are generally role-based and the attributes satisfying the policies are generally \emph{shared} by multiple users. If a malicious user, with his attributes shared with multiple other users, created a decryption blackbox for sale, this malicious user could be difficult to identify from the blackbox. Hence in practice, a useful CP-ABE scheme should have some tracing mechanism to identify this `traitor' from the blackbox. In this paper, we propose the first CP-ABE scheme which simultaneously achieves (1) fully collusion-resistant blackbox traceability in the standard model, (2) full security in the standard model, and (3) on prime order groups. When compared with the latest fully collusion-resistant blackbox traceable CP-ABE schemes, this new scheme achieves the same efficiency level, enjoying the sub-linear overhead of $O(\sqrt{N})$, where $N$ is the number of users in the system. This new scheme is highly expressive and can take any monotonic access structures as ciphertext policies.

In a celebrated paper published in 1951, von Neumann presented a simple procedure allowing to correct the bias of random sources. This device outputs bits at irregular intervals. However, cryptographic hardware is usually synchronous. This paper proposes a new building block called Pace Regulator, inserted between the randomness consumer and the von Neumann regulator to streamline the pace of random bits.

A generic way to design lightweight cryptographic primitives is to construct simple rounds using small nonlinear components such as 4x4 S-boxes and use these iteratively (e.g., PRESENT and SPONGENT). In order to efficiently implement the primitive, efficient implementations of its internal components are needed. Multiplicative complexity of a function is the minimum number of AND gates required to implement it by a circuit over the basis (AND, XOR, NOT). It is known that multiplicative complexity is exponential in the number of input bits n. Thus it came as a surprise that circuits for all 65 536 functions on four bits were found which used at most three AND gates. In this paper, we verify this result and extend it to five-variable Boolean functions. We show that the multiplicative complexity of a Boolean function with five variables is at most four.

In the last few years, the field of lightweight cryptography has seen an influx in the number of block ciphers and hash functions being proposed. One of the metrics that define a good lightweight design is the energy consumed per unit operation of the algorithm. For block ciphers, this operation is the encryption of one plaintext. By studying the energy consumption model of a CMOS gate, we arrive at the conclusion that the total energy consumed during the encryption operation of an r-round unrolled architecture of any block cipher is a quadratic function in r. We then apply our model to 9 well known lightweight block ciphers, and thereby try to predict the optimal value of r at which an r-round unrolled architecture for a cipher is likely to be most energy efficient. We also try to relate our results to some physical design parameters like the signal delay across a round and algorithmic parameters like the number of rounds taken to achieve full diffusion of a difference in the plaintext/key.

A major challenge in the study of cryptography is characterizing the necessary and sufficient assumptions required to carry out a given cryptographic task. The focus of this work is the necessity of a broadcast channel for securely computing symmetric functionalities (where all the parties receive the same output) when one third of the parties, or more, might be corrupted. Assuming all parties are connected via a peer-to-peer network, but no broadcast channel (nor a secure setup phase) is available, we prove the following characterization: * A symmetric n-party functionality can be securely computed facing n/3<=t<n/2 corruptions (i.e., honest majority), if and only if it is \emph{(n-2t)-dominated}; a functionality is k-dominated, if \emph{any} k-size subset of its input variables can be set to determine its output. * Assuming the existence of one-way functions, a symmetric n-party functionality can be securely computed facing t>=n/2 corruptions (i.e., no honest majority), if and only if it is 1-dominated and can be securely computed with broadcast. It follows that, in case a third of the parties might be corrupted, broadcast is necessary for securely computing non-dominated functionalities (in which "small" subsets of the inputs cannot determine the output), including, as interesting special cases, the Boolean XOR and coin-flipping functionalities.

In this short note, we analyze the security of the quadratic zero-testing procedure for the GGH13 graded encoding scheme, which was recently proposed by Gentry, Halevi and Lepoint. We show that this modification fails to immunize the GGH13 construction against zeroizing attacks, and that the modified scheme is susceptible to the same attacks as the original one.

We give a theoretical description of a new homomorphic encryption scheme DA-Encrypt that is based on (non-archimedean) Diophantine Approximation.

Sanitizable signatures, introduced by Ateniese et al. at ESORICS'05, allow to issue a signature on a message where certain predefined message blocks may later be changed (sanitized) by some dedicated party (the sanitizer) without invalidating the original signature. With sanitizable signatures, replacements for modifiable (admissible) message blocks can be chosen arbitrarily by the sanitizer. However, in various scenarios this makes sanitizers too powerful. To reduce the sanitizers power, Klonowski and Lauks at ICISC'06 proposed (among others) an extension that enables the signer to limit the allowed modifications per admissible block to a well defined set each. At CT-RSA'10 Canard and Jambert then extended the formal model of Brzuska et al. from PKC'09 to additionally include the aforementioned and other extensions. We, however, observe that the privacy guarantees of their model do not capture privacy in the sense of the original definition of sanitizable signatures. That is, if a scheme is private in this model it is not guaranteed that the sets of allowed modifications remain concealed. To this end, we review a stronger notion of privacy, i.e., (strong) unlinkability (defined by Brzuska et al. at EuroPKI'13), in this context. While unlinkability fixes this problem, no efficient unlinkable scheme supporting the aforementioned extensions exists and it seems to be hard to construct such schemes. As a remedy, in this paper, we propose a notion stronger than privacy, but weaker than unlinkability, which captures privacy in the original sense. Moreover, it allows to easily construct efficient schemes satisfying our notion from secure existing schemes in a black-box fashion.

Self-blindable credential schemes allow users to anonymously prove ownership of credentials. This is achieved by randomizing the credential before each showing in such a way that it still remains valid. As a result, each time a different version of the same credential is presented. A number of such schemes have been proposed, but unfortunately many of them are broken, in the sense that they are linkable (i.e., failing to protect the privacy of the user), or malleable (i.e., they allow users to create new credentials using one or more valid credentials given to them). In this paper we prove a general theorem that relates linkability and malleability in self-blindable credential schemes, and that can test whether a scheme is linkable or malleable. After that we apply the theorem to a number of self-blindable credential schemes to show that they suffer from one or both of these issues.

The energy cost of asymmetric cryptography is a vital component of modern secure communications, which inhibits its wide spread adoption within the ultra-low energy regimes such as Implantable Medical Devices (IMDs) and Radio Frequency Identification (RFID) tags. The ciphertext-policy attribute-based encryption (CP-ABE) is a promising cryptographic tool, where an encryptor can decide the access policy that who can decrypt the data. Thus, the data will be protected from the unauthorized users. However, most of the existing CP-ABE schemes require huge storage and computational overheads. Moreover, CP-ABE schemes based on bilinear map loose the high efficiency over the elliptic curve cryptography because of the requirement of the security parameters of larger size. These drawbacks prevent the use of ultra-low energy devices in practice. In this paper, we aim to propose a novel expressive AND-gate access structured CP-ABE scheme with constant-size secret keys (CSSK) with the cost efficient solutions for the encryption and decryption using ECC, called the CP-ABE-CSSK scheme. In the proposed CP-ABE-CSSK, the size of secret key is as small as 320 bits. In addition, ECC is efficient and more suitable for the lightweight devices as compared to the bilinear pairing based cryptosystem. Thus, the proposed CP-ABE-CSSK scheme provides the low computation and storage overheads with an expressive AND-gate access structure as compared to the related existing schemes in the literature. As a result, our scheme is very suitable for CP-ABE key storage and computation cost in the ultra-low energy devices.

Khudra is a 18-round lightweight block cipher proposed by Souvik Kolay and Debdeep Mukhopadhyay in the SPACE 2014 conference which is applicable to Field Programmable Gate Arrays (FPGAs). In this paper, we obtain $2^{16}$ 14-round related-key impossible differentials of Khudra, and based on these related-key impossible differentials for 32 related keys, we launch an attack on the full Khudra with data complexity of $2^{63}$ related-key chosen-plaintexts, time complexity of about $2^{68.46}$ encryptions and memory complexity of $2^{64}$.

In 2011, B.B.Brumley and N.Tuveri found a remote timing attack on OpenSSL’s ECDSA implementation for binary curves. We will study if the title of their paper was indeed relevant (Remote Timing Attacks are Still Practical). We improved on their lattice attack using the Embedding Strategy that reduces the Closest Vector Problem to the Shortest Vector Problem so as to avoid using Babai’s procedures to solve the CVP and rely on the better experimental results of LLL. We will detail (along with publishing the source code of the tools we used) our attempts to reproduce their experiments from a remote machine located on the same network with the server, and see that such attacks are not trivial and far from being practical. Finally we will see other attacks and countermeasures.

Witness encryption (WE) was introduced by Garg et al. (STOC'13). A WE scheme is defined for some NP language $L$ and lets a sender encrypt messages relative to instances $x$. A ciphertext for $x$ can be decrypted using $w$ witnessing $x\in L$, but hides the message if $x\notin L$. Garg et al. construct WE from multilinear maps and give another construction (FOCS'13) using indistinguishability obfuscation (iO) for encryption. Due to the reliance on such heavy tools, WE can currently hardly be implemented on powerful hardware and will unlikely be realizable on constrained devices like smart cards any time soon. We construct a WE scheme where \emph{encryption} is done by simply computing a Naor-Yung ciphertext (two CPA encryptions and a NIZK proof). To achieve this, our scheme has a setup phase, which outputs public parameters containing an obfuscated circuit (only required for decryption), two encryption keys and a common reference string (used for encryption). This setup need only be run once, and the parameters can be used for arbitrary many encryptions. Our scheme can also be turned into a \emph{functional} WE scheme, where a message is encrypted w.r.t. a statement and a function $f$, and decryption with a witness $w$ yields $f(m,w)$. Our construction is inspired by the functional encryption scheme by Garg et al. and we prove (selective) security assuming iO and statistically simulation-sound NIZK. We give a construction of the latter in bilinear groups and combining it with ElGamal encryption, our ciphertexts are of size $1.3$ kB at a 128-bit security level and can be computed on a smart card.

