In recent years, \emph{lattice-based} cryptography has been recognized for its many attractive properties, such as strong provable security guarantees and apparent resistance to quantum attacks, flexibility for realizing powerful tools like fully homomorphic encryption, and high asymptotic efficiency. Indeed, several works have demonstrated that for basic tasks like encryption and authentication, lattice-based primitives can have performance competitive with (or even surpassing) those based on classical mechanisms like RSA or Diffie-Hellman. However, there still has been relatively little work on developing lattice cryptography for deployment in \emph{real-world} cryptosystems and protocols. In this work we take a step toward that goal, by giving efficient and practical lattice-based protocols for key transport, encryption, and authenticated key exchange that are suitable as ``drop-in'' components for proposed Internet standards and other open protocols. The security of all our proposals is provably based (sometimes in the random-oracle model) on the well-studied ``learning with errors over rings'' problem, and hence on the conjectured worst-case hardness of problems on ideal lattices (against quantum algorithms). One of our main technical innovations (which may be of independent interest) is a simple, low-bandwidth \emph{reconciliation} technique that allows two parties who ``approximately agree'' on a secret value to reach \emph{exact} agreement, a setting common to essentially all lattice-based encryption schemes. Our technique reduces the ciphertext length of prior (already compact) encryption schemes nearly twofold, at essentially no cost.

The article proposes one-pass authenticated key establishment protocol in random oracles for Wireless Sensor Networks. Security of the protocol relies on Computational Diffie-Hellman Problem on Bilinear Pairings. In one-pass key establishment protocol, the initiator computes a session key and a related message. The key token is to be sent to the intended receiver using receiver’s public key and sender secret key. From the received key token the receiver compute the session key, which is the same as the one computed by the sender, using sender public key and receiver’s secret key. Because of low communication overhead, the scheme is better suited for Wireless Sensor Networks(WSNs) than the traditional key establishment protocol to establish the session key between two adjacent nodes.

The correctness in decrypting a ciphertext after some operations in the DGVH scheme depends heavily on the dimension of the secret key. In this paper we compute two bounds on the size of the secret key for the DGHV scheme to decrypt correctly a ciphertext after a fixed number of additions and a fixed number of multiplication. Moreover we improve the original bound on the dimension of the secret key for a general circuit.

The notion of domain-specific pseudonymous signatures (DSPS) has recently been introduced for private authentication of ID documents, like passports, that embed a chip with computational abilities. Thanks to this privacy-friendly primitive, the document authenticates to a service provider through a reader and the resulting signatures are anonymous, linkable inside the service and unlinkable across services. A subsequent work proposes to enhance security and privacy of DSPS through group signatures techniques. In this paper, we improve on these proposals in three ways. First, we spot several imprecisions in previous formalizations. We consequently provide a clean security model for \emph{dynamic domain-specific pseudonymous signatures}, where we correctly address the dynamic and adaptive case. Second, we note that using group signatures is somehow an overkill for constructing DSPS, and we provide an optimized construction that achieves the same strong level of security while being more efficient. Finally, we study the implementation of our protocol in a chip and show that our solution is well-suited for these limited environments. In particular, we propose a secure protocol for delegating the most demanding operations from the chip to the reader.

We show the first deterministic construction of an unconditionally secure multiparty computation (MPC) protocol in the passive adversarial model over black-box non-Abelian groups which is both optimal and has subexponential complexity of construction. More specifically, following the result of Desmedt et al. (2012) that the problem of MPC over non-Abelian groups can be reduced to finding a $t$-reliable $n$-coloring of planar graphs, we show the construction of such a graph which allows a path from the input nodes to the output nodes when any $t$-party subset is in the possession of the adversary. Unlike the (deterministic) constructions from Desmedt et al. (2012) our construction is subexponential and optimal at the same time, i.e., it is secure for any $t < \frac{n}{2}$.

This work builds on the variant of the function field sieve (FFS) algorithm for the medium prime case introduced by Joux and Lercier in 2006. We make several contributions. The first contribution uses a divisibility and smoothness technique and goes on to develop a sieving method based on the technique. This leads to significant practical efficiency improvements in the descent phase and also provides improvement to Joux's pinpointing technique. The second contribution is a detailed analysis of the degree of freedom and the use of a walk technique in the descent phase of the algorithm. Such analysis shows that it is possible to compute discrete logarithms over certain fields which are excluded by the earlier analyses performed by Joux and Lercier (2006) and Joux (2013). In concrete terms, we present computations of discrete logs for fields with 16 and 19-bit prime characteristic. We also provide concrete analysis of the effectiveness of the FFS algorithm for certain fields of characteristic ranging from 16-bit to 32-bit primes. The final contribution is to perform a complete asymptotic analysis of the FFS algorithm for fields $\mathbb{F}_Q$ with $p=L_Q(1/3,c)$. This closes gaps and corrects errors in the analysis earlier performed by Joux-Lercier and Joux and also provides new insights into the asymptotic behaviour of the algorithm.

We give a polynomial time attack on the McEliece public key cryptosystem based on algebraic geometry codes. Roughly speaking, this attacks runs in $O(n^4)$ operations in $\mathbb F_q$, where $n$ denotes the code length. Compared to previous attacks, allows to recover a decoding algorithm for the public key even for codes from high genus curves.

Recently, Baseri et al. proposed a secure untraceable off-line electronic cash system. They claimed that their scheme could achieve security requirements of an e-cash system such as, untraceability, anonymity, unlinkability, double spending checking, un-forgeability, date-attachability, and prevent forging coins. They further prove the un-forgeability security feature by using the hardness of discrete logarithm problems. However, after cryptanalysis, we found that the scheme cannot attain the security feature, untraceability. We, therefore, modify it to comprise this desired requirement, which is very important in an e-cash system.

We conduct a theoretical and practical comparison of two Ring-LWE-based, scale-invariant, leveled homomorphic encryption schemes – Fan and Vercauteren’s adaptation of BGV and the YASHE scheme proposed by Bos, Lauter, Loftus and Naehrig. In particular, we explain how to choose parameters to ensure correctness and security against lattice attacks. Our parameter selection improves the approach of van de Pol and Smart to choose parameters for schemes based on the Ring-LWE problem by using the BKZ-2.0 simulation algorithm. We implemented both encryption schemes in C++, using the arithmetic library FLINT, and compared them in practice to assess their respective strengths and weaknesses. In particular, we performed a homomorphic evaluation of the lightweight block cipher SIMON. Combining block ciphers with homomorphic encryption allows to solve the gargantuan ciphertext expansion in cloud applications.

Identity-based encryption (IBE) is a special case of public-key encryption where user identities replace public keys. Every user is given a corresponding secret key for decryp- tion, and encryptions for his or her identity must remain confidential even to attackers who learn the secret keys associated with other identities. Several IBE constructions are known to date, but their security relies on specific assumptions, such as quadratic residuosity, as well as different pairing-based and lattice-based assumptions. To circumvent the lack of generic constructions, Dodis et al. (EUROCRYPT ’02) introduced the notion of bounded-collusion IBE (BC-IBE), where attackers only learn secret keys of an a-priori bounded number t of identities. They provided a generic BC-IBE construction from any semantically-secure encryption scheme which, however, suffers from a &#969;(t) blow-up in ciphertext size. Goldwasser et al. (TCC 2012) recently presented a generic construction with no ciphertext-length blow-up. Their construction requires an underlying public-key scheme with a key homomorphism, as well as a hash-proof-style security definition that is strictly stronger than semantic security. This latter requirement in particular reduces the applicability of their construction to existing schemes. In this paper, we present the first generic constructions of BC-IBE from semantically-secure encryption schemes with no ciphertext-length blow-up. Our constructions require different degrees of key-homomorphism and malleability properties that are usually easy to verify. We provide concrete instantiations based on the DDH, QR, NTRU, and LWE assumptions. For all of these assumptions, our schemes present the smallest BC-IBE ciphertext size known to date. Our NTRU-based construction is particularly interesting, due to the lack of NTRU- based IBE constructions as well as the fact that it supports fully-homomorphic evaluation. Our results also yield new constructions of bounded CCA-secure cryptosystems.

We present a generic method for turning passively secure protocols into protocols secure against covert attacks. The method adds a post-execution verification phase to the protocol that allows a misbehaving party to escape detection only with negligible probability. The execution phase, after which the computed protocol result is already available for parties, has only negligible overhead added by our method. The checks, based on linear probabilistically checkable proofs, are done in zero-knowledge, thereby preserving the privacy guarantees of the original protocol. Our method is inspired by recent results in verifiable computation, adapting them to multiparty setting and significantly lowering their computational costs for the provers.

We introduce the first graph-theoretic proof-of-work system, based on finding small cycles or other structures in large random graphs. Such problems are trivially verifiable and arbitrarily scalable, presumably requiring memory linear in graph size to solve efficiently. Our cycle finding algorithm uses one bit per edge, and up to one bit per node. Runtime is linear in graph size and dominated by random access latency, ideal properties for a memory bound proof-of-work. We exhibit two alternative algorithms that allow for a memory-time trade-off (TMTO)---decreased memory usage, by a factor $k$, coupled with increased runtime, by a factor $\Omega(k)$. The constant implied in $\Omega()$ gives a notion of memory-hardness, which is shown to be dependent on cycle length, guiding the latter's choice. Our algorithms are shown to parallelize reasonably well.

FIDES is a lightweight authenticated cipher, presented at CHES 2013. The cipher has two version, providing either 80-bit or 96-bit security. In this paper, we describe internal state-recovery attacks on both versions of FIDES, and show that once we recover the internal state, we can use it to immediately forge any message. Our attacks are based on a guess-and-determine algorithm, exploiting the slow diffusion of the internal linear transformation of FIDES. Our most basic attacks have time complexities of 2^{75} and 2^{90} for FIDES-80 and FIDES-96, respectively, use a very small amount of memory, and their most distinctive feature is their very low data complexity: the attacks require at most 24 bytes of an arbitrary plaintext and its corresponding ciphertext, in order to break the cipher with probability 1. In addition to the basic attacks, we describe optimized attacks which exploit additional data in order to reduce the time complexities to 2^{73} and 2^{88} for FIDES-80 and FIDES-96, respectively.

We show that a Magma implementation of Joux's L[1/4+o(1)] algorithm can be used to compute discrete logarithms in the 1303-bit finite field F_{3^{6*137}} and the 1551-bit finite field F_{3^{6*163}} with very modest computational resources. Our F_{3^{6*137}} implementation was the first to illustrate the effectiveness of Joux's algorithm for computing discrete logarithms in small-characteristic finite fields that are not Kummer or twisted-Kummer extensions.

