Protocol authentication properties are generally trace-based, meaning that authentication holds for the protocol if authentication holds for individual traces (runs of the protocol and adversary). Computational secrecy conditions, on the other hand, often are not trace based: the ability to computationally distinguish a system that transmits a secret from one that does not is measured by overall success on the \textit{set} of all traces of each system. This presents a challenge for inductive or compositional methods: induction is a natural way of reasoning about traces of a system, but it does not appear applicable to non-trace properties. We therefore investigate the semantic connection between trace properties that could be established by induction and non-trace-based security requirements. Specifically, we prove that a certain trace property implies computational secrecy and authentication properties, assuming the encryption scheme provides chosen ciphertext security and ciphertext integrity. We also prove a similar theorem for computational secrecy assuming Decisional Diffie-Hellman and a chosen plaintext secure encryption scheme.

The security notion of indifferentiability was proposed by Maurer, Renner, and Holenstein in 2004. In 2005, Coron, Dodis, Malinaud, and Puniya discussed the indifferentiability of hash functions. They showed that the Merkle-Damgaard construction is not secure in the sense of indifferentiability. In this paper, we analyze the security of single-block-length and rate-1 compression functions in the sense of indifferentiability. We formally show that all single-block-length and rate-1 compression functions, which include the Davies-Meyer compression function, are insecure. Furthermore, we show how to construct a secure single-block-length and rate-1 compression function in the sense of indifferentiability. This does not contradict our result above.

We construct an efficient identity based encryption scheme from pairing. The basic version of the new scheme is provably secure against chosen plaintext attack, and the full version of the new scheme is provably secure against adaptive chosen ciphertext attack. Our scheme is based on a new assumption (decision weak bilinear Diffie-Hellman assumption ) which is no stronger than decision bilinear Diffie-Hellman assumption.

A time-bound hierarchical key assignment scheme is a method to assign time-dependent encryption keys to a set of classes in a partially ordered hierarchy, in such a way that each class in the hierarchy can compute the keys of all classes lower down in the hierarchy, according to temporal constraints. In this paper we propose new constructions for time-bound hierarchical key assignment schemes which are provably secure with respect to key indistinguishability. Our constructions use as a building block any provably-secure hierarchical key assignment scheme without temporal constraints and exhibit a tradeoff among the amount of private information held by each class, the amount of public data, the complexity of key derivation, and the computational assumption on which their security is based. Moreover, the proposed schemes support updates to the access hierarchy with local changes to the public information and without requiring any private information to be re-distributed.

Branch Prediction Analysis has been proposed as an attack method to obtain key bits from a cryptographic application. In this report, we put forth several solutions to avoid or prevent this attack. The reported countermeasures require only minimal hardware support that is commonly available in modern superscalar processors.

Recently, Shoichi Hirose \cite{Hirose06} proposed several double block length (DBL) hash functions. Each DBL hash function uses a constant which has a role to make the DBL hash function collision-resistant in the ideal cipher model. However, we have to instantiate a block cipher. In this paper, we show that the constant may be used as a trapdoor to help a attacker to find a collision easily. In case of 256-bit output size, we can find a collision with the complexity $2^{64}$. This is a gap between the security of the DBL hash function in the ideal cipher model and the security of the DBL hash function based on any block cipher.

A new public key cryptosystem, called REESSE1+, was proposed. REESSE1 consists of two primitive algorithms, a public key encryptio/decryption algorithm and a digital signature algorithm. We give some analysis to REESSE1+, and show that the system is totally unsecure. We show how to derive the private key from the public key. As the same time, we also show how to forge signatures for any messages, given two valid signatures.