Masking schemes based on tables recomputation are classical countermeasures against high-order side-channel attacks. Still, they are known to be attackable at order $d$ in the case the masking involves $d$ shares. In this work, we mathematically show that an attack of order strictly greater than $d$ can be more successful than an attack at order $d$. To do so, we leverage the idea presented by Tunstall, Whitnall and Oswald at FSE 2013: we exhibit attacks which exploit the multiple leakages linked to one mask during the recomputation of tables. Specifically, regarding first-order table recomputation, improved by a shuffled execution, we show that there is a window of opportunity, in terms of noise variance, where a novel highly multivariate third-order attack is more efficient than a classical bivariate second-order attack. Moreover, we show on the example of the high-order secure table computation presented by Coron at EUROCRYPT 2014 that the window of opportunity enlarges linearly with the security order $d$.

Broadcasting is a very efficient way to securely transmit information to a large set of geographically scattered receivers, and in practice, it is often the case that these receivers can be grouped in sets sharing common characteristics (or attributes). We describe in this paper an efficient ciphertext-policy attribute-based broadcast encryption scheme (CP-ABBE) supporting negative attributes and able to handle access policies in conjunctive normal form (CNF). Essentially, our scheme is a combination of the Boneh-Gentry-Waters broadcast encryption and of the Lewko-Sahai-Waters revocation schemes; the former is used to express attribute-based access policies while the latter is dedicated to the revocation of individual receivers. Our scheme is the first one that involves a public key and private keys having a size that is independent of the number of receivers registered in the system. Its selective security is proven with respect to the Generalized Diffie-Hellman Exponent (GDHE) problem on bilinear groups.

In this paper, we extend the method of Scott and Barreto and present an explicit and simple algorithm to generate families of generalized MNT elliptic curves. Our algorithm allows us to obtain all families of generalized MNT curves with any given cofactor. Then, we analyze the complex multiplication equations of these families of curves and transform them into generalized Pell equation. As an example, we describe a way to generate Edwards curves with embedding degree 6, that is, elliptic curves having cofactor h = 4.

Authentication based on cryptographic protocols is a key technology for recent security systems. However, the so-called relay attack where a malicious attacker tries to assume the role of the prover, is known to be a serious threat even for the cryptographically-secure authentication systems. This paper proposes a new authentication method that utilizes the side channel that already exists in many authentication systems. The side channel has been studied intensively from the attacker viewpoint, and it is best known for the key-recovery attack against cryptographic implementations via physical information. Here, reversing our way of thinking, we propose to use the information constructively via the side channel to enhance the existing cryptographic protocols. Using symmetric-key-based authentication as an example, we show based on experiments using an FPGA that each of the side-channel information leaked from provers is unique enough for the purpose of authentication.

After four decades of public key cryptography, both the industry and academia seek better solutions for the public key infrastructure. A recent proposal, the certificate transparency concept, tries to enable untrusted servers act as public key servers, such that any key owner can verify that her key is kept properly at those servers. Unfortunately, due to high computation and communication requirements, existing certificate transparency proposals fail to address the problem as a whole. We propose a new efficient key authentication service (KAS). It uses server-side gossiping as the source of trust, and assumes servers are not all colluding. KAS stores all keys of each user in a separate hash chain, and always shares the last ring of the chain among the servers, ensuring the users that all servers provide the same view about them (i.e., no equivocation takes place). Storing users’ keys separately reduces the server and client computation and communication dramatically, making our KAS a very efficient way of public key authentication. The KAS handles a key registration/change operation in O(1) time using only O(1) proof size; independent of the number of users. While the previous best proposal, CONIKS, requires the client to download 100 KB of proof per day, our proposal needs less than 1 KB of proof per key lifetime, while obtaining the same probabilistic guarantees as CONIKS.

This paper uses an Instruction Set Architecture (ISA) based statistical energy model of an ARM Cortex-M4 microprocessor to evaluate the energy consumption of an implementation of AES with different side channel attack (SCA) countermeasures and an implementation of lightweight ciphers PRESENT, KLEIN and ZORRO with and without Boolean first order masking. In this way, we assess the additional energy consumption of using different SCA countermeasures and using lightweight block ciphers on 32 bit embedded devices. In addition to this, we provide a methodology for developing an ISA based energy model for cryptographic software with an accuracy of $\pm5\%$. In addition to providing our methodology for developing this model, we also show that using variations of instructions that reduce the size of code can reduce the energy consumption by as much as $30\%-40\%$ and that memory instructions reduce the predictability of our energy model.

The challenges faced in securing embedded computing systems against multifaceted memory safety vulnerabilities have prompted great interest in the development of memory safety countermeasures. These countermeasures either provide protection only against their corresponding type of vulnerabilities, or incur substantial architectural modifications and overheads in order to provide complete safety, which makes them infeasible for embedded systems. In this paper, we propose M-MAP: a comprehensive system based on multi-factor memory authentication for complete memory safety, inspired by everyday user authentication factors. We examine certain crucial theoretical and practical implications of composing memory integrity verification and bounds checking protection schemes in a comprehensive system. Based on these implications, we implement M-MAP with hardware based memory integrity verification and software based bounds checking to achieve a balance between hardware modifications and performance. We demonstrate that M-MAP implemented on top of a lightweight out-of-order processor delivers complete memory safety with only $32\%$ performance overhead on average, and incurs minimal hardware modifications and area overhead.

We give a simple and efficient construction of unique signature on groups equipped with bilinear map. In contrast to prior works, our proof of security is based on computational Diffie-Hellman problem in the random oracle model. Meanwhile, the resulting signature consists of only one group element. Due to its simplicity, security and efficiency, our scheme is suitable for those situations that require to overcome communication bottlenecks. Moreover, the unique signature is a building block for designing chosen-ciphertext secure cryptosystems and verifiable random functions, which have found many interesting applications in cryptographic protocol design.

The candidate construction of multilinear maps by Garg, Gentry, and Halevi (Eurocrypt 2013) has lead to an explosion of new cryptographic constructions ranging from attribute-based encryption (ABE) for arbitrary polynomial size circuits, to program obfuscation, and to constrained pseudorandom functions (PRFs). Many of these constructions require k-linear maps for large k. In this work, we focus on the reduction of k in certain constructions of access control primitives that are based on k-linear maps; in particular, we consider the case of constrained PRFs and ABE. We construct the following objects: - A constrained PRF for arbitrary circuit predicates based on (n+l_{OR}-1)-linear maps (where n is the input length and l_{OR} denotes the OR-depth of the circuit). - For circuits with a specific structure, we also show how to construct such PRFs based on (n+l_{AND}-1)-linear maps (where l_{AND} denotes the AND-depth of the circuit). We then give a black-box construction of a constrained PRF for NC1 predicates, from any bit-fixing constrained PRF that fixes only one of the input bits to 1; we only require that the bit-fixing PRF have certain key homomorphic properties. This construction is of independent interest as it sheds light on the hardness of constructing constrained PRFs even for ``simple'' predicates such as bit-fixing predicates. Instantiating this construction with the bit-fixing constrained PRF from Boneh and Waters (Asiacrypt 2013) gives us a constrained PRF for NC1 predicates that is based only on n-linear maps, with no dependence on the predicate. In contrast, the previous constructions of constrained PRFs (Boneh and Waters, Asiacrypt 2013) required (n+l+1)-linear maps for circuit predicates (where l is the total depth of the circuit) and n-linear maps even for bit-fixing predicates. We also show how to extend our techniques to obtain a similar improvement in the case of ABE and construct ABE for arbitrary circuits based on (l_{OR}+1)-linear (respectively (l_{AND}+1)-linear) maps.

RC4 suffered from a range of plaintext-recovery attacks using statistical biases, which use substantial, albeit close-to-practical, amounts of known keystream in applications such as TLS or WEP/WPA. Spritz was recently proposed at the rump session of CRYPTO 2014 as a slower redesign of RC4 by Rivest and Schuldt, aiming at reducing the statistical biases that lead to these attacks on RC4. Even more devastating than those plaintext-recovery attacks from large amounts of keystream would be state- or key-recovery attacks from small amounts of known keystream. For RC4, there is unsubstantiated evidence that they may exist, the situation for Spritz is however not clear, as resistance against such attacks was not a design goal. In this paper, we provide the first cryptanalytic results on Spritz and introduce three different state recovery algorithms. Our first algorithm recovers an internal state, requiring only a short segment of keystream, with an approximated complexity of $2^{1400}$, which is much faster than exhaustive search through all possible states, but is still far away from a practical attack. Furthermore, we introduce a second algorithm that uses a pattern in the keystream to reduce the number of guessed values in our state recovery algorithm. Our third algorithm uses a probabilistic approach by considering the permutation table as probability distribution. All in all, rather than showing a weakness, our analysis supports the conjecture that compared to RC4, Spritz may also provide higher resistance against potentially devastating state-recovery attacks.

Hierarchical identity-based encryption (HIBE) is an extension of identity-based encryption (IBE) where an identity of a user is organized as a hierarchical structure and a user can delegate the private key generation to another user. Providing a revocation mechanism for HIBE is highly necessary to keep a system securely. Revocable HIBE (RHIBE) is an HIBE scheme that can revoke a user's private key if his credential is expired or revealed. In this paper, we first propose an unbounded HIBE scheme where the maximum hierarchy depth is not limited and prove its selective security under a q-type assumption. Next, we propose an efficient unbounded RHIBE scheme by combining our unbounded HIBE scheme and a binary tree structure, and then we prove its selective security. By presenting the unbounded RHIBE scheme, we solve the open problem of Seo and Emura in CT-RSA 2015.