So far, low probability differentials for the key schedule of block ciphers have been used as a straightforward proof of security against related-key differential attacks. To achieve the resistance, it is believed that for cipher with $k$-bit key it suffices the upper bound on the probability to be $2^{-k}$. Surprisingly, we show that this reasonable assumption is incorrect, and the probability should be (much) lower than $2^{-k}$. Our counter example is a related-key differential analysis of the block cipher CLEFIA-128. We show that although the key schedule of CLEFIA-128 prevents differentials with a probability higher than $2^{-128}$, the linear part of the key schedule that produces the round keys, and the Feistel structure of the cipher, allow to exploit particularly chosen differentials with a probability as low as $2^{-128}$. CLEFIA-128 has $2^{14}$ such differentials, which translate to $2^{14}$ pairs of weak keys. The probability of each differential is too low for attacks, but the weak keys have a special structure which allows with a divide-and-conquer approach to gain advantage of $2^7$ over generic attacks. We exploit the advantage and give a membership test for the weak-key class, provide analysis in the hashing mode, and show the importance for the secret-key mode. The proposed analysis has been tested with computer experiments on small-scale variants of CLEFIA-128. Our results do not threaten the practical use of CLEFIA.

Chuang and Chen propose an anonymous multi server authenticated key agreement scheme based on trust computing using smart card, password, and biometrics. Chuang and Chen say that this scheme not only supports multi-server but also achieves security requirements. but this scheme is vulnerable to masquerade attack, smart card attack, DoS attack and insufficient for perfect forward secrecy. To solve problems, this paper proposes security enhanced anonymous multi server authenticated key agreement scheme using smart card and biometrics.

We consider the Fourier Entropy-Influence (FEI) conjecture in the context of cryptographic Boolean functions. We show that the FEI conjecture is true for the functions satisfying the strict avalanche criterion, which forms a subset of asymptotic log--density~$1$ in the set of all Boolean functions. Further, we prove that the FEI conjecture is satisfied for plateaued Boolean functions, monomial algebraic normal form (with the best involved constant), direct sums, as well as concatenations of Boolean functions. As a simple consequence of these general results we find that each affine equivalence class of quadratic Boolean functions contains at least one function satisfying the FEI conjecture. Further, we propose some ``leveled'' FEI conjectures.

Securing cryptographic implementations against side-channel attacks is one of the most important challenges in modern cryptography. Many countermeasures have been introduced for this purpose, and analyzed in specialized security models. Formal solutions have also been proposed to extend the guarantees of provable security to physically observable devices. Masking and leakage-resilient cryptography are probably the most investigated and best understood representatives of these two approaches. Unfortunately, claims whether one, the other or their combination provides better security at lower cost remained vague so far. In this paper, we provide the first comprehensive treatment of this important problem. For this purpose, we analyze whether cryptographic implementations can be security-bounded, in the sense that the time complexity of the best side-channel attack is lower-bounded, independent of the number of measurements performed. Doing so, we first put forward a significant difference between stateful primitives such as leakage-resilient PRGs (that easily ensure bounded security), and stateless ones such as leakage-resilient PRFs (that hardly do). We then show that in practice, leakage-resilience alone provides the best security vs. performance tradeoff when bounded security is achievable, while masking alone is the solution of choice otherwise. That is, we highlight that~one (x)or the other approach should be privileged, which contradicts the usual intuition that physical security is best obtained by combining countermeasures. Besides, our experimental results underline that despite defined in exactly the same way, the bounded leakage requirement in leakage-resilient PRGs and PRFs imply significantly different challenges for hardware designers. Namely, such a bounded leakage is much harder to guarantee for stateless primitives (like PRFs) than for statefull ones (like PRGs). As a result, constructions of leakage-resilient PRGs and PRFs proven under the same bounded leakage assumption, and instantiated with the same AES implementation, may lead to different practical security levels.

In TPM2.0, a single signature primitive is proposed to support various signature schemes including Direct Anonymous Attestation (DAA), U-Prove and Schnorr signature. This signature primitive is implemented by several APIs which can be utilized as a static Diffie-Hellman oracle. In this paper, we measure the practical impact of the SDH oracle in TPM2.0 and show the security strength of these signature schemes can be weakened by 14-bit. We propose a novel property of DAA called forward anonymity and show how to utilize these DAA-related APIs to break forward anonymity. Then we propose new APIs which not only remove the Static Diffie-Hellman oracle but also support the foward anonymity, thus significantly improve the security of DAA and the other signature schemes supported by TPM2.0. We prove the security of our new APIs under the discrete logarithm assumption in the random oracle model. We prove that DAA satisfy forward anonymity using the new APIs under the Decision Diffie-Hellman assumption. Our new APIs are almost as efficient as the original APIs in TPM2.0 specification and can support LRSW-DAA and SDH-DAA together with U-Prove as the original APIs.

The Fibonacci-to-Galois transformation is useful for reducing the propagation delay of feedback shift register-based stream ciphers and hash functions. In this paper, we extend it to handle Galois-to-Galois case as well as feedforward connections. This makes possible transforming Trivium stream cipher and increasing its keystream data rate by 27\% without any penalty in area. The presented transformation might open new possibilities for cryptanalysis of Trivium, since it induces a class of stream ciphers which generate the same set of keystreams as Trivium, but have a different structure.

Menezes--Qu--Vanstone key agreement (MQV) is intended to provide implicit key authentication (IKA) and several other security objectives. MQV is approved and specified in five standards. This report focuses on the IKA of two-pass MQV, without key confirmation. Arguably, implicit key authentication is the most essential security objective in authenticated key agreement. The report examines various necessary or sufficient formal conditions under which MQV may provide IKA. Incidentally, this report defines, relies on, and inter-relates various conditions on the key deriviation function and Diffie--Hellman groups. While it should be expected that most such definitions and results are already well-known, a reader interested in these topics may be interested in this report as a kind of review, even if they have no interest in MQV whatsoever.

Technological advancements in cloud computing due to increased connectivity and exponentially proliferating data has resulted in migration towards cloud architecture. Cloud computing is technology where the users’ can use high end services in form of software that reside on different servers and access data from all over the world. Cloud storage enables users to access and store their data anywhere. It also ensures optimal usage of the available resources. There is no need for the user to maintain the overhead of hardware and software costs. With a promising technology like this, it certainly abdicates users’ privacy, putting new security threats towards the certitude of data in cloud. The user relies entirely for his data protection on the cloud providers, making them solely responsible for safeguarding it. The security threats such as maintenance of data integrity, data hiding and data safety dominate our concerns when the issue of cloud security come up. The voluminous data and time consuming encryption calculations related to applying any encryption method have been proved as a hindrance in this field. In this research paper, we have contemplated a design for cloud architecture which ensures secured movement of data at client and server end. We have used the non breakability of Elliptic curve cryptography for data encryption and Diffie Hellman Key Exchange mechanism for connection establishment. The proposed encryption mechanism uses the combination of linear and elliptical cryptography methods. It has three security checkpoints: authentication, key generation and encryption of data.

In this paper we study the problem that when a Boolean function can be represented as the sum of two bent functions. This problem was recently presented by N. Tokareva in studying the number of bent functions. Firstly, many functions, such as quadratic Boolean functions, Maiorana-MacFarland bent functions, partial spread functions etc, are proved to be able to be represented as the sum of two bent functions. Methods to construct such functions from low dimension ones are also introduced. N. Tokareva's main hypothesis is proved for $n\leq 6$. Moreover, two hypotheses which are equivalent to N. Tokareva's main hypothesis are presented. These hypotheses may lead to new ideas or methods to solve this problem. At last, necessary and sufficient conditions on the problem when the sum of several bent functions is again a bent function are given.

The paper is about methodology to detect and demonstrate impossible differentials in a block cipher. We were inspired by the shrinking technique proposed by Biham et al. in 1999 which recovered properties of scalable block cipher structures from numerical search on scaled down variants. Attempt to bind all concepts and techniques of impossible differentials together reveals a view of the search for impossible differentials that can benefit from the computational power of a computer. We demonstrate on generalized Feistel networks with internal permutations an additional clustering layer on top of shrinking which let us merge numerical data into relevant human-readable information to be used in an actual proof. After that, we show how initial analysis of scaled down TEA-like schemes leaks the relevant part of the design and the length and ends of the impossible differentials. We use that initial profiling to numerically discover 4 15-round impossible differentials (beating the current 13-round) and thousands of shorter ones.

Recently, Fan et al. proposed a user efficient recoverable off-line e-cash scheme with fast anonymity revoking. They claimed that their scheme could achieve security requirements of an e-cash system such as, anonymity, unlinkability, double spending checking, anonymity control, and rapid anonymity revoking on double spending. They further formally prove the unlinkability and the un-forgeability security features. However, after crypto-analysis, we found that the scheme cannot attain the two proven security features, anonymity and unlinkability. We, therefore, modify it to comprise the two desired requirements which are very important in an e-cash system.

Random number generators have direct applications in information security, online gaming, gambling, and computer science in general. True random number generators need an entropy source which is a physical source with inherent uncertainty, to ensure unpredictability of the output. In this paper we propose a new indirect approach to collecting entropy using human errors in the game play of a user against a computer. We argue that these errors are due to a large set of factors and provide a good source of randomness. To show the viability of this proposal, we design and implement a game, conduct a user study in which we collect user input in the game, and extract randomness from it. We measure the rate and the quality of the resulting randomness that clearly show effectiveness of the approach. Our work opens a new direction for construction of entropy sources that can be incorporated into a large class of video games.

Even as data and analytics driven applications are becoming increasingly popular, retrieving data from shared databases poses a threat to the privacy of their users. For example, investors/patients retrieving records about interested stocks/diseases from a stock/medical database leaks sensitive information to the database server. PIR (Private Information Retrieval) is a promising security primitive to protect the privacy of users' interests. PIR allows the retrieval of a data record from a database without letting the database server know which record is being retrieved. The privacy guarantees could either be information theoretic or computational. Ever since the first PIR schemes were proposed, a lot of work has been done to reduce the communication cost in the information-theoretic settings - particularly the question communication cost, i.e., the traffic from the user to the database server. The answer communication cost (the traffic from the database server to the user) has however barely been improved. When question communication cost is much lower than the record length, reducing question communication cost has marginal benefit on lowering overall communication cost. In contrast, reducing answer cost becomes very important. In this paper we propose ramp secret sharing based mechanisms that reduce the answer communication cost in information-theoretic PIR. We have designed four information-theoretic PIR schemes, using three ramp secret sharing approaches, achieving answer communication cost close to the cost of non-private information retrieval. Evaluation shows that our PIR schemes can achieve lower communication cost and the same level of privacy compared with existing schemes. Our PIR schemes' usages are demonstrated for realistic settings of outsourced data sharing and P2P content delivery scenarios. Thus, our approach makes PIR a viable communication efficient technique to protect user interest privacy.