A hierarchical key assignment scheme is a method to assign some private information and encryption keys to a set of classes in a partially ordered hierarchy, in such a way that the private information of a higher class can be used to derive the keys of all classes lower down in the hierarchy. In this paper we design and analyze hierarchical key assignment schemes which are provably-secure and support dynamic updates to the hierarchy with local changes to the public information and without requiring any private information to be re-distributed. We first consider the problem of constructing a hierarchical key assignment scheme by using as a building block a symmetric encryption scheme. We propose a new construction which is provably secure with respect to key indistinguishability, requires a single computational assumption, and improves on previous proposals. Then, we show how to reduce key derivation time at the expense of an increment of the amount of public information, by improving a previous result. Finally, we show how to construct a hierarchical key assignment scheme by using as a building block a public-key broadcast encryption scheme. In particular, one of our constructions provides constant private information and public information linear in the number of classes in the hierarchy.

IDEA is a block cipher designed by Xuejia Lai and James L. Massey and was first described in 1991. IDEA does not vary the constant in its key schedule. In \cite{ChYu06}, Donghoon Chang and Moti Yung showed that there may be a weakness of hash function based on block cipher whose key schedule does not use various constants. Based on their result, we investigate the security of double block length compression functions based on the block cipher IDEA such that the key size of IDEA is 128 bits and its block length is 64 bits. We use the double block length hash functions proposed by Shoichi Hirose in the second hash workshop in 2006 \cite{Hirose06}. Then, we can easily find a near-collision by hand. And also, for a constant $c$ of DBL hash functions, we can find a collision by hand. This means that the constant $c$ may be used as a trapdoor to make the attacker find collision easily.

We present the dynamic cryptographic hash function, a new type of hash function which takes two parameters instead of one. The additional parameter, the security parameter, specifies the internal workings and size of the digest produced. We provide a formal definitions for a dynamic cryptographic hash function and for the traditional security properties, modified for dynamic hash functions. Two additional properties, security parameter collision resistance and digest resistance, are also defined. The additional properties are motivated by scenarios where a dynamic hash functions more cleanly provides a solution to a typical cryptographic problem.

Password-authenticated key exchange (PAKE) allows two or multiple parties to share a session key using a human-memorable password only. PAKE has been applied in various environments, especially in the "clientserver" model of remotely accessed systems. Designing a secure PAKE scheme has been a challenging task because of the low entropy of password space and newly recognized attacks in the emerging environments. In this paper, we study PAKE for multi-party with different passwords which allows group users with different passwords to agree on a common session key by the help of a trusted server using their passwords only. In this setting, the users do not share a password between themselves but only with the server. The fundamental security goal of PAKE is security against dictionary attacks. We present the first two provably secure protocols for this problem in the standard model under the DDH assumption; our first protocol is designed to provide forward secrecy and to be secure against known-key attacks. The second protocol is designed to additionally provide key secrecy against curious servers. The protocols require a constant number of rounds.

Most of the recent cryptanalysis on symmetric key ciphers have focused on algebraic attacks. The cipher being attacked is represented as a non-linear equation system, and various techniques (Buchberger, F4/F5, XL, XSL) can be tried in order to solve the system, thus breaking the cipher. The success of these attacks has been limited so far. In this paper we take a different approach to the problem of solving non-linear equation systems, and propose a new method for solving them. Our method differs from the others in that the equations are not represented as multivariate polynomials, and that the core of the algorithm for finding the solution can be seen as message-passing on a graph. Bounds on the complexities for the main algorithms are presented and they compare favorably with the known bounds. The methods have also been tested on reduced-round versions of DES with good results. This paper was posted on ECRYPT's STVL website on January 16th 2006.

In this paper we present an algorithm for computing the bilinear pairings on a family of non-supersingular elliptic curves with non-trivial automorphisms. We obtain a short iteration loop in Miller's algorithm using non-trivial efficient automorphisms. The proposed algorithm is as efficient as Scott's algorithm in [12].