We introduce the notion of asymmetric programmable hash functions (APHFs, for short), which adapts Programmable Hash Functions, introduced by Hofheinz and Kiltz at Crypto 2008, with two main differences. First, an APHF works over bilinear groups, and it is asymmetric in the sense that, while only {\em secretly} computable, it admits an isomorphic copy which is publicly computable. Second, in addition to the usual programmability, APHFs may have an alternative property that we call programmable pseudorandomness. In a nutshell, this property states that it is possible to embed a pseudorandom value as part of the function's output, akin to a random oracle. In spite of the apparent limitation of being only secretly computable, APHFs turn out to be surprisingly powerful objects. We show that they can be used to generically implement both regular and linearly-homomorphic signature schemes in a simple and elegant way. More importantly, when instantiating these generic constructions with our concrete realizations of APHFs, we obtain: (1) the first linearly-homomorphic signature (in the standard model) whose public key is sub-linear in both the dataset size and the dimension of the signed vectors; (2) short signatures (in the standard model) whose public key is shorter than those by Hofheinz-Jager-Kiltz from Asiacrypt 2011, and essentially the same as those by Yamada, Hannoka, Kunihiro, (CT-RSA 2012).

While much has changed in Internet security over the past decades, textual passwords remain as the dominant method to secure user web accounts and they are proliferating in nearly every new web services. Nearly every web services, no matter new or aged, now enforce some form of password creation policy. In this work, we conduct an extensive empirical study of 50 password creation policies that are currently imposed on high-profile web services, including 20 policies mainly from US and 30 ones from mainland China. We observe that no two sites enforce the same password creation policy, there is little rationale under their choices of policies when changing policies, and Chinese sites generally enforce more lenient policies than their English counterparts. We proceed to investigate the effectiveness of these 50 policies in resisting against the primary threat to password accounts (i.e. online guessing) by testing each policy against two types of weak passwords which represent two types of online guessing. Our results show that among the total 800 test instances, 541 ones are accepted: 218 ones come from trawling online guessing attempts and 323 ones come from targeted online guessing attempts. This implies that, currently, the policies enforced in leading sites largely fail to serve their purposes, especially vulnerable to targeted online guessing attacks.

We construct both randomizable and strongly existentially unforgeable structure-preserving signatures for messages consisting of many group elements. To sign a message consisting of N=mn group elements we have a verification key size of $m$ group elements and signatures contain n+2 elements. Verification of a signature requires evaluating n+1 pairing product equations. We also investigate the case of fully structure-preserving signatures where it is required that the secret signing key consists of group elements only. We show a variant of our signature scheme allowing the signer to pick part of the verification key at the time of signing is still secure. This gives us both randomizable and strongly existentially unforgeable fully structure-preserving signatures. In the fully structure preserving scheme the verification key is a single group element, signatures contain m+n+1 group elements and verification requires evaluating n+1 pairing product equations.

Combining the efficient cross-polytope locality-sensitive hash family of Terasawa and Tanaka with the heuristic lattice sieve algorithm of Micciancio and Voulgaris, we show how to obtain heuristic and practical speedups for solving the shortest vector problem (SVP) on both arbitrary and ideal lattices. In both cases, the asymptotic time complexity for solving SVP in dimension n is 2^(0.298n). For any lattice, hashes can be computed in polynomial time, which makes our CPSieve algorithm much more practical than the SphereSieve of Laarhoven and De Weger, while the better asymptotic complexities imply that this algorithm will outperform the GaussSieve of Micciancio and Voulgaris and the HashSieve of Laarhoven in moderate dimensions as well. We performed tests to show this improvement in practice. For ideal lattices, by observing that the hash of a shifted vector is a shift of the hash value of the original vector and constructing rerandomization matrices which preserve this property, we obtain not only a linear decrease in the space complexity, but also a linear speedup of the overall algorithm. We demonstrate the practicability of our cross-polytope ideal lattice sieve IdealCPSieve by applying the algorithm to cyclotomic ideal lattices from the ideal SVP challenge and to lattices which appear in the cryptanalysis of NTRU.

A re-encryption program (or a circuit) transforms a ciphertext encrypted under Alice's public key $pk_1$ to a ciphertext of the same message encrypted under Bob's public key $pk_2$. Hohenberger et al. (TCC 2007) constructed a pairing-based obfuscator for a family of circuits implementing the re-encryption functionality under a new notion of obfuscation called as \textit{average-case secure obfuscation}. Chandran et al. (PKC 2014) proposed a lattice-based construction for the same. The construction given by Hohenberger et al. could only support encryptions of messages from a polynomial space and the decryption algorithm may have to perform a polynomial number of pairing operations in the worst case. Moreover, the proof of security relies on strong assumptions. On the other hand, the construction given by Chandran et al. relies on standard assumptions on lattices but could only satisfy a relaxed notion of correctness. In this work we propose a simple and efficient obfuscator for the re-encryption functionality which doesn't suffer from \textit{any} of the above mentioned drawbacks. In particular, our construction satisfies the strongest notion of correctness, supports encryption of messages from an exponential sized domain and relies on the standard DDH-assumption. We also strengthen the black-box security model for encryption - re-encryption system proposed by Hohenberger et al. and prove the average-case virtual black box property of our obfuscator as well as the security of our encryption - re-encryption system (in the strengthened model) under the DDH-assumption. All our proofs are in the standard model.

We present a general framework for developing and analyzing homomorphic cryptosystems whose security relies on the difficulty of solving systems of nonlinear equations over Z/nZ, n being an RSA modulus. In this framework, many homomorphic cryptosystems can be conceptualized. Based on symmetry considerations, we propose a general assumption that ensures the security of these schemes. To highlight this, we present an additive homomorphic private-key cryptosystem and we prove its security. Finally, we propose two motivating perspectives of this work. We first propose an FHE based on the previous scheme by defining a simple multiplicative operator. Secondly, we propose ways to remove the factoring assumption in order to get pure multivariate schemes.

The notion of extended nested dual system groups (ENDSG) was recently proposed by Hofheinz et al. [PKC 2015] for constructing almost-tight identity based encryptions (IBE) in the multi-instance, multi-ciphertext (MIMC) setting. However only a composite-order instantiation was proposed and more efficient prime-order instantiations are absent. The paper fills the blank by presenting two constructions. We revise the definition of ENDSG and realize it using prime-order bilinear groups based on Chen and Wee's prime-order instantiation of nested dual system groups [CRYPTO 2013]. This yields the first almost-tight IBE in the prime-order setting achieving weak adaptive security in MIMC scenario under the $d$-linear ($d$-Lin) assumption. We further enhanced the revised ENDSG to capture stronger security notions for IBE, including $B$-weak adaptive security and full adaptive security. We show that our prime-order instantiation is readily $B$-weak adaptive secure and full adaptive secure without introducing extra assumption. We then try to find better solution by fine-tuning ENDSG again and realizing it using the technique of Chen, Gay, and Wee [EUROCRYPT 2015]. This leads to an almost-tight secure IBE in the same setting with better performance than our first result, but the security relies on a non-standard assumption, $d$-linear assumption with auxiliary input ($d$-LinAI) for an even positive integer $d$. However we note that, the $2$-LinAI assumption is implied by the external decisional linear (XDLIN) assumption. This concrete instantiation could also be realized using symmetric bilinear groups under standard decisional linear assumption.

At CHES 2001, Walter introduced the Big Mac attack against an implementation of RSA. It is an horizontal collision attack, based on the detection of common operands in two multiplications. The attack is very powerful since one single power trace of an exponentiation permits to recover all bits of the secret exponent. Moreover, the attack works with unknown or blinded input. The technique was later studied and improved by Clavier et alii and presented at INDOCRYPT 2012. At SAC 2013, Bauer et alii presented the first attack based on the Big Mac principle on implementations based on elliptic curves with simulation results. In this work, we improve the attack presented by Bauer et alii to considerably increase the success rate. Instead of comparing only two multiplications, the targeted implementation permits to compare many multiplications. We give experiment results with traces taken from a real target to prove the soundness of our attack. In fact, the experimental results show that the original Big Mac technique given by Walter was better that the technique given by Clavier et alii. With our experiments on a real target, we show that the theoretical improvements are not necessarily the more suitable methods depending on the targeted implementations.

We introduce a CUDA GPU library to accelerate evaluations with homomorphic schemes defined over polynomial rings enabled with a number of optimizations including algebraic techniques for efficient evaluation, memory minimization techniques, memory and thread scheduling and low level CUDA hand-tuned assembly optimizations to take full advantage of the mass parallelism and high memory bandwidth GPUs offer. The arithmetic functions constructed to handle very large polynomial operands using number-theoretic transform (NTT) and Chinese remainder theorem (CRT) based methods are then extended to implement the primitives of the leveled homomorphic encryption scheme proposed by Löpez-Alt, Tromer and Vaikuntanathan. To compare the performance of the proposed CUDA library we implemented two applications: the Prince block cipher and homomorphic sorting algorithms on two GPU platforms in single GPU and multiple GPU configurations. We observed a speedup of 25 times and 51 times over the best previous GPU implementation for Prince with single and triple GPUs, respectively. Similarly for homomorphic sorting we obtained 12-41 times speedup depending on the number and size of the sorted elements.

The society today is better connected as a result of advancement in technology. The study of these social interactions and its resulting structure, is an integral component in the field of network science. However, the study of these social networks is limited to the availability of data. Privacy concerns restrict the access to network data with sensitive information. Networks that capture the relations such as trust, enmity, sexual contact, are a few examples of sensitive networks. A study of these sensitive networks is important in unraveling the behavioral aspects of the concerned individuals. The current paper proposes a multiparty computation algorithm that allows the construction of the unlabeled isomorphic version of the underlying network. The algorithm is information theoretic secure and works under the malicious adversarial model with the threshold of one third total corrupt parties.