When represented as a bit string in a standard way, even using point compression, an elliptic curve point is easily distinguished from a random bit string. This property potentially allows an adversary to tell apart network traffic that makes use of elliptic curve cryptography from random traffic, and then intercept, block or otherwise tamper with such traffic. Recently, Bernstein, Hamburg, Krasnova and Lange proposed a partial solution to this problem in the form of Elligator: an algorithm for representing around half of the points on a large class of elliptic curves as close to uniform random strings. Their proposal has the advantage of being very efficient, but suffers from several limitations: * Since only a subset of all elliptic curve points can be encoded as a string, their approach only applies to cryptographic protocols transmitting points that are rerandomizable in some sense. * Supported curves all have non-trivial $2$-torsion, so that Elligator cannot be used with prime-order curves, ruling out standard ECC parameters and many other cryptographically interesting curves such as BN curves. * For indistinguishability to hold, transmitted points have to be uniform in the whole set of representable points; in particular, they cannot be taken from a prime order subgroup, which, in conjunction with the non-trivial $2$-torsion, rules out protocols that require groups of prime order. In this paper, we propose an approach to overcome all of these limitations. The general idea is as follows: whereas Bernstein et al. represent an elliptic curve point P as the bit string \iota^{-1}(P), where \iota is an injective encoding to the curve (which is only known to exist for some curve families, and reaches only half of all possible points), we propose to use a randomly sampled preimage of P under an admissible encoding of the form f^{\otimes 2}: (u,v)\mapsto f(u)+f(v), where f is essentially any algebraic encoding. Such encodings f exist for all elliptic curves, and the corresponding admissible encodings f^{\otimes 2} are essentially surjective, inducing a close to uniform distribution on the curve. As a result, our bit string representation is somewhat less compact (about twice as long as Elligator), but it has none of the limitations above, and can be computed quite efficiently when the function f is suitably chosen.

In this paper, we propose a new algorithm for solving the general approximate common divisors (GACD) problems, which is based on lattice reduction algorithms on certain special lattices and linear equation solving algorithms over integers. Through both theoretical arguments and experimental data, we show that our new algorithm works in polynomial time but under roughly the following condition: \begin{itemize} \item There is a positive integer $t$ such that $$\frac{\gamma+\eta}{t} + \frac{t}{H}+\rho < \eta;$$ \item We have more than $t$ GACD samples. \end{itemize} or equivalently \begin{itemize} \item $$H(\eta-\rho)^{2}-4(\gamma+\eta)>0$$ \item We have more than $t=\lceil\frac{H(\eta-\rho)-\sqrt{H^{2}(\eta-\rho)^{2}-4H(\gamma+\eta)}}{2}\rceil$ GACD samples. \end{itemize} Here $\gamma$, $\eta$ and $\rho$ are parameters describing a GACD problem, $H =1/ \log_{2}F$ and $F$ is the Hermite Factor. In our experiments, $H$ is shown to be roughly $40$ when using the LLL reduction algorithm and it should be around $80$ when using Deep or BKZ algorithms. % We use our algorithm to solve concrete problems that no other algorithm could solve before. We show how our algorithm can be applied to attack the fully homomorphic encryption schemes which are based on the general approximate common divisors problem and its limitations.

We introduce a method for obtaining provable polynomial time solutions of problems in nonabelian algebraic cryptography. This method is widely applicable, easier to apply, and more efficient than earlier methods. After demonstrating its applicability to the major classic nonabelian protocols, we use this method to cryptanalyze the Triple Decomposition key exchange protocol, the only classic group theory based key exchange protocol that could not be cryptanalyzed by earlier methods.

We put forth a lookup-table-based modular reduction method which partitions the binary string of an integer to be reduced into blocks according to its runs. Its complexity depends on the amount of runs in the binary string. We show that the new reduction is almost twice as fast as the popular Barrett's reduction, and provide a thorough complexity analysis of the method.

Since its introduction more than a decade ago the homomorphic properties of the NTRU encryption scheme have gone largely ignored. A variant of NTRU proposed by Stehle and Steinfeld was recently extended into a full fledged multi-key fully homomorphic encryption scheme by Alt-Lopez, Tromer and Vaikuntanathan (ATV). This NTRU based FHE presents a viable alternative to the currently dominant BGV style FHE schemes. While the scheme appears to be more efficient, a full implementation and comparison to BGV style implementations has been missing in the literature. In this work, we develop a customized implementation of the ATV scheme. First parameters are selected to yield an efficient and yet secure ATV instantiation. We present an analysis of the noise growth that allows us to formulate a modulus cutting strategy for arbitrary circuits. Furthermore, we introduce a specialization of the ring structure that allows us to drastically reduce the public key size making evaluation of deep circuits such as the AES block cipher viable on a standard computer with a reasonable amount of memory. Moreover, with the modulus specialization the need for key switching is eliminated. Finally, we present a generic bit-sliced implementation of the ATV scheme that embodies a number of optimizations. To assess the performance of the scheme we homomorphically evaluate the full 10 round AES circuit in 31 hours with 2048 message slots resulting in 55 sec per AES block evaluation time.

In our previous work, we have proposed a framework which allows tools that can check standard noninterference properties but a priori cannot deal with cryptography to establish cryptographic indistinguishability properties, such as privacy properties, for Java programs. We refer to this framework as the CVJ framework (Cryptographic Verification of Java Programs) in this paper. While so far the CVJ framework directly supports public-key encryption (without corruption and without a public-key infrastructure) only, in this work we further instantiate the framework to support, among others, public-key encryption and digital signatures, both with corruption and a public-key infrastructure, as well as (private) symmetric encryption. Since these cryptographic primitives are very common in security-critical applications, our extensions make the framework much more widely applicable. To illustrate the usefulness and applicability of the extensions proposed in this paper, we apply the framework along with the tool Joana, which allows for the fully automatic verification of noninterference properties of Java programs, to establish cryptographic privacy properties of a (non-trivial) cloud storage application, where clients can store private information on a remote server.

TLS is by far the most important protocol on the Internet for negotiating secure session keys and providing authentication. Only very recently, the standard ciphersuites of TLS have been shown to provide provably secure guarantees under a new notion called authenticated and Confidential Channel Establishment (ACCE) introduced by Jager et al. at CRYPTO'12. In this work, we analyse the variants of TLS that make use of pre-shared keys (TLS-PSK). In various environments, TLS-PSK is an interesting alternative for remote authentication between servers and constrained clients like smart cards, for example for mobile phone authentication, EMV-based payment transactions or authentication via electronic ID cards. First, we introduce a new and strong definition of ACCE security that covers protocols with pre-shared keys. Next, we prove that all ciphersuite families of TLS-PSK meet our strong notion of ACCE security. Our results do not rely on random oracles nor on any non-standard assumption.

Mobile text messages are currently vulnerable to inspection, modification, and replay by network operators and those that influence network operators. This paper describes a set of protocols that provide end-to-end message confidentiality, integrity, and authenticity over the high latency, low bandwidth, Short Message Service provided by GSM networks.

In this paper, we consider an RSA modulus $N=pq$, where the prime factors $p$, $q$ are of the same size. We present an attack on RSA when the decryption exponent $d$ is in the form $d=Md_1+d_0$ where $M$ is a given positive integer and $d_1$ and $d_0$ are two suitably small unknown integers. In 1999, Boneh and Durfee presented an attack on RSA when $d<N^{0.292}$. When $d=Md_1+d_0$, our attack enables one to overcome Boneh and Durfee's bound and to factor the RSA modulus.

In this paper, we provide performance measures for software implementations of the NSA-designed Speck128 block cipher together with various existing authenticated encryption modes. We investigated Speck128 using GCM, CCM, EAX, OCB3, COPA, and PAEAD-1, and we briefly discuss performance advantages and disadvantages of each mode. Our results indicate that Speck128 is capable of performing extremely fast authenticated encryption, as fast as 3.4 cycles/byte on a modern x86-based 64-bit processor.

Support of membership revocation is a desirable functionality for any group signature scheme. Among the known revocation approaches, verifier-local revocation (VLR) seems to be the most flexible one, because it only requires the verifiers to possess some up-to-date revocation information, but not the signers. All of the contemporary VLR group signatures operate in the bilinear map setting, and all of them will be insecure once quantum computers become a reality. In this work, we introduce the first lattice-based VLR group signature, and thus, the first such scheme that is believed to be quantum-resistant. In comparison with existing lattice-based group signatures, our scheme has several noticeable advantages: support of membership revocation, logarithmic-size signatures, and milder hardness assumptions. In the random oracle model, our scheme is proven secure based on the hardness of the SIVP_O(n^{2.5}) problem in general lattices. Moreover, our construction works without relying on public-key encryption schemes, which is an intriguing feature for group signatures.

At Crypto 2012, Brakerski constructed a scale-invariant fully homomorphic encryption scheme based on the LWE problem, in which the same modulus is used throughout the evaluation process, instead of a ladder of moduli when doing “modulus switching”. In this paper we describe a variant of the van Dijk et al. FHE scheme over the integers with the same scale-invariant property. Our scheme has a single secret modulus whose size is linear in the multiplicative depth of the circuit to be homomorphically evaluated, instead of exponential; we therefore construct a leveled fully homomorphic encryption scheme. This scheme can be transformed into a pure fully homomorphic encryption scheme using bootstrapping, and its security is still based on the Approximate-GCD problem. We also describe an implementation of the homomorphic evaluation of the full AES encryption circuit, and obtain significantly improved performance compared to previous implementations: about 23 seconds (resp. 3 minutes) per AES block at the 72-bit (resp. 80-bit) security level on a mid-range workstation. Finally, we prove the equivalence between the (error-free) decisional Approximate-GCD problem introduced by Cheon et al. (Eurocrypt 2013) and the classical computational Approximate-GCD problem. This equivalence allows to get rid of the additional noise in all the integer-based FHE schemes described so far, and therefore to simplify their security proof.

Random numbers have been one of the most useful objects in statistics, computer science, cryptography, modeling, simulation, and other applications though it is very difficult to construct true randomness. Many solutions (e.g., cryptographic pseudorandom generators) have been proposed to harness or simulate randomness and many statistical testing techniques have been proposed to determine whether a pseudorandom generator produces high quality randomness. NIST SP800-22 (2010) proposes the state of art testing suite for (pseudo) random generators to detect deviations of a binary sequence from randomness. On the one hand, as a counter example to NIST SP800-22 test suite, it is easy to construct functions that are considered as GOOD pseudorandom generators by NIST SP800-22 test suite though the output of these functions are easily distinguishable from the uniform distribution. Thus these functions are not pseudorandom generators by definition. On the other hand, NIST SP800-22 does not cover some of the important laws for randomness. Two fundamental limit theorems about random binary strings are the central limit theorem and the law of the iterated logarithm (LIL). Several frequency related tests in NIST SP800-22 cover the central limit theorem while no NIST SP800-22 test covers LIL. This paper proposes techniques to address the above challenges that NIST SP800-22 testing suite faces. Firstly, we propose statistical distance based testing techniques for (pseudo) random generators to reduce the above mentioned Type II errors in NIST SP800-22 test suite. Secondly, we propose LIL based statistical testing techniques, calculate the probabilities, and carry out experimental tests on widely used pseudorandom generators by generating around 30TB of pseudorandom sequences. The experimental results show that for a sample size of 1000 sequences (2TB), the statistical distance between the generated sequences and the uniform distribution is around 0.07 (with 0 for statistically indistinguishable and 1 for completely distinguishable) and the root-mean-square deviation is around 0.005. Though the statistical distance 0.07 and RMSD 0.005 are acceptable for some applications, for a cryptographic "random oracle", the preferred statistical distance should be smaller than 0.03 and RMSD be smaller than 0.001 at the sample size 1000. These results justify the importance of LIL testing techniques designed in this paper. The experimental results in this paper are reproducible and the raw experimental data are available at author's website.