In a proxy re-encryption scheme a semi-trusted proxy converts a ciphertext for Alice into a ciphertext for Bob {\em without} seeing the underlying plaintext. A number of solutions have been proposed in the public-key setting. In this paper, we address the problem of Identity-Based proxy re-encryption, where ciphertexts are transformed from one {\it identity} to another. Our schemes are compatible with current IBE deployments and do not require any extra work from the IBE trusted-party key generator. In addition, they are non-interactive and one of them permits multiple re-encryptions. Their security is based on a standard assumption (DBDH) in the random oracle model.

Using a model based on \textit{probabilistic functions} (\textit{PF}), it's introduced the concept of \textit{perfect zero knowledge} (\textit{PZK}) \textit{commitment scheme} (\textit{CS}) allowing \textit{quasigroupic} \textit{homomorphic commitment} (\textit{QHC}). Using \textit{QHC} of $+_m$ (modular sum in $\mathbb{Z}_m$), application is considered in interactive argument systems (\textit{IAS}) for several languages. In four of the examples -- generalized nand ($\Lnandalpha$), string equality ($\left[=_{\left(m,\alpha,\right)}\right]$), string inequality ($\left[\neq_{\left(m,\alpha,\right)}\right]$) and graph three-colourations ($G3C$) -- complexity improvements are obtained, in comparison to other established results. Motivation then arises to define a general framework for \textit{PZK}-\textit{IAS} for membership in language with committed alphabet (\textit{MLCA}), such that the properties of soundness and \textit{PZK} result from high-level parametrizable aspects. A general simulator is constructed for sequential and (most interestingly) for parallel versions of execution. It therefore becomes easier to conceptualize functionalities of this kind of \textit{IAS} without the consideration of low level aspects of cryptographic primitives. The constructed framework is able to embrace \AcroCS\; allowing \textit{QHC} of functions that are not themselves quasigroupic. Several theoretical considerations are made, namely recognizing a necessary requirements to demand on an eventual \AcroCS \;allowing \textit{QHC} of some complete function in a Boolean sense.

Pairing-friendly fields are finite fields that are suitable for the implementation of cryptographic bilinear pairings. In this paper we review multiplication and squaring methods for pairing-friendly fields $\fpk$ with $k \in \{2,3,4,6\}$. For composite $k$, we consider every possible towering construction. We compare the methods to determine which is most efficient based on the number of basic $\fp$ operations, as well as the best constructions for these finite extension fields. We also present experimental results for every method.

In this paper we show that the group key agreement protocol proposed by Tseng suffers from a number of serious security vulnerabilities.

We present an attack on one of the Hidden Pairing schemes proposed by Dent and Galbraith. We drastically reduce the number of variables necessary to perform a multivariate attack and in some cases we can completely recover the private key. Our attack relies only on knowledge of the public system parameters.

At CMS 2006 Bringer et al. show how to conceal the algebraic structure of a ``traceable block cipher'' by adding perturbations to its description. We here exploit and strengthen their ideas by further perturbing the representation of a cipher towards a white box implementation. Our technique is quite general, and we apply it -- as a challenging example in the domain of white box cryptography -- to a variant of the block cipher AES.

The recent collision attacks on the MD hash function family do not depend on the constants used in the function, but rather on its structure (i.e., changing the constants will not affect the differential analysis based attacks). Thus, is seems that the role of constants in maintaining security and preventing these attacks is unclear, at best, for this case and in particular fixing or varying the constants will not matter for these analyses. % In this work we present a methodological investigation into the case of block-cipher based PGV hash functions family, and investigate the importance of constants in securing these designs. % To this end we consider the twelve variants of the PGV family that yield secure hash in the generic ideal cipher case (as was shown by Black, Rogaway and Shrimpton), but consider them under concrete instantiation. % % To investigate the role of constant in the key derivation procedure we just ignore the constants. In this more uniform setting we further consider a very regular cipher, namely AES modified to have Mixcolumn also in the last round (which should still be a strong cipher). % Analyzing this modified-AES based hashing, we show that with about 16\% probability we can find collisions with complexity $2^{49}$ (much smaller than the birthday attack complexity $2^{64}$). While we do not claim to break the AES based version, this nevertheless shows that constants in block cipher have an important role in resisting collision attack (in particular there is a need to vary the constant). It also shows that (in the symmetric modified version) merely the concrete AES structure does not guarantee the security of AES-based hash function (shown secure under the ideal cipher model). This is undesirable and non-robust, because this means that even though a block cipher has complicated structures in its round function and its key scheduling algorithm, we can not have a confidence about the security of hash functions based solely on it (note that there are several block ciphers such as IDEA, 3-key triple DES which do not use any constants). % Given the above methodological findings, we suggest new AES-based hash function constructions (essentially modified PGV) which can be generalized to any block cipher. The functions inherit the security under the ideal cipher model on the one hand, while, on the other hand, concretely assure in their structure that the weakness exhibited herein is dealt with.