A cryptosystem for wireless communications, recently proposed by T.~Dean and A.~Goldsmith, is considered. That system can be regarded as a second revolution in cryptography because the confidentiality of the messages transmitted over a wireless massive MIMO-based channel is provided by the difference in the space locations of legal and illegal users and it does not require any secret key distribution. However our investigation shows that there is a chance of eavesdropping the cipher texts by using a suboptimal algorithm. Therefore we investigate some additional conditions for channel matrices and additive noises in order to provide a desired security. A combination of wiretap channel coding with a MIMO-based cryptosystem is also considered.

We prove that there is no fully black-box construction of collision-resistant hash functions (CRH) from hierarchical identity-based encryption (HIBE) with arbitrary polynomial number of identity levels. As a corollary we obtain a series of separations showing that none of the primitives implied by HIBE in a black-box way (e.g., IBE, CCA-secure public-key encryption) can be used in a black-box way to construct fully homomorphic encryption or any other primitive that is known to imply CRH in a black-box way. To the best of our knowledge, this is the first limitation proved for the power of HIBE. Our proof relies on the reconstruction paradigm of Gennaro and Trevisan (FOCS 2000) and Haitner et al (FOCS 2007) and extends their techniques for one-way and trapdoor permutations to the setting of HIBE. A technical challenge for our separation of HIBE stems from the adaptivity of the adversary who is allowed to obtain keys for different identities before she selects the attacked identity. Our main technical contribution is to show how to achieve compression/reconstruction in the presence of such adaptive adversaries.

Keyword search on encrypted data enables one to search keyword ciphertexts without compromising keyword security. We further investigate this problem and propose a novel variant, dubbed certificateless keyword search on encrypted data (CLKS). CLKS not only supports keyword search on encrypted data, but also brings promising features due to the certificateless cryptography. In contrast to the certificated-based keyword search, CLKS requires no validation on the trustworthy of the public key before encrypting keywords; in contrast to the identity-based keyword search, CLKS prevents the key issuer (e.g., key generator center) from penetrating any information on keyword ciphertexts by leveraging the capability of accessing all data users’ (partial) private keys. Specifically, we rigorously define the syntax and security definitions for CLKS, and present the construction that is provably secure in the standard model under the Decisional Linear assumption. We implemented the proposed CLKS scheme and evaluated its performance. To the best of our knowledge, this is the first attempt to integrate certificateless cryptography with keyword search on encrypted data.

In 'Turning Online Ciphers Off', a class of constructions was defined based on layers of secure online ciphers interleaved with simple mixing layers (like reversing and block-shifting). Here we show that an SPRP construction proposed in the work cited is insecure. Howevewr, the same construction is secure under the assumption that the underlying construction is online-but-last ciphers. We include a simpler proof for beyond-birthday security of other constructions proposed in the same work.

The last hash function and block cipher standardized by the Russian standardization body (GOST) both use the same S-Box. It is also used by an independent CAESAR candidate. This transformation is only specified as a look up table and the reason behind its choice is unknown. We managed to reverse-engineer this S-Box and describe its unpublished structure. Our decomposition allows a much more efficient hardware implementation but the choice of the components used is puzzling from a cryptographic perspective. This extended abstract does not explain \emph{how} we found this decomposition. We will describe our process in an extended version of this paper.

Chaskey is a Message Authentication Code (MAC) for 32-bit microcontrollers proposed by Mouha et. al at SAC 2014. Its underlying blockcipher uses an Even-Mansour construction with a permutation based on the ARX methodology. In this paper, we present key-recovery attacks against Chaskey in the single and multi-user setting. These attacks are based on recent work by Fouque, Joux and Mavromati presented at Asiacrypt 2014 on Even-Mansour based constructions. We first show a simple attack on the classical single-user setting which confirms the security properties of Chaskey. Then, we describe an attack in the multi-user setting and we recover all keys of 2^{43} users by doing 2^{43} queries per user. Finally, we show a variant of this attack where we are able to recover keys of two users in a smaller group of 2^{32} users.

In [CDS94] Cramer, Damgård and Schoenmakers (CDS) devise an OR-composition technique for Sigma-protocols that allows to construct highly-efficient proofs for compound statements. Since then, such technique has found countless applications as building block for designing efficient protocols. Unfortunately, the CDS OR-composition technique works only if both statements are fixed before the proof starts. This limitation restricts its usability in those protocols where the theorems to be proved are defined at different stages of the protocol, but, in order to save rounds of communication, the proof must start even if not all theorems are available. Many round-optimal protocols ([KO04,DPV04,YZ07,SV12]) crucially need such property to achieve round-optimality, and, due to the inapplicability of CDS's technique, are currently implemented using proof systems that requires expensive NP reductions, but that allow the proof to start even if no statement is defined a.k.a., LS proofs from Lapidot-Shamir [LS90]). In this paper we show an improved OR-composition technique for Sigma-protocols, that requires only one statement to be fixed when the proof starts, while the other statement can be defined in the last round. This seemingly weaker property is sufficient for the applications, where typically one of the theorems is fixed before the proof starts. Concretely, we show how our new OR-composition technique can directly improve the round complexity of the efficient perfect quasi-polynomial time simulatable argument system of Pass [Pass03] (from four to three rounds) and of efficient resettable WI arguments (from five to four rounds).

This paper presents a novel unifying framework for electronic voting in the universal composability model that includes a property which is new to universal composability but well-known to voting systems: universal verifiability. Additionally, we propose three new techniques for secure electronic voting and prove their security and universal verifiability in the universal composability framework. 1. A tally-hiding voting system, in which the tally that is released consists of only the winner without the vote count. Our proposal builds on a novel solution to the millionaire problem which is of independent interest. 2. A self-tallying vote, in which the tally can be calculated by any observer as soon as the last vote has been cast --- but before this happens, no information about the tally is leaked. 3. Authentication of voting credentials, which is a new approach for electronic voting systems based on anonymous credentials. In this approach, the vote authenticates the credential so that it cannot afterwards be used for any other purpose but to cast that vote. We propose a practical voting system that instantiates this high-level concept.

We present new algorithm-substitution attacks (ASAs) on symmetric encryption that improve over prior ones in two ways. First, while prior attacks only broke a sub-class of randomized schemes having a property called coin injectivity, our attacks break ALL randomized schemes. Second, while prior attacks are stateful, ours are stateless, achieving a notion of strong undetectability that we formalize. Together this shows that ASAs are an even more dangerous and powerful mass surveillance method than previously thought. Our work serves to increase awareness about what is possible with ASAs and to spur the search for deterrents and counter-measures.

A fair distributed protocol ensures that dishonest parties have no advantage over honest parties in learning their protocol’s output. This is a desirable property, as honest parties are more reluctant to participate in an (unfair) protocol in which cheaters learn their outputs while the honest parties waste their time and computation resources. But what makes fairness an even more intriguing topic is Cleve’s seminal result [STOC’86], which proves that it is impossible to achieve in the presence of dishonest majorities. Cleve’s result ignited a quest for more relaxed, yet meaningful definitions of fairness, with numerous works suggesting such relaxations and protocols satisfying them. A common pattern in these works, however, is that they only treat the case of non-reactive computation--i.e., distributed computation of “one-shot” (stateless) functions, in which parties give inputs strictly before any output is computed. Yet, many natural cryptographic tasks are of a reactive (stateful) nature, where parties provide inputs and receive outputs several times during the course of the computation. This is the case, for example, when computing multi-stage auctions or emulating a virtual stock-exchange market, or even when computing basic cryptographic tasks such as commitments and secret sharing. In this work we introduce the first notion of fairness tailored to reactive distributed computation, which can be realized in the presence of dishonest majorities. Our definition builds on the recently suggested utility-based fairness notion (for non-reactive functions) by Garay, Katz, Tackmann and Zikas [PODC’15], which, informally, defines the utility of an adversary who wants to break fairness and uses it as a measure of a protocol’s success in satisfying the property. Similarly to the non-reactive notion, our definition enjoys the advantage of offering a comparative notion of fairness for reactive functions, inducing a partial order on protocols with respect to fairness. We then turn to the question of finding protocols that restrict the adversary’s utility. We provide, for each parameter choice of the adversary’s utility, a protocol for fair and reactive two-party computation, and prove the optimality of this protocol for one (natural) class of parameter values and (non-tight) lower bounds for all remaining values. Our study shows that achieving fairness in the reactive setting is more complex than in the much-studied case of one-shot functions. For example, in contrast to the non-reactive case, (a) increasing the number of rounds used for reconstructing the output can lead to improved fairness, and (b) the minimal number or rounds required in the reconstruction depends on the exact values of the adversary’s utility.

Classical fault attacks such as Differential Fault Analysis~(DFA) as well as biased fault attacks such as the Differential Fault Intensity Analysis~(DFIA) have been a major threat to cryptosystems in recent times. DFA uses pairs of fault-free and faulty ciphertexts to recover the secret key. DFIA, on the other hand, combines principles of side channel analysis and fault attacks to try and extract the key using faulty ciphertexts only. Till date, no effective countermeasure that can thwart both DFA as well as DFIA based attacks has been reported in the literature to the best of our knowledge. In particular, traditional redundancy based countermeasures that assume uniform fault distribution are found to be vulnerable against DFIA due to its use of biased fault models. In this work, we propose a novel generic countermeasure strategy that combines the principles of redundancy with that of fault space transformation to achieve security against both DFA and DFIA based attacks on AES-like block ciphers. As a case study, we have applied our proposed technique to to obtain temporal and spatial redundancy based countermeasures for AES-128, and have evaluated their security against both DFA and DFIA via practical experiments on a SASEBO-GII board. Results show that our proposed countermeasure makes it practically infeasible to obtain a single instance of successful fault injection, even in the presence of biased fault models.