We present Lyra, a password-based key derivation scheme based on cryptographic sponges. Lyra was designed to be strictly sequential (i.e., not easily parallelizable), providing strong security even against attackers that use multiple processing cores (e.g., custom hardware or a powerful GPU). At the same time, it is very simple to implement in software and allows legitimate users to fine-tune its memory and processing costs according to the desired level of security against brute force password guessing. We compare Lyra with similar-purpose state-of-the-art solutions, showing how our proposal provides a higher security level and overcomes limitations of existing schemes. Specfically, we show that if we fix Lyra's total processing time t in a legitimate platform, the cost of a memory-free attack against the algorithm is exponential, while the best known result in the literature (namely, against the scrypt algorithm) is quadratic. In addition, for an identical same processing time, Lyra allows for a higher memory usage than its counterparts, further increasing the cost of brute force attacks.

Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation. Unfortunately, recent advances in quantum computation show that many of the existing schemes completely break down once quantum computers reach maturity (mainly due to Shor’s algorithm). This leads to the challenge of constructing quantum-resistant group homomorphic cryptosystems. In this work, we prove the general impossibility of (abelian) group homomorphic encryption in the presence of quantum adversaries, when assuming the IND-CPA security notion as the minimal security requirement. To this end, we prove a new result on the probability of sampling generating sets of finite (sub-)groups if sampling is done with respect to an arbitrary, unknown distribution. Finally, we provide a sufficient condition on homomorphic encryption schemes for our quantum attack to work and discuss its satisfiability in non-group homomorphic cases. The impact of our results on recent fully homomorphic encryption schemes poses itself as an open question.

This paper introduces the use of channel equalization as a method of simplifying side channel analysis attacks, by effectively collapsing all points in a power measurement trace into a single random variable. This uses a simple Finite Impulse Response (FIR) linear equalizer, which has been studied extensively in communications systems. In addition the estimation of a channel model is used in developing the Channel Estimation Analysis (CEA), which is a generic attack requiring similar assumptions to the Correlation Power Analysis (CPA) attack. Both channel equalization and the CEA attack are straight-forward to apply to real systems, and Python examples are provided. Results of attacking unprotected AES-128 and protected AES-256RSM on a microcontroller are provided.

Edwards’ elliptic curve form is popular in modern cryptographic implementations thanks to their fast, strongly unified addition formulas. Twisted Edwards curves with a = &#8722;1 are slightly faster, but their addition formulas are not complete over Fp where p &#8801; 3 (mod 4). In this short note, we propose that designers specify Edwards curves, but implement scalar multiplications and the like using an isogenous twisted Edwards curve.

We study in this work the potential side channel leakages of a hardware biometric comparison system that has been designed for fingerprints. An embedded biometric system for comparison aims at comparing a stored biometric data with a freshly acquired one without the need to send the stored biometric data outside the system. Here one may try to retrieve the stored data via side channel, similarly as for embedded cryptographic modules where one may try to exploit side channel for attacking the modules. On one hand, we show that we can find partial information by the means of simple Side Channel Analysis that may help to retrieve the stored fingerprint. On the other hand, we illustrate that reconstructing the fingerprint remains not trivial and we give some simple countermeasures to protect further the comparison algorithm.

By shrinking the technology static power consumption of CMOS circuits is becoming a major concern. In this paper, we present the first practical results of exploiting static power consumption of FPGA-based cryptographic devices in order to mount a key-recovery side-channel attack. The experiments represented here are based on three Xilinx FPGAs built on 65nm, 45nm, and 28nm process technologies. By means of a sophisticated measurement setup and methodology we demonstrate an exploitable information leakage through static power of the underlying FPGAs. The current work highlights the feasibility of side-channel analysis attacks by static power that have been known for years but have not been performed and investigated in practice yet. This is a starting point for further research investigations, and may have a significant impact on the efficiency of DPA countermeasures in the near future.

We present a pseudo-random bit generator expanding a uniformly random bit-string r of length k/2, where k is the security parameter, into a pseudo-random bit-string of length 2k &#8722; log^2(k) using one modular exponentiation. In contrast to all previous high expansion-rate pseudo-random bit generators, no hashing is necessary. The security of the generator is proved relative to Paillier’s composite degree residuosity assumption. As a first application of our pseudo-random bit generator we exploit its efficiency to optimise Paillier’s crypto-system by a factor of (at least) 2 in both running time and usage of random bits. We then exploit the algebraic properties of the generator to construct an efficient protocol for secure constant-round multiparty function evaluation in the cryptographic setting. This construction gives an improvement in communication complexity over previous protocols in the order of nk^2, where n is the number of participants and k is the security parameter, resulting in a communication complexity of O(nk^2|C|) bits, where C is a Boolean circuit computing the function in question.

It is well known that almost all random subset sum instances with density less than 0.6463... can be solved with an $l_{2}$-norm SVP oracle by Lagarias and Odlyzko. Later, Coster \emph{et al.} improved the bound to 0.9408... by using a different lattice. In this paper, we generalize this classical result to $l_p$-norm. More precisely, we show that for $p\in \mathbb{Z}^{+}$, an $l_p$-norm SVP oracle can be used to solve almost all random subset sum instances with density bounded by $\delta_p$, where $\delta_1=0.5761$ and $\delta_p = 1/(\frac{1}{2^p}\log_2(2^{p+1}-2)+\log_2(1+\frac{1}{(2^p-1)(1-(\frac{1}{2^{p+1}-2})^{(2^p-1)})})))$ for $p\geq 3$(asymptotically, $\delta_p\approx 2^p/(p+2)$). Since $\delta_p$ goes increasingly to infinity when $p$ tends to infinity, it can be concluded that an $l_p$-norm SVP oracle with bigger $p$ can solve more subset sum instances. An interesting phenomenon is that an $l_p$-norm SVP oracle with $p\geq 3$ can help solve almost all random subset sum instances with density one, which are thought to be the most difficult instances.

Most of the lightweight block ciphers are nibble-oriented as the implementation of a 4-bit S-box is much more compact than an 8-bit S-box. This paper proposes a novel implementation of multiplicative inverse for 8-bit S-boxes using LFSR requiring only 138 gate-equivalent. It can be shown that if such S-boxes are adopted for the AES it takes less than 50 gate-equivalent per S-box in parallel implementation. Canright's \cite{Canright} implementation of the AES S-box is five times more expensive compared to this method for AES-like S-boxes. With this powerful scheme, a lightweight block cipher can be designed using an 8-bit S-box.

Attribute-based encryption (ABE) is a type of public key encryption that allows users to encrypt and decrypt messages based on user attributes. For instance, one can encrypt a message to any user satisfying the boolean formula (``crypto conference attendee'' AND ``PhD student'') OR ``IACR member''. One drawback is that encryption and key generation computational costs scale with the complexity of the access policy or number of attributes. In practice, this makes encryption and user key generation a possible bottleneck for some applications. To address this problem, we develop new techniques for ABE that split the computation for these algorithms into two phases: a preparation phase that does the vast majority of the work to encrypt a message or create a secret key *before* it knows the message or the attribute list/access control policy that will be used (or even the size of the list or policy). A second phase can then rapidly assemble an ABE ciphertext or key when the specifics become known. This concept is sometimes called ``online/offline'' encryption when only the message is unknown during the preparation phase; we note that the addition of unknown attribute lists and access policies makes ABE significantly more challenging. One motivating application for this technology is mobile devices: the preparation work can be performed while the phone is plugged into a power source, then it can later rapidly perform ABE operations on the move without significantly draining the battery.

TLS is one of the most widely deployed cryptographic protocols on the Internet; it is used to protect the confidentiality and integrity of transmitted data in various client-server protocols. Its non-standard use of cryptographic primitives, however, makes it hard to formally assess its security. It is in fact difficult to use traditional (well-understood) security notions for the key-exchange (here: handshake) and the encryption/authentication (here: record layer) parts of the protocol due to the fact that, on the one hand, traditional game-based notions do not easily support composition, and on the other hand, all TLS versions up to and including 1.2 combine the two phases in a non-standard way. In this paper, we provide a modular security analysis of the handshake in TLS version 1.2 and a slightly sanitized version of the handshake in the current draft of TLS version 1.3, following the constructive cryptography approach of Maurer and Renner (ICS 2011). We provide a deconstruction of the handshake into modular sub-protocols and a security proof for each such sub-protocol. We also show how these results can be combined with analyses of the respective record layer protocols, and the overall result is that in all cases the protocol constructs (unilaterally) secure channels between the two parties from insecure channels and a public-key infrastructure. This approach ensures that (1) each sub-protocol is proven in isolation and independently of the other sub-protocols, (2) the overall security statement proven can easily be used in higher-level protocols, and (3) TLS can be used in any composition with other secure protocols. In more detail, for the key-exchange step of TLS 1.2, we analyze the RSA-based and both Diffie-Hellman-based variants (with static and ephemeral server key share) under a non-randomizability assumption for RSA-PKCS and the Gap Diffie-Hellman assumption, respectively; in all cases we make use of random oracles. For the respective step of TLS 1.3, we prove security under the Decisional Diffie-Hellman assumption in the standard model. In all statements, we require additional standard computational assumptions on other primi- tives. In general, since the design of TLS is not modular, the constructive decomposition is less fine-grained than one might wish to have and than it is for a modular design. This paper therefore also suggests new insights into the intrinsic problems incurred by a non-modular protocol design such as that of TLS.

Some recent constructions based on LWE do not sample the secret uniformly at random but rather from some distribution which produces small entries. The most prominent of these is the binary-LWE problem where the secret vector is sampled from {0, 1}&#8727; or {&#8722;1, 0, 1}&#8727;. We present a variant of the BKW algorithm for binary-LWE and other small secret variants and show that this variant reduces the complexity for solving binary-LWE. We also give estimates for the cost of solving binary-LWE instances in this setting and demonstrate the advantage of this BKW variant over standard BKW and lattice reduction techniques applied to the SIS problem. Our variant can be seen as a combination of the BKW algorithm with a lazy variant of modulus switching which might be of independent interest.

Understanding the minimal assumptions required for carrying out cryptographic tasks is one of the fundamental goals of theoretical cryptography. A rich body of work has been dedicated to understanding the complexity of cryptographic tasks in the context of (semi-honest) secure two-party computation. Much of this work has focused on the characterization of trivial and complete functionalities (resp., functionalities that can be securely implemented unconditionally, and functionalities that can be used to securely compute all functionalities). All previous works define reductions via an ideal implementation of the functionality; \ie $f$ reduces to $g$ if one can implement $f$ using an ideal box (or oracle) that computes the function $g$ and returns the output to both parties. Such a reduction models the computation of $f$ as an \emph{atomic operation}. However, in the real-world, protocols proceed in rounds, and the output is not learned by the parties simultaneously. In this paper we show that this distinction is significant. Specifically, we show that there exist symmetric functionalities (where both parties receive the same outcome), that are neither trivial nor complete under ``ideal-box reductions'', and yet the existence of a constant-round protocol for securely computing such a functionality implies infinitely-often oblivious transfer (meaning that it is secure for infinitely-many $n$'s). In light of the above, we propose an alternative definitional infrastructure for studying the triviality and completeness of functionalities.