We use the Bateman-Horn conjecture to study the order of the set of $\mathbb{F}_q$-rational points of primitive subgroups that arise in torus-based cryptography. We provide computational evidence to support the heuristics and make some suggestions regarding parameter selection for torus-based cryptography.

What does it mean for a cryptographic protocol to be "secure"? Capturing the security requirements of cryptographic tasks in a meaningful way is a slippery business: On the one hand, we want security criteria that prevent "all feasible attacks" against a protocol. On the other hand, we want our criteria to not be overly restrictive; that is, we want them to accept those protocols that do not succumb to "feasible attacks". This tutorial studies a general methodology for defining security of cryptographic protocols. The methodology, often dubbed the "trusted party paradigm", allows for defining the security requirements of practically any cryptographic task in a unified and natural way. We first review a basic formulation that captures security in isolation from other protocol instances. Next we address the secure composition problem, namely the vulnerabilities resulting from the often unexpected interactions among different protocol instances that run alongside each other in the same system. We demonstrate the limitations of the basic formulation and review a formulation that guarantees security of protocols even in general composite systems.

In \cite{Cao}, a putative framing ``attack'' against the ACJT group signature scheme \cite{ACJT00} is presented. This note shows that the attack framework considered in \cite{Cao} is \emph{invalid}. As we clearly illustrate, there is \textbf{no security weakness} in the ACJT group signature scheme as long as all the detailed specifications in \cite{ACJT00} are being followed.

An obfuscation O of a function F should satisfy two requirements: firstly, using O it should be possible to evaluate F; secondly, O should not reveal anything about F that cannot be learnt from oracle access to F. Several definitions for obfuscation exist. However, most of them are either too weak for or incompatible with cryptographic applications, or have been shown impossible to achieve, or both. We give a new definition of obfuscation and argue for its reasonability and usefulness. In particular, we show that it is strong enough for cryptographic applications, yet we show that it has the potential for interesting positive results. We illustrate this with the following two results: - If the encryption algorithm of a secure secret-key encryption scheme can be obfuscated according to our definition, then the result is a secure public-key encryption scheme. - A uniformly random point function can be easily obfuscated according to our definition, by simply applying a one-way permutation. Previous obfuscators for point functions, under varying notions of security, are either probabilistic or in the random oracle model (but work for arbitrary distributions on the point function). On the negative side, we show that - Following Hada and Wee, any family of deterministic functions that can be obfuscated according to our definition must already be ``approximately learnable.'' Thus, many deterministic functions cannot be obfuscated. However, a probabilistic functionality such as a probabilistic secret-key encryption scheme can potentially be obfuscated. In particular, this is possible for a public-key encryption scheme when viewed as a secret-key scheme. - There exists a secure probabilistic secret-key encryption scheme that cannot be obfuscated according to our definition. Thus, we cannot hope for a general-purpose cryptographic obfuscator for encryption schemes.