The GHS attack is known to solve discrete logarithm problems (DLP) in the Jacobian of a curve C_0 defined over the d degree extension field k_d of k:=GF(q) by mapping it to the DLP in the Jacobian of a covering curve C of C_0 over k. Recently, classifications for all elliptic curves and hyperelliptic curves C_0/k_d of genus 2,3 which possess (2,...,2)-covering C/k of P^1 were shown under an isogeny condition (i.e. when g(C) = d * g(C_0)). This paper presents a systematic classification procedure for hyperelliptic curves in the odd characteristic case. In particular, we show a complete classification of elliptic curves C_0 over k_d which have (2,...,2)-covering C/k of P^1 for d=2,3,5,7. It has been reported by Diem that the GHS attack fails for elliptic curves C_0 over odd characteristic definition field k_d with prime extension degree d greater than or equal to 11 since g(C) become very large. Therefore, for elliptic curves over k_d with prime extension degree d, it is sufficient to analyze cases of d=2,3,5,7. As a result, a complete list of all elliptic curves C_0/k which possess (2,...,2)-covering C/k of P^1 thus are subjected to the GHS attack with odd characteristic and prime extension degree d is obtained.

Abstract: This work defines the security intelligence of a system based on secure multi-party computation in terms of correctness, fairness, rationality, trust, honesty, transparency, accountability, reliability, consistency, confidentiality, data integrity, non-repudiation, authentication, authorization, correct identification, privacy, safety and audit. It defines the security intelligence of a system comprehensively with a novel concept of collective intelligence. The cryptographic notion of security is applied to assess, analyze and mitigate the risks of bio-terrorism today. The definition of bioterrorism has been changed in terms of information security. This work also tries to resolve the conflict between the security intelligence and business intelligence in the context of bio-terrorism and highlights the new cryptographic challenges. Keywords: Security intelligence, Threat analytics, Business intelligence, Cross border bio-terrorism, Secure multi-party computation, Applied cryptography.

D. Davies and S. Murphy found that there are at most 660 different probability distributions on the output from any three adjacent S-boxes after 16 rounds of DES [1]. In this paper it is shown that there are only 72 different distributions for S-boxes 4, 5 and 6. The distributions from S-box triplets are linearly dependent and the dependencies are described. E.g. there are only 13 linearly independent distributions for S-boxes 4, 5 and 6. A coset representation of DES S-boxes which reveals their hidden linearity is studied. That may be used in algebraic attacks. S-box 4 can be represented by significantly fewer cosets than the other S-boxes and therefore has more linearity. Open cryptanalytic problems are stated. [1] D. Davies and S. Murphy, "Pairs and Triplets of DES S-boxes", Journal of Crypt. vol. 8(1995), pp. 1--25

Hill is a classical cipher which is generally believed to be resistant against ciphertext-only attack. In this paper, by using a divide-and-conquer technique, it is first shown that Hill with d*d key matrix over Z_26 can be broken with computational complexity of O(d26^d), for the English language. This is much less than the only publicly known attack, i.e., the brute-force with complexity of O(d^3(26)^(d^2)). Then by using the Chinese Remainder Theorem, it is shown that the computational complexity of the proposed attack can be reduced to O(d13^d). Using an information-theoretic approach, supported by extensive simulation results, it is shown that the minimum ciphertext length required for a successful attack increases by a factor of about 7 and 9.8, respectively for these two attacks in comparison with the brute-force attack. This is the only serious attack on Hill since its invention in 1929.

This paper shows how scalar blinding can provide protection against side channel attacks when performing elliptic curve operations with modest cost, even if the characteristic of the field has a sparse representation. This may indicate that, for hardware implementations, random primes might not have as large of an advantage over special primes as previously claimed.

We analyse and dene practical requirements in white-box attack environment, and then propose secure and eective cryptographic constructions combining WBC primitive and standard block cipher, pro- viding security and reasonable performance. The proposed design also delivers great eectiveness in the commercial development of crypto- graphic systems, transforming the existing cryptographic libraries secure in the black-box model to those secure in the white-box model. Further- more, the suggested architecture potentially gives a novel direction of the design of WBC primitives.

Binary eld multiplication is the most fundamental building block of binary eld Elliptic Curve Cryptography (ECC) and Galois/Counter Mode (GCM). Both bit-wise scanning and Look-Up Table (LUT) based methods are commonly used for binary eld multiplication. In terms of Side Channel Attack (SCA), bit-wise scanning exploits insecure branch operations which leaks information in a form of timing and power consumption. On the other hands, LUT based method is regarded as a relatively secure approach because LUT access can be conducted in a regular and atomic form. This ensures a constant time solution as well. In this paper, we conduct the SCA on the LUT based binary eld multiplication. The attack exploits the horizontal Correlation Power Analysis (CPA) on weights of LUT. We identify the operand with only a power trace of binary eld multiplication. In order to prevent SCA, we also suggest a mask based binary eld multiplication which ensures a regular and constant time solution without LUT and branch statements.

We present the first stateless construction of a cryptographically-secure Physical Unclonable Function. Our construct requires no non-volatile (permanent) storage, secure or otherwise, and its computational security can be clearly reduced to the hardness of Learning Parity with Noise (LPN) in the random oracle model. The construction is ``stateless,'' because there is \emph{no} information stored between subsequent queries, which mitigates attacks against the PUF via tampering. Moreover, our stateless construction corresponds to a PUF whose outputs are free of noise because of internal error-correcting capability, which enables a host of applications beyond authentication. We describe the construction, provide a proof of computational security, and present experimental evidence that this construct is viable.

Katz and Ostrovsky (Crypto 2004) proved that five rounds are necessary for stand-alone general black-box constructions of secure two-party protocols and at least four rounds are necessary if only one party needs to receive the output. Recently, Ostrovsky, Richelson and Scafuro (Crypto 2015) proved optimality of this result by showing how to realize stand-alone, secure two-party computation under general assumptions (with black-box proof of security) in four rounds where only one party receives the output, and an extension to five rounds where both parties receive the output. In this paper we study the question of what security is achievable for stand-alone two-party protocols within four rounds and show the following results: 1. A 4-round two-party protocol for coin-tossing that achieves 1/p-security (i.e. simulation fails with probability at most 1/p+negl), in the presence of malicious corruptions. 2. A 4-round two-party protocol for general functionalities where both parties receive the output, that achieves 1/p-security and privacy in the presence of malicious adversaries corrupting one of the parties, and full security in the presence of non-aborting malicious adversaries corrupting the other party. 3. A 3-round oblivious-transfer protocol that achieves 1/p-security against arbitrary malicious senders, while simultaneously guaranteeing a meaningful notion of privacy against malicious corruptions of either party. 4. Finally, we show that the simulation-based security guarantees for our 3-round protocols are optimal by proving that 1/p-simulation security is impossible to achieve against both parties in three rounds or less when requiring some minimal guarantees on the privacy of their inputs.

Selfish mining, originally discovered by Eyal et al.~\cite{selfish_mining}, is a well-known attack where a selfish miner, under certain conditions, can gain a disproportionate share of reward by deviating from the honest behavior. In this paper, we expand the mining strategy space to include novel ``stubborn'' strategies that, for a large range of parameters, earn the miner more revenue. Consequently, we show that the selfish mining attack is not (in general) optimal. Further, we show how a miner can further amplify its gain by non-trivially composing mining attacks with network-level eclipse attacks. We show, surprisingly, that given the attacker's best strategy, in some cases victims of an eclipse attack can actually benefit from being eclipsed!

Side-channel attacks are powerful techniques to attack implementations of cryptographic algorithms by observing its physical parameters such as power consumption and electromagnetic radiation that are modulated by the secret state. Most side-channel attacks are of divide-and-conquer nature, that is, they yield a ranked list of secret key chunks, e.g., the subkey bytes in AES. The problem of the key recovery is then to find the correct combined key. An optimal key enumeration algorithm (OKEA) was proposed by Charvillon et al at SAC'12. Given the ranked key chunks together with their probabilities, this algorithm outputs the full combined keys in the optimal order -- from more likely to less likely ones. OKEA uses plenty of memory by its nature though, which limits its practical efficiency. Especially in the cases where the side-channel traces are noisy, the memory and running time requirements to find the right key can be prohibitively high. To tackle this problem, we propose a score-based key enumeration algorithm (SKEA). Though it is suboptimal in terms of the output order of cadidate combined keys, SKEA's memory and running time requirements are more practical than those of OKEA. We verify the advantage at the example of a DPA attack on an 8-bit embedded software implementation of AES-128. We vary the number of traces available to the adversary and report a significant increase in the success rate of the key recovery due to SKEA when compared to OKEA, within practical limitations on time and memory. We also compare SKEA to the probabilistic key enumeration algorithm (PKEA) by Meier and Staffelbach and show its practical superiority in this case. SKEA is efficiently parallelizable. We propose a high-performance solution for the entire conquer stage of side-channel attacks that includes SKEA and the subsequent full key testing, using AES-NI on Haswell Intel CPUs.

ECDSA is one of the most important public-key signature scheme, however it is vulnerable to lattice attack once a few bits of the nonces are leaked. To protect Elliptic Curve Cryptography (ECC) against Simple Power Analysis, many countermeasures have been proposed. Doubling and Additions of points on the given elliptic curve require several additions and multiplications in the base field and this number is not the same for the two operations. The idea of the atomicity protection is to use a fixed pattern, i.e. a small number of instructions and rewrite the two basic operations of ECC using this pattern. Dummy operations are introduced so that the different elliptic curve operations might be written with the same atomic pattern. In an adversary point of view, the attacker only sees a succession of patterns and is no longer able to distinguish which one corresponds to addition and doubling. Chevallier-Mames, Ciet and Joye were the first to introduce such countermeasure. In this paper, we are interested in studying this countermeasure and we show a new vulnerability since the ECDSA implementation succumbs now to C Safe-Error attacks. Then, we propose an effective solution to prevent against C Safe-Error attacks when using the Side-Channel Atomicity. The dummy operations are used in such a way that if a fault is introduced on one of them, it can be detected. Finally, our countermeasure method is generic, meaning that it can be adapted to all formulae. We apply our methods to different formulae presented for side-channel Atomicity.