We present the first provably-secure 3-party password-only authenticated key exchange (PAKE) protocol that can run in only two communication rounds. Our protocol is generic in the sense that it can be constructed from any 2-party PAKE protocol. The protocol is proven secure in a variant of the widely accepted model of Bellare, Pointcheval and Rogaway (2000) without any idealized assumptions on the cryptographic primitives used. We also investigate the security of the 2-round 3-party PAKE protocol of Wang, Hu and Li (2010), and demonstrate that this protocol cannot achieve implicit key authentication in the presence of an active adversary.

Triple encryption is a cascade of three block cipher evaluations with independent keys, in order to enlarge its key size. This design is proven secure up to approximately 2^{kappa+min{kappa/2,n/2}} queries (by Bellare and Rogaway, EUROCRYPT 2006, and Gaži and Maurer, ASIACRYPT 2009), where kappa denotes the key size and n the block length of the underlying block cipher. On the other hand, the best known attack requires about 2^{kappa+n/2} queries (by Lucks, FSE 1998, and Gaži, CRYPTO 2013). These bounds are non-tight for kappa <= n. In this work, we close this gap. By strengthening the best known attack as well as tightening the security bound, we prove that triple encryption is tightly secure up to 2^{kappa+min{kappa,n/2}} queries. Additionally, we prove that the same tight security bound holds for quadruple encryption (which consists of four sequentially evaluated block ciphers), and derive improved security and attack bounds for cascades consisting of five or more rounds. This work particularly solves the longstanding open problem of proving tight security of the well-known Triple-DES construction.

In this paper, we revisit the old problem asking the exact provable security of triple encryption in the ideal cipher model. For a blockcipher with key length k and block size n, triple encryption is known to be secure up to 2^{k+min{k/2,n/2}} queries, while the best attack requires 2^{k+min{k,n/2}} query complexity. So there is a gap between the upper and lower bounds for the security of triple encryption. We close this gap by proving the security up to 2^{k+min{k,n/2}} query complexity. With the DES parameters, triple encryption is secure up to 2^{82.5} queries, greater than the current bound of 2^{78.3} and comparable to 2^{83.5} for 2-XOR-cascade. We also analyze the security of two-key triple encryption, where the first and the third keys are identical. We prove that two-key triple encryption is secure up to 2^{k+min{k,n/2}} queries to the underlying blockcipher and 2^{min{k,n/2}} queries to the outer permutation. For the DES parameters, this result is interpreted as the security of two-key triple encryption up to 2^{32} plaintext-ciphertext pairs and 2^{81.7} blockcipher encryptions.

Digital signatures are one of the most extensively used cryptographic primitives today. It is well-understood that they guarantee practical security only if the corresponding verification keys are distributed authentically; however, arguably, satisfying solutions for the latter haven't been found yet, or at least aren't in large-scale deployment. This paper introduces a novel approach for cryptographic message authentication where this problem does not arise: A linkable message tagging scheme (LMT) identifies pairs of messages and accompanying authentication tags as related if and only if these tags were created using the same secret key. In other words, in contrast to signature schemes, our primitive does not aim at detecting whether individually considered messages originate from an explicitly specified entity, but instead decides whether all messages from a given collection originate from the same (possibly anonymous) source. The appealing consequence is that our primitive fully avoids public keys and hence elegantly sidesteps the key distribution problem of signature schemes. As an interesting application of LMT we envision an email authentication system with minimal user interaction. Email clients could routinely generate a secret LMT key upon their first invocation, and then equip all outgoing messages with corresponding tags. On the receiver's side, client software could automatically verify for incoming messages whether they indeed originate from the same entity as previously or subsequently received messages with identical sender address. Although this form of authentication does not provide as strong guarantees of message's origin as signature schemes would do, we do believe that trading the apparently discouraging obstacles implied by the authentic distribution of signature verification keys for the assumption that an attacker does not forge every message exchanged between parties is quite attractive. As technical contributions we formalize the notions of LMT and its (more efficient) variant CMT (classifiable message tagging), including corresponding notions of unforgeability. For both variants we propose a range of provably secure constructions, basing on different hardness assumptions, with and without requiring random oracles.

In this paper a novel, low latency family of adders and modular adders has been proposed. This family efficiently combines the ideas of high-radix carry-save addition and the parallel prefix networks. It also takes advantage of fast carry chains of modern FPGAs. The implementation results reveal that these hybrid adders have great potential for efficient implementation of modular addition of long integers used in various public key cryptography schemes.

Abstract In the domain of the Side Channel Attacks, various statistical tools have succeeded to retrieve a secret key, as the Pearson coefficient or the Mutual Information. In this paper we propose to study the Maximal Information Coefficient (MIC) which is a non-parametric method introduced by Reshef et al. [13] to compare two random variables. The MIC is based on the mutual information but it is easier to implement and is robust to the noise. We show how apply this tool in the particular case of the side channel attacks. As in statistics, benefits only appears with drawbacks, the computing complexity of the MIC is high. Therefore, we propose a way to efficiently compute the MIC. The obtained attack called the Maximal Information Coefficient Analysis is compared to the CPA [3] and the MIA [8]. The results show the interest of this approach when the leakage is noisy and bad modeleled.

Diffusion layers are crucial components of symmetric ciphers&#8206;. &#8206;These components&#8206;, &#8206;along with suitable Sboxes&#8206;, &#8206;can make symmetric ciphers resistant against statistical attacks like linear and differential cryptanalysis&#8206;. &#8206;Conventional &#8206;&#8206;MDS diffusion layers, which are defined as matrices over finite fields, have been used in symmetric ciphers such as AES&#8206;, &#8206;Twofish and SNOW&#8206;. &#8206;In this paper&#8206;, &#8206;we study linear, linearized and nonlinear MDS diffusion layers&#8206;. We investigate linearized diffusion layers, &#8206;which are a generalization of conventional diffusion layers&#8206;; t&#8206;hese diffusion layers are used in symmetric ciphers like SMS4&#8206;, &#8206;Loiss and ZUC&#8206;. W&#8206;e introduce some &#8206;new &#8206;families of linearized MDS diffusion layers &#8206;and as a consequence, &#8206;we &#8206;present a&#8206; &#8206;method &#8206;for &#8206;construction of &#8206;&#8206;&#8206;&#8206;randomized linear &#8206;&#8206;&#8206;&#8206;&#8206;diffusion &#8206;layers over a finite field. Nonlinear MDS diffusion layers are introduced in Klimov's thesis; we investigate nonlinear MDS diffusion layers theoretically, and we present a new family of nonlinear MDS diffusion layers. We show that these nonlinear diffusion layers can be made randomized with a low &#8206;implementatio&#8206;n cost. An important fact about linearized and nonlinear diffusion layers is that they are more resistant against algebraic attacks in comparison to conventional diffusion layers. A &#8206;special case of diffusion layers are &#8206;&#8206;&#8206;(0,1)&#8206;-&#8206;diffusion layers. This type of diffusion layers are used in symmetric ciphers like ARIA&#8206;. &#8206;W&#8206;e examine (0,1)&#8206;-&#8206;diffusion layers and prove a theorem about them&#8206;. &#8206;At last&#8206;, &#8206;we study linearized MDS diffusion layers of symmetric ciphers Loiss, SMS4 and ZUC&#8206;, from the mathematical viewpoint.

In this paper, we propose the first provable secure certificate-based proxy signature with message recovery without bilinear pairing. The notion of certificate-based cryptography was initially introduced by Gentry in 2003, in order to simplify certificate management in traditional public key cryptography(PKC)and to solve the key escrow problem in identity-based cryptosystems. To date, a number of certificate-based proxy signature(CBPS)schemes from bilinear pairing have been proposed. Nonetheless, the total computation cost of a pairing is higher than that of scalar multiplication(e.g., over elliptic curve group). Consequently, schemes without pairings would be more appealing in terms of efficiency. According to the available research in this regard, our scheme is the first provable secure CBPS scheme with message recovery which is based on the elliptic curve discrete logarithm problem. We prove the security of the presented scheme against existential forgery under adaptive chosen message and ID attacks in the random oracle model. Moreover, the paper will also show how it would be possible to convert this scheme to the CBPS scheme without message recovery. This scheme has more applications in situations with limited bandwidth and power-constrained devices.

Encrypt-Mix-Encrypt is a type of SPRP based construction, where a masked plaintext is encrypted in ECB mode of, then a non-linear mixing is performed and then again an encryption is performed in ECB mode which is masked to produce the ciphertext. Using the property of the binary field, the authors proved that the construction is not SPRP secure if the mixing used is linear. In this paper, we observe that relaxing the mixing operation to some specific efficient linear mixing provides the PRP property of the construction. Moreover choosing a linear mixing that gives the online property is not a difficult task. We can use this fact to construct an efficient Online PRP using Encrypt-Mix-Encrypt type of construction with the mix operation being a linear online mixing, making the construction efficient and online. We also show that the construction with linear mixing doesn't provide SPRP security even if we perform all the operations in a prime field instead of binary field. Thus, we fully characterize EME with linear mixing.

In this paper, we carry out a detailed mathematical study of two theoretical distinguishers based on the Kolmogorov-Smirnov (KS) distance. This includes a proof of soundness and the derivation of closed- form expressions, which can be split into two factors: one depending only on the noise and the other on the confusion coefficient of Fei, Luo and Ding. This allows one to have a deeper understanding of the relative influences of the signal-to-noise ratio and the confusion coefficient on the distinguisher’s performance. Moreover, one is able to directly compare distinguishers based on their closed-form expressions instead of using evaluation metric that might obscure the actual performance and favor one distinguisher over the other. Furthermore, we formalize the link between the confusion coefficient and differential cryptanalysis, which shows that the stronger an S-box is resistant to differential attacks the weaker it is against side-channel attacks, and vice versa.

Abstract—A recent result in Bitcoin is the selfish mining strategy in which a selfish cartel withholds blocks they mine to gain an advantage. This strategy is both incentive-compatible and harmful to Bitcoin. In this paper we introduce a new defense against selfish mining that improves on the previous best result, we raise the threshold of mining power necessary to profitably selfishly mine from 25% to 32% under all propagation advantages. While the security of our system uses unforgeable timestamps, it is robust to their compromise. Additionally, we discuss the difficulty a mining conspiracy would face attempting to keep the compromise of our scheme secret and we analyze incentives for getting miners to adopt these changes.

We propose a non-interactive zero knowledge \emph{pairwise multiset sum equality test (PMSET)} argument in the common reference string (CRS) model that allows a prover to show that the given committed multisets $\AAA_j$ for $j \in \set{1, 2, 3, 4}$ satisfy $\AAA_1 \uplus \AAA_2 = \AAA_3 \uplus \AAA_4$, i.e., every element is contained in $\AAA_1$ and $\AAA_2$ exactly as many times as in $\AAA_3$ and $\AAA_4$. As a corollary to the $\PUTME$ argument, we present arguments that enable to efficiently verify the correctness of various (multi)set operations, for example, that one committed set is the intersection or union of two other committed sets. The new arguments have constant communication and verification complexity (in group elements and group operations, respectively), whereas the CRS length and the prover's computational complexity are both proportional to the cardinality of the (multi)sets. We show that one can shorten the CRS length at the cost of a small increase of the communication and the verifier's computation.