The main problem in designing effective code obfuscation is to guarantee security. State of the art obfuscation techniques rely on an unproven concept of security, and therefore are not regarded as provably secure. In this paper, we undertake a theoretical investigation of code obfuscation security based on Kolmogorov complexity and algorithmic mutual information. We introduce a new definition of code obfuscation that requires the algorithmic mutual information between a code and its obfuscated version to be minimal, allowing for controlled amount of information to be leaked to an adversary. We argue that our definition avoids the impossibility results of Barak et al. and is more advantageous then obfuscation indistinguishability definition in the sense it is more intuitive, and is algorithmic rather than probabilistic.

In a selective opening attack (SOA) on an encryption scheme, the adversary is given a collection of ciphertexts and selectively chooses to see some subset of them ``opened'', meaning that the messages and the encryption randomness are revealed to her. A scheme is SOA secure if the data contained in the unopened ciphertexts remains hidden. A fundamental question is whether every CPA secure scheme is necessarily also SOA secure. The work of Bellare et al. (EUROCRYPT '12) gives a partial negative answer by showing that some CPA secure schemes do not satisfy a simulation-based definition of SOA security called SIM-SOA. However, until now, it remained possible that every CPA secure scheme satisfies an indistinguishability-based definition of SOA security called IND-SOA. In this work, we resolve the above question in the negative and construct a highly contrived encryption scheme which is CPA (and even CCA) secure but is not IND-SOA secure. In fact, it is broken in a very obvious sense by a selective opening attack as follows. A random value is secret-shared via Shamir's scheme so that any t out of n shares reveal no information about the shared value. The n shares are individually encrypted under a common public key and the n resulting ciphertexts are given to the adversary who selectively chooses to see t of the ciphertexts opened. Counter-intuitively, this suffices for the adversary to completely recover the shared value. Our contrived scheme relies on strong assumptions: public-coin differing inputs obfuscation and a certain type of correlation intractable hash functions. We also extend our negative result to the setting of SOA attacks with key opening (IND-SOA-K) where the adversary is given a collection of ciphertexts under different public keys and selectively chooses to see some subset of the secret keys.

Garg et al. [FOCS 2013] showed how to construct indistinguishability obfuscation (iO) from a restriction of cryptographic multilinear maps called Multilinear Jigsaw Puzzles. Since then, a number of other works have shown constructions and security analyses for iO from different abstractions of multilinear maps. However, the converse question --- whether some form of multilinear maps follows from iO --- has remained largely open. We offer an abstraction of multilinear maps called Polynomial Jigsaw Puzzles, and show that iO for circuits implies Polynomial Jigsaw Puzzles. This implication is unconditional: no additional assumptions, such as one-way functions, are needed. Furthermore, we show that this abstraction of Polynomial Jigsaw Puzzles is sufficient to construct iO for NC1, thus showing a near-equivalence of these notions.

In this paper we introduce a sequence of discrete Fourier transforms and define new versions of bent functions, which we shall call (weak, strong) octa/hexa/2^k-bent functions. We investigate relationships between these classes and completely characterize the octabent and hexabent functions in terms of bent functions.

Pseudorandom number generators (PRNGs) are very important for EPC Class 1 Generation 2 (EPC C1 G2) Radio Frequency Identification (RFID) systems. A PRNG is able to provide a 16-bit random number that is used in many commands of the EPC C1 G2 standard, and it can also be used in future security extensions of the EPC C1 G2 standard, such as mutual authentication protocols between the readers and tags. In this paper, we investigate efficient ASIC hardware implementations of Warbler (a lightweight PRNG), and demonstrate that Warbler can meet the area and power consumption requirements in passive RFID systems. Warbler is built upon three nonlinear feedback shift registers (NLFSRs) and four WG-5 transformation modules. We employ two design options to implement Warbler and three different compilation methods to further optimize the area, maximum operating frequency, and power consumption. We can achieve an area of 498 GEs after the place and route phase in a CMOS 65nm ASIC, with a maximum frequency of 1430 MHz and a total power consumption of 1.239uW at 100 KHz. Accordingly, an area of 534 GEs after the place and route phase, with a maximum frequency of 250 MHz and a total power consumption of 0.296 uW at 100 KHz can be obtained in a CMOS 130nm ASIC. Our results show that the LFSR counter based design is better than the binary counter-based one in terms of area and power consumption. In addition, we show that the areas of WG-5 transformation look-up tables depend on the specific decimation values.

Password vaults are increasingly popular applications that store multiple passwords encrypted under a single master password that the user memorizes. A password vault can greatly reduce the burden on a user of remembering passwords, but introduces a single point of failure. An attacker that obtains a user’s encrypted vault can mount offline brute-force attacks and, if successful, compromise all of the passwords in the vault. In this paper, we investigate the construction of encrypted vaults that resist such offline cracking attacks and force attackers instead to mount online attacks. Our contributions are as follows. We present an attack and supporting analysis showing that a previous design for cracking-resistant vaults—the only one of which we are aware—actually degrades security relative to conventional password-based approaches. We then introduce a new type of secure encoding scheme that we call a natural language encoder (NLE). An NLE permits the construction of vaults which, when decrypted with the wrong master password, produce plausible-looking decoy passwords. We show how to build NLEs using existing tools from natural language processing, such as n-gram models and probabilistic context-free grammars, and evaluate their ability to generate plausible decoys. Finally, we present, implement, and evaluate a full, NLE-based cracking-resistant vault system called NoCrack.

This paper describes a new multiplication algorithm, particularly suited to lightweight microprocessors when one of the operands is known in advance. The method uses backtracking to find a multiplicationfriendly encoding of the operand known in advance. A 68HC05 microprocessor implementation shows that the new algorithm indeed yields a twofold speed improvement over classical multiplication for 128-byte numbers.

Fault and power attacks are two common ways of extracting secrets from tamper-resistant chips. Although several protections have been proposed to thwart these attacks, resistant designs usually claim significant area or speed overheads. Furthermore, circuit-level countermeasures are usually not reconfigurable at runtime. This paper exploits the AES’ algorithmic features to propose low-cost and low-latency protections. We provide Verilog and FPGA implementation details. Using our design, real-life applications can be configured during runtime to meet the user’s needs and the system’s constraints.

Modular multiplication and modular reduction are the atomic constituents of most public-key cryptosystems. Amongst the numerous algorithms for performing these operations, a particularly elegant method was proposed by Barrett. This method builds the operation $a \bmod b$ from bit shifts, multiplications and additions in $\mathbb{Z}$. This allows building modular reduction at very marginal code or silicon costs by leveraging existing hardware or software multipliers. This paper presents a method allowing doubling the speed of Barrett’s algorithm by using specific composite moduli. This is particularly useful for lightweight devices where such an optimization can make a difference in terms of power consumption, cost and processing time. The generation of composite moduli with a predetermined portion is a well-known technique and the use of such moduli is considered, in statu scientae, as safe as using randomly generated composite moduli.

We examine a FlipIt game in which there are multiple resources which a monolithic attacker is trying to compromise. This extension to FlipIt was considered in a paper in GameSec 2014, and was there called FlipThem. Our analysis of such a situation is focused on the situation where the attacker's goal is to compromise a threshold of the resources. We use our game theoretic model to enable a defender to choose the correct configuration of resources (number of resources and the threshold) so as to ensure that it makes no sense for a rational adversary to try to attack the system. This selection is made on the basis of the relative costs of the attacker and the defender.

COFFE is a hash-based authenticated encryption scheme. In the original paper, it was claimed to have IND-CPA security and also ciphertext integrity even in nonce-misuse scenario. In this paper, we analyse the security of COFFE. Our attack shows that even under the assumption that the primitive hash function is ideal, a valid ciphertext can be forged with 2 enquiries with success probability close to 1. The motivation of the attack is to find a collision on the input of each of the hash calls in the COFFE instantiation. It can be done in two ways. The first way is by modifying nonce and last message block size. Chosen appropriately, we can ensure two COFFE instantiations with different nonce and different last message block size can have exactly the same intermediate state value. This hence leads to a valid ciphertext to be generated. Another way is by considering two different COFFE instantiations with different message block size despite same key. In this case, we will use the existence of consecutive zero in the binary representation the initial value to achieve identical intermediate state value on two different COFFE instantiations. Having the state collisions, the forgery attack is then conducted by choosing two different plaintexts with appropriate nonce and tag size to query. Having this fact, without knowing the secret key, we can then validly encrypt another plaintext with probability equal to 1.

Secure two-party computation allows two mutually distrusting parties to compute a function together, without revealing their secret inputs to each other. Traditionally, the security properties desired in this context, and the corresponding security proofs, are based on a notion of simulation, which can be symbolic or computational. Either way, the proofs of security are intricate, requiring first to find a simulator, and then to prove a notion of indistinguishability. Furthermore, even for classic protocols such as Yao's (based on garbled circuits and oblivious transfer), we do not have adequate symbolic models for cryptographic primitives and protocol roles, that can form the basis for automated security proofs. We therefore propose new models in applied pi-calculus in order to address these gaps. Our contributions, formulated in the context of Yao's protocol, include: - an equational theory for specifying the primitives of garbled computation and oblivious transfer; - process specifications for the roles of the two parties in Yao's protocol; - definitions of security that are more clear and direct: result integrity, input agreement (both based on correspondence assertions) and input privacy (based on observational equivalence). We put these models together and illustrate their use with ProVerif, providing a first automated verification of security for Yao's two-party computation protocol.

This paper presents new speed records for arithmetic on a large family of elliptic curves with cofactor 3: specifically, 8.77M per bit for 256-bit variable-base single-scalar multiplication when curve parameters are chosen properly. This is faster than the best results known for cofactor 1, showing for the first time that points of order 3 are useful for performance and narrowing the gap to the speeds of curves with cofactor 4.

We provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs. This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction. We provide two distinct, but closely related constructions and show that multilinear analogues of the DDH assumption hold for them. Our first construction is symmetric and comes with a \kappa-linear map e : G^\kappa \to G_T for prime-order groups G and G_T . To establish the hardness of the \kappa-linear DDH problem, we rely on the existence of a base group for which the \kappa-strong DDH assumption holds. Our second construction is for the asymmetric setting, where e : G_1 \times \dots \times G_\kappa \to G_T for a collection of \kappa + 1 prime-order groups G_i and G_T , and relies only on the 1-strong DDH assumption in its base group. In both constructions the linearity \kappa can be set to any arbitrary but a priori fixed polynomial value in the security parameter. We rely on a number of powerful tools in our constructions: probabilistic indistinguishability obfuscation, dual-mode NIZK proof systems (with perfect soundness, witness indistinguishability and zero knowledge), and additively homomorphic encryption for the group Z^+_N . At a high level, we enable “bootstrapping” multilinear assumptions from their simpler counterparts in standard cryptographic groups, and show the equivalence of PIO and multilinear maps under the existence of the aforementioned primitives.

In this paper we present a very simple scheme for strengthening the conventional product-sum type PKC which has been long considered insecure against the various attacks such as the secret key attack, LLL attack, etc. We show that with the proposed strengthening scheme, the securities of the conventional product-sum type PKC's can be much improved.

The Modular Inversion Hidden Number Problem (MIHNP) was introduced by Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001 (BHH'01). They provided two heuristics - in Method I, two-third of the output bits are required to solve the problem, whereas the more efficient heuristic (Method II) requires only one-third of the bits of the output. After more than a decade, here we identify that the claim in Method II is actually not correct and a detailed calculation justifies that this method too requires two-third of the bits of the output, contrary to the claim in BHH'01. Further, we show that using the same relations as in Boneh et al., one can reconstruct the lattice so that the problem can be heuristically solved by the knowledge of five-eighth of the bits. Finally, we could accumulate additional relations to solve the problem heuristically with only half of the output bits in asymptotic sense. Experimental results support the claim corresponding to our heuristics.

Arithmetic Walsh transform(AWT) of Boolean function caught our attention due to their arithmetic analogs of Walsh-Hadamard transform(WHT) recently. We present new results on AWT in this paper. Firstly we characterize the existence of linear structure of Boolean functions in terms of AWT. Secondly we show that the relation between AWT and WHT of a balanced Boolean function with a linear structure 1^n is sectionally linear. Carlet and Klapper's recent work showed that the AWT of a diagonal Boolean function can be expressed in terms of the AWT of a diagonal Boolean function of algebraic degree at most 3 in a larger number of variables.However their proof is right only when c has even weight.We complement their proof by considering the case of c with odd weight.

In this work, we construct an adaptively secure functional encryption for Turing machines scheme, based on indistinguishability obfuscation for circuits. Our work places no restrictions on the types of Turing machines that can be associated with each secret key, in the sense that the Turing machines can accept inputs of unbounded length, and there is no limit to the description size or the space complexity of the Turing machines. Prior to our work, only special cases of this result were known, or stronger assumptions were required. More specifically, previous work (implicitly) achieved selectively secure FE for Turing machines with a-priori bounded input based on indistinguishability obfuscation (STOC 2015), or achieved FE for general Turing machines only based on knowledge-type assumptions such as public-coin differing-inputs obfuscation (TCC 2015). A consequence of our result is the first constructions of succinct adaptively secure garbling schemes (even for circuits) in the standard model. Prior succinct garbling schemes (even for circuits) were only known to be adaptively secure in the random oracle model.

Diffusion layers are critical components of symmetric ciphers. MDS matrices are diffusion layers of maximal branch number which have been used in various symmetric ciphers. In this article, we examine decomposition of cyclic matrices from mathematical viewpoint and based on that, we present new cyclic MDS matrices. From the aspect of implementation, the proposed matrices have lower implementation costs both in software and hardware, compared to what is presented in cryptographic literature, up to our knowledge.

Recently Sarkar (DCC 2014) has proposed a new attack on small decryption exponent when RSA Modulus is of the form N=p^rq for r>=2. This variant is known as Prime Power RSA. The work of Sarkar improves the result of May (PKC 2004) when r<=5. In this paper, we improve the existing results for r=3,4. We also study partial key exposure attack on Prime Power RSA. Our result improves the work of May (PKC 2004) for certain parameters.

An oracle chooses a function f from the set of n bits strings to itself, which is either a randomly chosen permutation or a randomly chosen function. When queried by an n-bit string w, the oracle computes f(w), truncates the m last bits, and returns only the first n-m bits of f(w). How many queries does a querying adversary need to submit in order to distinguish the truncated permutation from a random function? In 1998, Hall et al. showed an algorithm for determining (with high probability) whether or not f is a permutation, using O ( 2^((m+n)/2) ) queries. They also showed that if m < n/7, a smaller number of queries will not suffice. For m > n/7, their method gives a weaker bound. In this manuscript, we show how a modification of the method used by Hall et al. can solve the porblem completely. It extends the result to essentially every m, showing that Omega ( 2^((m+n)/2) ) queries are needed to get a non-negligible distinguishing advantage. We recently became aware that a better bound for the distinguishing advantage, for every m<n, follows from a result of Stam published, in a different context, already in 1978.

In a seminal paper, Dolev et al. (STOC'91) introduced the notion of non-malleable encryption (NM-CPA). This notion is very intriguing since it suffices for many applications of chosen-ciphertext secure encryption (IND-CCA), and, yet, can be generically built from semantically secure (IND-CPA) encryption, as was shown in the seminal works by Pass et al. (CRYPTO'06) and by Choi et al. (TCC'08), the latter of which provided a black-box construction. In this paper we investigate three questions related to NM-CPA security: - Can the rate of the construction by Choi et al. of NM-CPA from IND-CPA be improved? - Is it possible to achieve multi-bit NM-CPA security more efficiently from a single-bit NM-CPA scheme than from IND-CPA? - Is there a notion stronger than NM-CPA that has natural applications and can be achieved from IND-CPA security? We answer all three questions in the positive. First, we improve the rate in the construction of Choi et al. by a factor O(k), where k is the security parameter. Still, encrypting a message of size O(k) would require ciphertext and keys of size O(k^2) times that of the IND-CPA scheme, even in our improved scheme. Therefore, we show a more efficient domain extension technique for building a k-bit NM-CPA scheme from a single-bit NM-CPA scheme with keys and ciphertext of size O(k) times that of the NM-CPA one-bit scheme. To achieve our goal, we define and construct a novel type of continuous non-malleable code (NMC), called secret-state NMC, as we show that standard continuous NMCs are not enough for the natural "encode-then-encrypt-bit-by-bit" approach to work. Finally, we introduce a new security notion for public-key encryption (PKE) that we dub non-malleability under (chosen-ciphertext) self-destruct attacks (NM-SDA). After showing that NM-SDA is a strict strengthening of NM-CPA and allows for more applications, we nevertheless show that both of our results---(faster) construction from IND-CPA and domain extension from one-bit scheme---also hold for our stronger NM-SDA security. In particular, the notions of IND-CPA, NM-CPA, and NM-SDA security are all equivalent, lying (plausibly, strictly?) below IND-CCA security.

A homomorphic public key cryptography scheme based on the Boolean Satisfiability Problem (SAT) is proposed. The public key is a SAT formula satisfied by the private key. The probabilistic encryption algorithm generates random Boolean functions, which are implied to be false by the public key. Adding the message bits to them yields the cipher functions. A variant of Blum's Hamilton cycle zero-knowledge proof, adapted to SAT, is used to provide an identification and, via a Fiat-Shamir heuristic, a signature scheme. These are conceptually independent from the encryption scheme.

The Fiat-Shamir (FS) transform uses a hash function to generate, without any further overhead, non-interactive zero-knowledge (NIZK) argument systems from constant-round public-coin honest-verifier zero-knowledge (public-coin HVZK) proof systems. In the proof of zero knowledge, the hash function is modeled as a programmable random oracle (PRO). In TCC 2015, Lindell embarked on the challenging task of obtaining a similar transform with improved heuristic security. Lindell showed that, for several interesting and practical languages, there exists an efficient transform in the non-programmable random oracle (NPRO) model that also uses a common reference string (CRS). A major contribution of Lindell's transform is that zero knowledge is proved without random oracles and this is an important step towards achieving efficient NIZK arguments in the CRS model without random oracles. In this work, we analyze the efficiency and generality of Lindell's transform and notice a significant gap when compared with the FS transform. We then propose a new transform that aims at filling this gap. Indeed our transform is almost as efficient as the FS transform and can be applied to a broad class of public-coin HVZK proof systems. Our transform requires a CRS and an NPRO in the proof of soundness, similarly to Lindell's transform.

We show the following reductions from the learning with errors problem (LWE) to the learning with rounding problem (LWR): (1) Learning the secret and (2) distinguishing samples from random strings is at least as hard for LWR as it is for LWE for efficient algorithms if the number of samples is no larger than O(q/Bp), where q is the LWR modulus, p is the rounding modulus and the noise is sampled from any distribution supported over the set {-B,...,B}. Our second result generalizes a theorem of Alwen, Krenn, Pietrzak and Wichs (CRYPTO 2013) and provides an alternate proof of it. Unlike Alwen et al., we do not impose any number theoretic restrictions on the modulus q. The first result also extends to variants of LWR and LWE over polynomial rings. As additional results we show that (3) distinguishing any number of LWR samples from random strings is of equivalent hardness to LWE whose noise distribution is uniform over the integers in the range [-q/2p,...,q/2p) provided q is a multiple of p and (4) the "noise flooding" technique for converting faulty LWE noise to a discrete Gaussian distribution can be applied whenever q = \Omega(B\sqrt{m}). All our reductions preserve sample complexity and have time complexity at most polynomial in q, the dimension, and the number of samples.