The Keccak hash function is chosen of the SHA-3 competition. This function has the appropriate structural and so far it has been resistant against collision attacks. In the last few years after efforts cryptanalysis, first, the collision in the second round and near collision in the third rounds, was found. After Shamir and Et al succeeded find collision in fourth round and near collision in 5 rounds for keccak 224,256. In this paper we propose a method that it can used, for the texts with size smaller than r and finds,collision in first round and near collision, in the second round, regardless of any probability. Our attack technique, using the find the text that have the same parity such original text in &#952; function. It is practical for all keccak varies and it finds collision in first round and near collision for second round in few minute. We have named this method " Parity Analyse”.

Asymptotical complexity of sparse equation systems over finite field $F_q$ is studied. Let the variable sets belong to a fixed family $\mathcal{X}=\{X_1,\ldots,X_m\}$ while the polynomials $f_i(X_i)$ are taken independently and uniformly at random from the set of all polynomials of degree $\leq q-1$ in each of the variables in $X_i$. In particular, for $|X_i|\le3$, $m=n$, we prove the average complexity of finding all solutions to $f_i(X_i)=0, i=1,\ldots,m$ by Gluing algorithm ( Semaev, Des. Codes Cryptogr., vol. 49 (2008), pp.47--60) is at most $ q^{\frac{n}{5.7883}+O(\log n)}$ for arbitrary $\mathcal{X}$ and $q$. The proof results from a detailed analysis of 3-MaxMinMax problem, a novel problem for hyper-graphs.

We present explicit formulae and complexities of bit-parallel $GF(2^{n})$ squarers for a new class of irreducible pentanomials $x^{n}+x^{n-1}+x^{k}+x+1$, where $n$ is odd and $1<k<(n-1)/2$. The squarer is based on the generalized polynomial basis of $GF(2^{n})$. Its gate delay matches the best results, while its XOR gate complexity is $n+1$, which is only about 2/3 of the current best results.

This paper studies how to construct a pseudorandom generator using hard lattice problems. We use a variation of the classical hard problem \emph{Inhomogeneous Small Integer Solution} ISIS of lattice, say \emph{Inhomogeneous Subset Sum Solution} ISSS. ISSS itself is a hash function. Proving the preimage sizes ISSS hash function images are almost the same, we construct a pseudorandom generator using the method in \cite{GKL93}. Also, we construct a pseudoentropy generator using the method in \cite{HILL99}. Most theoretical PRG constructions are not feasible in fact as they require rather long random bits as seeds. Our PRG construction only requires seed length to be $O(n^{2}\log_{2} n)$ which is feasible practically.

Recently, Shm et al. Proposed an efficient identity-based broadcast authentication scheme based on Tso et al.’s IBS scheme with message recovery to achieve security requirements in wireless sensor networks. They claim that their scheme can achieve security requirements and mitigated DOS attack by limiting the times of signature verification failures in wireless sensor networks (WSN). However, we found that the scheme cannot attain the security level as they claimed. We will demonstrate it in this article.

Modular multiplication of large integers is a performance-critical arithmetic operation of many public-key cryptosystems such as RSA, DSA, Diffie-Hellman (DH) and their elliptic curve-based variants ECDSA and ECDH. The computational cost of modular multiplication and related operations (e.g. exponentiation) poses a practical challenge to the widespread deployment of public-key cryptography, especially on embedded devices equipped with 8-bit processors (smart cards, wireless sensor nodes, etc.). In this paper, we describe basic software techniques to improve the performance of Montgomery modular multiplication on 8-bit AVR-based microcontrollers. First, we present a new variant of the widely-used hybrid method for multiple precision multiplication that is 10.6% faster than the original hybrid technique of Gura et al. Then, we discuss different hybrid Montgomery multiplication algorithms, including Hybrid Finely Integrated Product Scanning (HFIPS), and introduce a novel approach for Montgomery multiplication, which we call Hybrid Separated Product Scanning (HSPS). Finally, we show how to perform the modular subtraction of Montgomery reduction in a regular fashion without execution of conditional statements so as to counteract Simple Power Analysis (SPA) attacks. Our AVR implementation of the HFIPS and HSPS method outperforms the Montgomery multiplication of the MIRACL Crypto SDK by 21.6% and 14.3%, respectively, and is twice as fast as the modular multiplication of the TinyECC library.

Bitcoin is a potentially disruptive new crypto-currency based on a decentralized open-source protocol which is gradually gaining popularity. Perhaps the most important question that will affect Bitcoin's success, is whether or not it will be able to scale to support the high volume of transactions required from a global currency system. We investigate the restrictions on the rate of transaction processing in Bitcoin as a function of both the bandwidth available to nodes and the network delay, both of which lower the efficiency of Bitcoin's transaction processing. The security analysis done by Bitcoin's creator Satoshi Nakamoto~\cite{nakamoto2008bitcoin} assumes that block propagation delays are negligible compared to the time between blocks---an assumption that does not hold when the protocol is required to process transactions at high rates. We improve upon the original analysis and remove this assumption. Using our results, we are able to give bounds on the number of transactions per second the protocol can handle securely. Building on previously published measurements by Decker and Wattenhofer~\cite{Decker2013Information}, we show these bounds are currently more restrictive by an order of magnitude than the bandwidth needed to stream all transactions. We additionally show how currently planned improvements to the protocol, namely the use of transaction hashes in blocks (instead of complete transaction records), will dramatically alleviate these restrictions. Finally, we present an easily implementable modification to the way Bitcoin constructs its main data structure, the blockchain, that immensely improves security from attackers, especially when the network operates at high rates. This improvement allows for further increases in the number of transactions processed per second. We show that with our proposed modification, significant speedups can be gained in confirmation time of transactions as well. The block generation rate can be securely increased to more than one block per second -- a 600 fold speedup compared to today's rate, while still allowing the network to processes many transactions per second.

A revocation mechanism in cryptosystems for a large number of users is absolutely necessary for maintaining the security of whole systems. A revocable identity-based encryption (RIBE) provides an efficient revocation method in IBE in which a trusted authority periodically broadcasts an update key for non-revoked users and a user can decrypt a ciphertext if his private key is not revoked in the update key. Boldyreva, Goyal, and Kumar (CCS 2008) defined RIBE and proposed an RIBE scheme that uses a tree-based revocation encryption scheme to revoke users' private keys. However, this approach has an inherent limitation in that the number of private key elements and update key elements cannot be constant. In this paper, to overcome this limitation, we devise a new technique for RIBE and propose RIBE schemes with a constant number of private key elements. We achieve the following results: - We first devise a new technique for RIBE that combines a hierarchical IBE (HIBE) scheme and a public-key broadcast encryption (PKBE) scheme by using multilinear maps. In contrast to the previous technique for RIBE, our technique uses a PKBE scheme in bilinear maps for revocation to achieve short private keys and update keys. - Following our new technique for RIBE, we propose an RIBE scheme in three-leveled multilinear maps that combines the HIBE scheme of Boneh and Boyen (EUROCRYPT 2004) and the PKBE scheme of Boneh, Gentry, and Waters (CRYPTO 2005). The private key and update key of our scheme possess a constant number of group elements. We introduce a new complexity assumption in multilinear maps and prove the security of our scheme in the selective revocation list model. - Next, we propose another RIBE scheme with reduced public parameters by combining the HIBE scheme of Boneh and Boyen and the PKBE scheme of Boneh, Waters, and Zhandry (CRYPTO 2014), which uses multilinear maps. Compared with our first RIBE scheme, our second RIBE scheme requires high-leveled multilinear maps since the underlying PKBE scheme is based on high-leveled multilinear maps.

We build a system that provides succinct non-interactive zero-knowledge proofs (zk-SNARKs) for program executions on a von Neumann RISC architecture. The system has two components: a cryptographic proof system for verifying satisfiability of arithmetic circuits, and a circuit generator to translate program executions to such circuits. Our design of both components improves in functionality and efficiency over prior work, as follows. Our circuit generator is the first to be universal: it does not need to know the program, but only a bound on its running time. Moreover, the size of the output circuit depends additively (rather than multiplicatively) on program size, allowing verification of larger programs. The cryptographic proof system improves proving and verification times, by leveraging new algorithms and a pairing library tailored to the protocol. We evaluated our system for programs with up to 10,000 instructions, running for up to 32,000 machine steps, each of which can arbitrarily access random-access memory; and also demonstrated it executing programs that use just-in-time compilation. Our proofs are 230 bytes long at 80 bits of security, or 288 bytes long at 128 bits of security. Typical verification time is 5 milliseconds, regardless of the original program's running time.

PMI+ is a Multivariate Quadratic (MQ) public key algorithm used for encryption and decryption operations, and belongs to post quantum cryptography.We designs a hardware on FPGAs to efficiently implement PMI+ in this paper.Our main contributions are that,firstly, a hardware architecture of encryption and decryption of PMI+ is developed, and description of corresponding hardware algorithm is proposed;secondly, basic arithmetic units are implemented with higher efficiency that multiplication, squaring, vector dot product and power operation are implemented in full parallel;and thirdly, an optimized implementation for core module, including optimized large power operation, is achieved. The encryption and decryption hardware of PMI+ is efficiently realized on FPGA by the above optimization and improvement.It is verified by experiments that the designed hardware can complete an encryption operation within 497 clock cycles, and the clock frequency can be up to 145.6MHz,and the designed hardware can complete a decryption operation within 438 clock cycles wherein the clock frequency can be up to 37.04MHz.

Multivariate public key cryptography which relies on MQ (Multivariate Quadratic) problems is one of the main approaches to guarantee the security of communication in the post-quantum world. In this paper, we propose a combined MQ signature scheme based on the yet unbroken UOV (Unbalanced Oil and Vinegar) signature if parameters are properly chosen. Our scheme can not only reduce the public key size of the UOV signature, but also provide more tighter bound of security against chosen-message attack in the random oracle model. On the other hand, we propose a proxy signature scheme based on our proposed combined signature scheme. Additionally, we give a strict security proof for our proxy signature scheme. Finally, we present experiments for all of our proposed schemes and the baseline schemes. Comparisons with related schemes show that our work has some advantages on performance along with more strict security.

In a public-key encryption scheme, if a sender is not concerned about the security of a message and is unwilling to generate costly randomness, the security of the encrypted message can be compromised. In this work, we characterize such \emph{lazy parties}, who are regraded as honest parties, but are unwilling to perform a costly task when they are not concerned about the security. Specifically, we consider a rather simple setting in which the costly task is to generate randomness used in algorithms, and parties can choose either perfect randomness or a fixed string. We model lazy parties as rational players who behave rationally to maximize their utilities, and define a security game between the parties and an adversary. Since a standard secure encryption scheme does not work in the setting, we provide constructions of secure encryption schemes in various settings.

We consider the problem of outsourced computation that operates on encrypted inputs supplied by multiple independent parties. To facilitate fine-grained access control, it would be desirable if each party could encrypt her input under an appropriate access policy. Moreover, a party should only be authorized to decrypt the result of a computation performed on a set of encrypted inputs if his credentials satisfy the composition of all input policies. There has been limited success so far achieving homomorphic encryption in the functional setting; that is, for primitives such as Ciphertext-Policy Attribute Based Encryption (CP-ABE) and Identity Based Encryption (IBE). We introduce a new primitive that captures homomorphic encryption with support for access policies and policy composition. We then present a generic construction using CP-ABE and multikey Fully-Homomorphic encryption (FHE). Furthermore, we show that a CP-ABE scheme that is homomorphic for circuits of polylogarithmic depth in some parameter $m$ implies a CP-ABE scheme that is homomorphic for circuits of arity $m$ and unbounded depth.

We present a general construction of a rational secret-sharing protocol that converts any rational secret-sharing protocol to a protocol with an expected constant-round reconstruction. Our construction can be applied to protocols for synchronous channels, and preserves a strict Nash equilibrium of the original protocol. Combining with an existing protocol, we obtain the first expected constant-round protocol that achieves a strict Nash equilibrium with the optimal coalition resilience $\ceil{\frac{n}{2}}-1$, where $n$ is the number of players. Our construction can be extended to a construction that preserves the \emph{immunity} to unexpectedly behaving players. Then, for any constant $m \geq 1$, we obtain an expected constant-round protocol that achieves a Nash equilibrium with the optimal coalition resilience $\ceil{\frac{n}{2}}-m-1$ in the presence of $m$ unexpectedly behaving players. The same protocol also achieves a strict Nash equilibrium with coalition resilience $1$. We show that our protocol with immunity achieves the optimal coalition resilience among constant-round protocols with immunity with respect to both Nash and strict Nash equilibria.

We show how to extract an arbitrary polynomial number of simultaneously hardcore bits from any one-way function. In the case the one-way function is injective or has polynomially-bounded pre-image size, we assume the existence of indistinguishability obfuscation (iO). In the general case, we assume the existence of differing-input obfuscation (diO), but of a form weaker than full auxiliary-input diO. Our construction for injective one-way functions extends to extract hardcore bits on multiple, correlated inputs, yielding new D-PKE schemes. Of independent interest is a definitional framework for differing-inputs obfuscation in which security is parameterized by circuit-sampler classes.

The most widely accepted models in the security proofs of Authenticated Key Exchange protocols are the Canetti-Krawczyk and extended Canetti-Krawczyk models that admit different adversarial queries with ambiguities and incomparable strength. It is desirable to incorporate specific and powerful adversarial queries into a single unified security model and establish a more practical-oriented security notion. Concerning the security of one-round implicitly authenticated Diffie-Hellman key exchange protocols, we present a unified security model that has many advantages over the previous ones. In the model, a system environment is set up, all of adversarial queries are practically interpreted and definitely characterized through physical environment, and some rigorous rules of secret leakage are also specified. To demonstrate usability of our model, a new protocol based on the OAKE protocol is proposed, which satisfies the presented strong security notion and attains high efficiency. The protocol is proven secure in random oracle model under gap Diffie-Hellman assumption.

This paper is devoted to the characterization of hyper-bent functions. Several classes of hyper-bent functions have been studied, such as Charpin and Gong's $\sum\limits_{r\in R}\mathrm{Tr}_{1}^{n} (a_{r}x^{r(2^m-1)})$ and Mesnager's $\sum\limits_{r\in R}\mathrm{Tr}_{1}^{n}(a_{r}x^{r(2^m-1)}) +\mathrm{Tr}_{1}^{2}(bx^{\frac{2^n-1}{3}})$, where $R$ is a set of representations of the cyclotomic cosets modulo $2^m+1$ of full size $n$ and $a_{r}\in \mathbb{F}_{2^m}$. In this paper, we generalize their results and consider a class of Boolean functions of the form $\sum_{r\in R}\sum_{i=0}^{2}Tr^n_1(a_{r,i}x^{r(2^m-1)+\frac{2^n-1}{3}i}) +Tr^2_1(bx^{\frac{2^n-1}{3}})$, where $n=2m$, $m$ is odd, $b\in\mathbb{F}_4$, and $a_{r,i}\in \mathbb{F}_{2^n}$. With the restriction of $a_{r,i}\in \mathbb{F}_{2^m}$, we present the characterization of hyper-bentness of these functions with character sums. Further, we reformulate this characterization in terms of the number of points on hyper-elliptic curves. For some special cases, with the help of Kloosterman sums and cubic sums, we determine the characterization for some hyper-bent functions including functions with four, six and ten traces terms. Evaluations of Kloosterman sums at three general points are used in the characterization. Actually, our results can generalized to the general case: $a_{r,i}\in \mathbb{F}_{2^n}$. And we explain this for characterizing binomial, trinomial and quadrinomial hyper-bent functions.

Consider a joint distribution $(X,A)$ on a set ${\cal X}\times\{0,1\}^\ell$. We show that for any family ${\cal F}$ of distinguishers $f \colon {\cal X} \times \{0,1\}^\ell \rightarrow \{0,1\}$, there exists a simulator $h \colon {\cal X} \rightarrow \{0,1\}^\ell$ such that \begin{enumerate} \item no function in ${\cal F}$ can distinguish $(X,A)$ from $(X,h(X))$ with advantage $\epsilon$, \item $h$ is only $O(2^{3\ell}\epsilon^{-2})$ times less efficient than the functions in ${\cal F}$. \end{enumerate} For the most interesting settings of the parameters (in particular, the cryptographic case where $X$ has superlogarithmic min-entropy, $\epsilon > 0$ is negligible and ${\cal F}$ consists of circuits of polynomial size), we can make the simulator $h$ \emph{deterministic}. As an illustrative application of this theorem, we give a new security proof for the leakage-resilient stream-cipher from Eurocrypt'09. Our proof is simpler and quantitatively much better than the original proof using the dense model theorem, giving meaningful security guarantees if instantiated with a standard blockcipher like AES. Subsequent to this work, Chung, Lui and Pass gave an interactive variant of our main theorem, and used it to investigate weak notions of Zero-Knowledge. Vadhan and Zheng give a more constructive version of our theorem using their new uniform min-max theorem.

A widespread security claim of the Bitcoin system, presented in the original Bitcoin whitepaper, states that the security of the system is guaranteed as long as there is no attacker in possession of half or more of the total computational power used to maintain the system. This claim, however, is proved based on theoretically flawed assumptions. In the paper we analyze two kinds of attacks based on two theoretical flaws: the Block Discarding Attack and the Difficulty Raising Attack. We argue that the current theoretical limit of attacker's fraction of total computational power essential for the security of the system is in a sense not $\frac{1}{2}$ but a bit less than $\frac{1}{4}$, and outline proposals for protocol change that can raise this limit to be as close to $\frac{1}{2}$ as we want. The basic idea of the Block Discarding Attack has been noted as early as 2010, and lately was independently though-of and analyzed by both author of this paper and authors of a most recently pre-print published paper. We thus focus on the major differences of our analysis, and try to explain the unfortunate surprising coincidence. To the best of our knowledge, the second attack is presented here for the first time.

In this paper, we propose a new lightweight hash function supporting three different digest sizes: 80, 96 and 128 bits, providing preimage security from 64 to 120 bits, second preimage and collision security from 40 to 60 bits. LHash requires about 817 GE and 1028 GE with a serialized implementation. In faster implementations based on function $T$, LHash requires 989 GE and 1200 GE with 54 and 72 cycles per block, respectively. Furthermore, its energy consumption evaluated by energy per bit is also remarkable. LHash allows to make trade-offs among security, speed, energy consumption and implementation costs by adjusting parameters. The design of LHash employs a kind of Feistel-PG structure in the internal permutation, and this structure can utilize permutation layers on nibbles to improve the diffusion speed. The adaptability of LHash in different environments is good, since different versions of LHash share the same basic computing module. The low-area implementation comes from the hardware-friendly S-box and linear diffusion layer. We evaluate the resistance of LHash against known attacks and confirm that LHash provides a good security margin.

In this paper we propose an efficient and compact processor for a ring-LWE based encryption scheme. We present three optimizations for the Number Theoretic Transform (NTT) used for polynomial multiplication: we avoid pre-processing in the negative wrapped convolution by merging it with the main algorithm, we reduce the fixed computation cost of the twiddle factors and propose an advanced memory access scheme. These optimization techniques reduce both the cycle and memory requirements. Finally, we also propose an optimization of the ring-LWE encryption system that reduces the number of NTT operations from five to four resulting in a 20\% speed-up. We use these computational optimizations along with several architectural optimizations to design an instruction-set ring-LWE cryptoprocessor. For dimension 256, our processor performs encryption/decryption operations in 20/9 $\mu s$ on a Virtex 6 FPGA and only requires 1349 LUTs, 860 FFs, 1 DSP-MULT and 2 BRAMs. Similarly for dimension 512, the processor takes 48/21 $\mu s$ for performing encryption/decryption operations and only requires 1536 LUTs, 953 FFs, 1 DSP-MULT and 3 BRAMs. Our processors are therefore more than three times smaller than the current state of the art hardware implementations, whilst running somewhat faster.

Many profiling power analysis attacks estimate the multivariate probability distribution using a profiling step, and thus, can optimally combine the leakages of multiple sample points. Though there exist several approaches like filtering, Principal Component Analysis for combining the leakages of multiple sample points in non-profiling DPA, their optimality has been been rarely studied. We study the issue of optimally combining the leakages of multiple sample points in non-profiling DPA attacks using a linear function. In this work, our contributions are three-fold: 1) we first derive a relation between the success rate of a CPA attack and the SNR of the power traces, 2) we introduce a multivariate leakage model for Virtex-5 FPGA device, and 3) using the proposed multivariate leakage model, we devise linear filters to maximize the SNR of the output leakage which, in turn, optimizes the success rate of the CPA attacks in a non-profiling setup.

We develop new schemes for deterministically updating a stored cryptographic key that provide security against an internal adversary who can control the update computation and leak bounded amounts of information to the outside world. Our schemes are much more efficient than the previous schemes for this model, due to Dziembowski, Kazana and Wichs (CRYPTO 2011). Specifically, our update operation runs in time quasilinear in the key length, rather than quadratic, while offering a similar level of leakage resilience. In order to design our scheme, we strengthen the connections between the model of Dziembowski et al. and ``pebbling games'', showing that random-oracle-based key evolution schemes are secure as long as the graph of the update function's calls to the oracle has appropriate combinatorial properties. This builds on a connection between pebbling and the random oracle model first established by Dwork, Naor and Wee (CRYPTO 2005). Our scheme's efficiency relies on the existence (which we show) of families of ``local'' bipartite expander graphs of constant degree.