As part of the revelations about the NSA activities, the notion of interdiction has become known to the public: the interception of deliveries to manipulate hardware in a way that backdoors are introduced. Manipulations can occur on the firmware or at hardware level. With respect to hardware, FPGAs are particular interesting targets as they can be altered by manipulating the corresponding bitstream which configures the device. In this paper, we demonstrate the first successful real-world FPGA hardware Trojan insertion into a commercial product. On the target device, a FIPS-140-2 level 2 certified USB flash drive from Kingston, the user data is encrypted using AES-256 in XTS mode, and the encryption/decryption is processed by an off-the-shelf SRAM-based FPGA. Our investigation required two reverse-engineering steps, related to the proprietary FPGA bitstream and to the firmware of the underlying ARM CPU. In our Trojan insertion scenario the targeted USB flash drive is intercepted before being delivered to the victim. The physical Trojan insertion requires the manipulation of the SPI flash memory content, which contains the FPGA bitstream as well as the ARM CPU code. The FPGA bitstream manipulation alters the exploited AES-256 algorithm in a way that it turns into a linear function which can be broken with 32 known plaintext-ciphertext pairs. After the manipulated USB flash drive has been used by the victim, the attacker is able to obtain all user data from the ciphertexts. Our work indeed highlights the security risks and especially the practical relevance of bitstream modification attacks that became realistic due to FPGA bitstream manipulations.

Dual EC is an algorithm to compute pseudorandom numbers starting from some random input. Dual EC was standardized by NIST, ANSI, and ISO among other algorithms to generate pseudorandom numbers. For a long time this algorithm was considered suspicious -- the entity designing the algorithm could have easily chosen the parameters in such a way that it can predict all outputs -- and on top of that it is much slower than the alternatives and the numbers it provides are more biased, i.e., not random. The Snowden revelations, and in particular reports on Project Bullrun and the SIGINT Enabling Project, have indicated that Dual EC was part of a systematic effort by NSA to subvert standards. This paper traces the history of Dual EC including some suspicious changes to the standard, explains how the back door works in real-life applications, and explores the standardization and patent ecosystem in which the standardized back door stayed under the radar.

Universal hash functions (UHFs) have been extensively used in the design of cryptographic schemes. If we consider the related-key attack (RKA) against these UHF-based schemes, some of them may not be secure, especially those using the key of UHF as a part of the whole key of scheme, due to the weakness of UHF in the RKA setting. In order to solve the issue, we propose a new concept of related-key almost universal hash function, which is a natural extension to almost universal hash function in the RKA setting. We define related-key almost universal (RKA-AU) hash function and related-key almost XOR universal (RKA-AXU) hash function. However almost all the existing UHFs do not satisfy the new definitions. We construct one fixed-input-length universal hash functions named RH1 and two variable-input-length universal hash functions named RH2, RH3. We show that RH1 and RH2 are both RKA-AXU, and RH3 is RKA-AU for the RKD set $\Phi^\oplus$. Furthermore, RH1, RH2 and RH3 are nearly as efficient as previous similar constructions. RKA-AU (RKA-AXU) hash functions can be used as components in the related-key secure cryptographic schemes. If we replace the universal hash functions in the schemes with our corresponding constructions, the problems about related-key attack can be solved for some RKD sets. More specifically, we give four concrete applications of RKA-AU and RKA-AXU in related-key secure message authentication codes and tweakable block ciphers.

We initiate the study of a new functional signcryption primitive, by exploring sanitizable signatures over encrypted data. While previous solutions for sanitizable signatures require the sanitizer to know, in clear, the original message-signature pair in order to generate the new signature, we investigate the case where it should be hidden from the sanitizer and how this can be achieved with encryption. We call this primitive sanitizable signcryption, and argue that there are two options concerning what the sanitizer learns about the sanitized output: in semi-oblivious sanitizable signcryption schemes the sanitizer may get to know the sanitized message-signature pair, while fully oblivious sanitizable signcryption schemes even protect the output data. Depending on the application, either notion may be preferable. We give feasibility results for both settings by showing that semi-oblivious sanitizable signcryption schemes can be constructed by wraping a regular sanitizable signature scheme into a multi-input functional encryption scheme, such that functional decryption corresponds to the sanitization process. Remarkably, the multi-input functional encryption scheme cannot easily be transferred to a fully oblivious sanitizable signcryption version, so we give a restricted solution based on fully homomorphic encryption for this case. We stress that we see our contribution in directing the attention the question of sanitizable signcryption and show that solutions can be constructed in principle; it yet remains to &#64257;nd truly practical instantiations.

There are q^3 + q right PGL_2(\F_q)-cosets in the group PGL_2(\F_{q^2}). In this paper, we present a method of generating all the coset representatives, which runs in time \tilde{O}(q^3), thus achieves the optimal time complexity up to a constant factor. Our algorithm has applications in solving discrete logarithms and finding primitive elements in finite fields of small characteristic.

This paper proposes a compact and efficient GF(2^8) inversion circuit design based on a combination of non-redundant and redundant Galois Field (GF) arithmetic. The proposed design utilizes redundant GF representations, called Polynomial Ring Representation (PRR) and Redundantly Represented Basis (RRB), to implement GF(2^8) inversion using a tower field GF((2^4)^2). In addition to the redundant representations, we introduce a specific normal basis that makes it possible to map the former components for the 16th and 17th powers of input onto logic gates in an efficient manner. The latter components for GF(2^4) inversion and GF(2^4) multiplication are then implemented by PRR and RRB, respectively. The flexibility of the redundant representations provides efficient mappings from/to the GF(2^8). This paper also evaluates the efficacy of the proposed circuit by means of gate counts and logic synthesis with a 65 nm CMOS standard cell library and comparisons with conventional circuits, including those with tower fields GF(((2^2)^2)^2). Consequently, we show that the proposed circuit achieves approximately 40% higher efficiency in terms of area-time product than the conventional best GF(((2^2)^2)^2) circuit excluding isomorphic mappings. We also demonstrate that the proposed circuit achieves the best efficiency (i.e., area-time product) for an AES encryption S-Box circuit including isomorphic mappings.

Kalyna is an SPN-based block cipher that was selected during Ukrainian national public cryptographic competition (2007-2010), and its slight modification was approved as the new encryption standard of Ukraine (DSTU 7624:2014) in 2015. The cipher supports a block size and a key length of 128, 256 and 512 bits where the size of the key can be either double or equal to that of the block length. According to its designers, the cipher provides strength to several cryptanalytic methods after the fifth and sixth rounds of the 128-bit and 256-bit block versions, respectively. In this paper, we present a meet-in-the-middle attack on the 7-round reduced versions of Kalyna where the key size is double the block length. Our attack is based on the differential enumeration approach where we carefully deploy a four round distinguisher in the first four rounds to bypass the effect of the carry bits resulting from the pre-whitening modular key addition. We also exploit the linear relation between consecutive odd and even indexed round keys which enables us to attack seven rounds and recover all the round keys incrementally. The attack on Kalyna with 128-bit block has a data complexity of $2^{89}$ chosen plaintexts, time complexity of $2^{230.2}$ and a memory complexity of $2^{202.64}$. The data, time and memory complexities of our attack on Kalyna with 256-bit block are $2^{233}$, $2^{502.2}$ and $2^{170}$, respectively.

The encryption mode of the Tweakable Block Cipher (TBC) of the SCREAM Authenticated Cipher is implemented in the MSP430 microcontroller. Assembly language versions of the TBC are prepared using both precomputed tweak keys and tweak keys computed “on-the-fly.” Both versions are compared against published results for the assembly language version of SCREAM on the ATMEL AVR microcontroller, and against the C reference implementation in terms of performance and size. The assembly language version using precomputed tweak keys achieves a speedup of 1.7 and memory savings of 9 percent over the reported SCREAM implementation in the ATMEL AVR. The assembly language version using tweak keys computed “on-the-fly” achieves a speedup of 1.6 over the ATMEL AVR version while reducing memory usage by 15 percent.

Physically unclonable functions (PUFs) provide data that can be used for cryptographic purposes: on the one hand randomness for the initialization of random-number generators; on the other hand individual fingerprints for unique identification of specific hardware components. However, today's off-the-shelf personal computers advertise randomness and individual fingerprints only in the form of additional or dedicated hardware. This paper introduces a new set of tools to investigate whether intrinsic PUFs can be found in PC components that are not advertised as containing PUFs. In particular, this paper investigates AMD64 CPU registers as potential PUF sources in the operating-system kernel, the bootloader, and the system BIOS; investigates the CPU cache in the early boot stages; and investigates shared memory on Nvidia GPUs. This investigation found non-random non-fingerprinting behavior in several components but revealed usable PUFs in Nvidia GPUs.

In March, 2015 Gu Chunsheng proposed a candidate ideal multilinear map [eprint 2015/269]. An ideal multilinear map allows to perform as many multiplications as desired, while in k-multilinear maps like GGH [EC 2013] or CLT [CR2013, CR2015] one we canperform at most a predetermined number k of multiplications. In this note, we show that the extraction Multilinear Computational Diffie-Hellman problem (ext-MCDH) associated to Gu's map can be solved in polynomial-time: this candidate ideal multilinear map is insecure. We also give intuition on why we think that the two other ideal multilinear maps proposed by Gu in [eprint 2015/269] are not secure either.

In this paper, we survey the status of attacks on the ring and polynomial learning with errors problems (RLWE and PLWE). Recent work on the security of these problems [EHL, ELOS] gives rise to interesting questions about number fields. We extend these attacks and survey related open problems in number theory, including spectral distortion of an algebraic number and its relationship to Mahler measure, the monogenic property for the ring of integers of a number field, and the size of elements of small order modulo q.