Electronic voting systems are among the most security critical distributed systems. Different trust concepts are implemented to mitigate the risk of conspiracies endangering security properties. These concepts render systems often very complex and end users no longer recognize whom they need to trust. Correspondingly, specific trust considerations are necessary to support users. Recently, resilience terms have been proposed in order to express, which entities can violate the addressed security properties in particular by illegal collaborations. However, previous works derived these resilience terms manually. Thus, successful attacks can be missed. Based on this approach, we propose a framework to formally and automatically derive these terms. Our framework comprises a knowledge calculus, which allows us to model knowledge and reason about knowledge of collaborating election entities. The introduced framework is applied to deduce previously manually derived resilience terms of three remote electronic voting systems, namely Polyas, Helios and the Estonian voting system. Thereby, we were able to discover mistakes in previous derivations.

We construct a 1-round delegation scheme (i.e., argument-system) for every language computable in time t=t(n), where the running time of the prover is poly(t) and the running time of the verifier is n*polylog(t). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. Our construction relies on the existence of a computational sub-exponentially secure private information retrieval (PIR) scheme. The proof exploits a curious connection between the problem of computation delegation and the model of multi-prover interactive proofs that are sound against no-signaling (cheating) strategies, a model that was studied in the context of multi-prover interactive proofs with provers that share quantum entanglement, and is motivated by the physical principle that information cannot travel faster than light. For any language computable in time t=t(n), we construct a multi-prover interactive proof (MIP) that is sound against no-signaling strategies, where the running time of the provers is poly(t), the number of provers is polylog(t), and the running time of the verifier is n*polylog(t). In particular, this shows that the class of languages that have polynomial-time MIPs that are sound against no-signaling strategies, is exactly EXP. Previously, this class was only known to contain PSPACE. To convert our MIP into a 1-round delegation scheme, we use the method suggested by Aiello et-al (ICALP, 2000), which makes use of a PIR scheme. This method lacked a proof of security. We prove that this method is secure assuming the underlying MIP is secure against no-signaling provers.

The enforcement of sensitive policies in untrusted environments is still an open challenge for policy-based systems. On the one hand, taking any appropriate security decision requires access to these policies. On the other hand, if such access is allowed in an untrusted environment then confidential information might be leaked by the policies. The key challenge is how to enforce sensitive policies and protect content in untrusted environments. In the context of untrusted environments, we mainly distinguish between outsourced and distributed environments. The most attractive paradigms concerning outsourced and distributed environments are cloud computing and opportunistic networks, respectively. In this dissertation, we present the design, technical and implementation details of our proposed policy-based access control mechanisms for untrusted environments. First of all, we provide full confidentiality of access policies in outsourced environments, where service providers do not learn private information about policies during the policy deployment and evaluation phases. Our proposed architecture is such that we are able to support expressive policies and take into account contextual information before making any access decision. The system entities do not share any encryption keys and even if a user is deleted, the system is still able to perform its operations without requiring any action. For complex user management, we have implemented a policy-based Role-Based Access Control (RBAC) mechanism, where users are assigned roles, roles are assigned permissions and users execute permissions if their roles are active in the session maintained by service providers. Finally, we offer the full-fledged RBAC policies by incorporating role hierarchies and dynamic security constraints. In opportunistic networks, we protect content by specifying expressive access control policies. In our proposed approach, brokers match subscriptions against policies associated with content without compromising privacy of subscribers. As a result, an unauthorised broker neither gains access to content nor learns policies and authorised nodes gain access only if they satisfy fine-grained policies specified by publishers. Our proposed system provides scalable key management in which loosely-coupled publishers and subscribers communicate without any prior contact. Finally, we have developed a prototype of the system that runs on real smartphones and analysed its performance.

The notion of differing-inputs obfuscation (diO) was introduced by Barak et al. (CRYPTO 2001). It guarantees that, for any two circuits $C_0, C_1$, if it is difficult to come up with an input $x$ on which $C_0(x) \neq C_1(x)$, then it should also be difficult to distinguish the obfuscation of $C_0$ from that of $C_1$. This is a strengthening of indistinguishability obfuscation, where the above is only guaranteed for circuits that agree on all inputs: $C_0(x) = C_1(x)$ for all $x$. Two recent works of Ananth et al. (ePrint 2013) and Boyle et al. (TCC 2014) study the notion of diO in the setting where the attacker is also given some auxiliary information related to the circuits, showing that this notion leads to many interesting applications. In this work, we show that the existence of general-purpose diO with general auxiliary input has a surprising consequence: it implies that a specific circuit $C^*$ with specific auxiliary input $\aux^*$ cannot be obfuscated in a way that hides some specific information. In other words, under the conjecture that such special-purpose obfuscation exists, we show that general-purpose diO cannot exist. We do not know if this special-purpose obfuscation assumption is implied by diO itself, and hence we do not get an unconditional impossibility result. However, the special-purpose obfuscation assumption is a falsifiable assumption which we do not know how to break for candidate obfuscation schemes. Showing the existence of general-purpose diO with general auxiliary input would necessitate showing how to break this assumption. We also show that the special-purpose obfuscation assumption implies the impossibility of extractable witness encryption with auxiliary input, a notion proposed by Goldwasser et al. (CRYPTO 2013). A variant of this assumption also implies the impossibility of ``output-only dependent'' hardcore bits for general one-way functions, as recently constructed by Bellare and Tessaro (ePrint 2013) using diO.

The Side Channel Analysis is now a classic way to retrieve a secret key in the smart-card world. Unfortunately, most of the ensuing attacks require the plaintext or the ciphertext used by the embedded algorithm. In this article, we present a new method for exploiting the leakage of a device without this constraint. Our attack is based on a study of the leakage distribution of internal data of a cryptographic function and can be performed not only at the beginning or the end of the algorithm, but also at every instant that involves the secret key. This paper focuses on the distribution study and the resulting attack. We also propose a way to proceed in a noisy context using smart distances. We validate our proposition by practical results on an AES128 software implemented on a ATMega2561 and on the DPA contest v4.

We reformalize and recast dual-receiver encryption (DRE) proposed in CCS '04, a public-key encryption (PKE) scheme for encrypting to two independent recipients in one shot. We start by defining the crucial soundness property for DRE, which ensures that two recipients will get the same decryption result. While conceptually simple, DRE with soundness turns out to be a powerful primitive for various goals for PKE, such as complete non-malleability (CNM) and plaintext-awareness (PA). We then construct practical DRE schemes without random oracles under the Bilinear Decisional Diffie-Hellman assumption, while prior approaches rely on random oracles or inefficient non-interactive zero-knowledge proofs. Finally, we investigate further applications or extensions of DRE, including DRE with CNM, combined use of DRE and PKE, strengthening two types of PKE schemes with plaintext equality test, off-the-record messaging with a stronger notion of deniability, etc.

Many computers emit a high-pitched noise during operation, due to vibration in some of their electronic components. These acoustic emanations are more than a nuisance: they can convey information about the software running on the computer, and in particular leak sensitive information about security-related computations. In a preliminary presentation (Eurocrypt'04 rump session), we have shown that different RSA keys induce different sound patterns, but it was not clear how to extract individual key bits. The main problem was that the acoustic side channel has a very low bandwidth (under 20 kHz using common microphones, and a few hundred kHz using ultrasound microphones), many orders of magnitude below the GHz-scale clock rates of the attacked computers. In this paper we describe a new acoustic cryptanalysis key extraction attack, applicable to GnuPG's current implementation of RSA. The attack can extract full 4096-bit RSA decryption keys from laptop computers (of various models), within an hour, using the sound generated by the computer during the decryption of some chosen ciphertexts. We experimentally demonstrate that such attacks can be carried out, using either a plain mobile phone placed next to the computer, or a more sensitive microphone placed 4 meters away. Beyond acoustics, we demonstrate that a similar low-bandwidth attack can be performed by measuring the electric potential of a computer chassis. A suitably-equipped attacker need merely touch the target computer with his bare hand, or get the required leakage information from the ground wires at the remote end of VGA, USB or Ethernet cables.

In this paper we present three digital signature schemes with tight security reductions. Our first signature scheme is a particularly efficient version of the short exponent discrete log based scheme of Girault et al. (J. of Cryptology 2006). Our scheme has a tight reduction to the decisional Short Discrete Logarithm problem, while still maintaining the non-tight reduction to the computational version of the problem upon which the original scheme of Girault et al. is based. The second signature scheme we construct is a modification of the scheme of Lyubashevsky (Asiacrypt 2009) that is based on the worst-case hardness of the shortest vector problem in ideal lattices. And the third scheme is a very simple signature scheme that is based directly on the hardness of the Subset Sum problem. We also present a general transformation that converts what we term lossy identification schemes into signature schemes with tight security reductions. We believe that this greatly simplifies the task of constructing and proving the security of such signature schemes.

Many RFID authentication protocols have been proposed to provide desired security and privacy level for RFID systems. Almost all of these protocols are based symmetric cryptography because of the limited resources of RFID tags. Recently Cheng et. al have been proposed an RFID security protocol based on chaotic maps. In this paper, we analyze the security of this protocol and discover its vulnerabilities. We firstly present a de-synchronization attack in which a passive adversary makes the shared secrets out-of-synchronization by eavesdropping just one protocol session. We secondly present a secret disclosure attack in which a passive adversary extracts secrets of a tag by eavesdropping just one protocol session. An adversary having the secrets of the tag can launch some other attacks.

Ecash is a concept of electronic cash which would allow users to carry money in form of digital coins. Transaction can be done both offline and online in absence of a third party/financial institution. This paper proposes an offline model which supports multiple usage of transferable ecoin. The protocol is based on RSA, digital signature and a two-step encryption process. In this two step encryption, the user account details are encrypted in the coin using unique numbers in each step. The first encryption takes place during the successful receipt of the coin, where a receive end number is used for encryption,which is unique for every receipt. The second step of encryption takes place during successful spending of the coin,where a spending end receive number is used for encryption, which is unique for every spending of the coin. These two unique numbers comprise the major part of encryption in this model, prevents double spending and preserves user anonymity.

We propose a tool for automatic search for differential trails in ARX ciphers. By introducing the concept of a partial difference distribution table (pDDT) we extend Matsui's algorithm, originally proposed for DES-like ciphers, to the class of ARX ciphers. To the best of our knowledge this is the first application of Matsui's algorithm to ciphers that do not have S-boxes. The tool is applied to the block ciphers TEA, XTEA, SPECK and RAIDEN. For RAIDEN we find an iterative characteristic on all 32 rounds that can be used to break the full cipher using standard differential cryptanalysis. This is the first cryptanalysis of the cipher in a non-related key setting. Differential trails on 9, 10 and 13 rounds are found for SPECK32, SPECK48 and SPECK64 respectively. The 13 round trail covers half of the total number of rounds. These are the first public results on the security analysis of SPECK. For TEA multiple full (i.e. not truncated) differential trails are reported for the first time, while for XTEA we confirm the previous best known trail reported by Hong et al. We also show closed formulas for computing the exact additive differential probabilities of the left and right shift operations. The source code of the tool is publicly available as part of a larger toolkit for the analysis of ARX at the following address: https://github.com/vesselinux/yaarx .