Preneel, Govaerts, and Vandewalle[14](PGV) considered 64 most basic ways to construct a hash function from a block cipher, and regarded 12 of those 64 schemes as secure. Black, Pogaway and Shrimpton[3](BRS) provided a formal and quantitative treatment of those 64 constructions and proved that, in black-box model, the 12 schemes ( group-1 ) that PGV singled out as secure really are secure. By step ping outside of the Merkle-Damgard[4] approach to analysis, an additional 8 (group-2) of the 64 schemes are just as collision resistant as the first group of schemes. Tight upper and lower bounds on collision resistance of those 20 schemes were given. In this paper, those collision resistance and preimage resistance bounds are improved, which shows that, in black box model, collision bounds of those 20 schemes are same. In Group-1 schemes, 8 out of 12 can find fixed point easily. Bounds on second preimage, multicollisions of Joux[6], fixed-point multicollisons[8] and combine of the two kinds multicollisions are also given. From those bounds, Group-1 schemes can also be deviled into two group.

This essay relates to a recent article of Koblitz & Menezes (Cryptology ePrint Report 2004/152) that ``criticizes several typical `provable security' results'' and argues that the ``theorem-proof paradigm of theoretical mathematics is often of limited relevance'' to cryptography. Although it feels ridiculous to answer such a claim, we undertake to do so in this essay. In particular, we point out some of the fundamental philosophical flaws that underly the said article and some of its misconceptions regarding theoretical research in Cryptography in the last quarter of a century.

`Provably Secure FFT Hashing' (We call FFT-Hash in this paper) was suggested by Lyubashevsky et al.. in Second Hash Workshop in Aug. 2006. This paper shows preimage attacks on hash functions based on three modes of FFT-Hash. In case of `Nano' whose output size is 513 bits, we can find a preimage with complexity $2^{385}$. In case of `Mini' whose output size is 1025 bits, we can find a preimage with complexity $2^{769}$. In case of `Mini' whose output size is 28672 bits, we can find a preimage with complexity $2^{24576}$. This means that the structure of FFT-Hash is weak in the viewpoint of the preimage resistance. We recommend that FFT-Hash can not be used in case of the output size less than 256 bits because the full security against the preimage attack are crucial in such a short output size. And also we should not chop the hash output in order to get a short hash output like SHA-224 and SHA-384, because for example we can find a preimage with complexity $2^{128}$ (not $2^{256}$) in case of `Nano' with chopping 257 bits whose hash output is 256 bits.

The nonlinearity profile of a Boolean function (i.e. the sequence of its minimum Hamming distances $nl_r(f)$ to all functions of degrees at most $r$, for $r\geq 1$) is a cryptographic criterion whose role against attacks on stream and block ciphers has been illustrated by many papers. It plays also a role in coding theory, since it is related to the covering radii of Reed-Muller codes. We introduce a method for lower bounding its values and we deduce bounds on the second order nonlinearity for several classes of cryptographic Boolean functions, including the Welch and the multiplicative inverse functions (used in the S-boxes of the AES). In the case of this last infinite class of functions, we are able to bound the whole profile, and we do it in an efficient way when the number of variables is not too small. This allows showing the good behavior of this function with respect to this criterion as well.

Copyrighting a function is the process of embedding hard-to-remove marks in the function's implementation while retaining its original functionality. Here we consider the above problem in the context of public-key encryption and we parallel the process of copyrighting a function to the process of designing traitor tracing schemes. We derive two copyrighted public-key encryption functions for the $2$-key setting, solving an open question left by earlier work with respect to copyrighting discrete-logarithm based functions. We then follow a modular design approach and show how to elevate the $2$-key case to the multi-user setting, employing collusion secure codes. Our methodology provides a general framework for constructing public-key traitor tracing schemes that has the interesting property that the transmission rate remains constant if the plaintext size can be calibrated to reach an appropriate minimal length. Achieving a constant rate, i.e., constant expansion in the size of ciphertexts and keys, is an important open problem in the area of traitor tracing schemes. Our design shows how one can solve it for settings that accommodate the required plaintext calibration (e.g., when a bulk of symmetric cipher keys can be encrypted in one message). Our constructions support ``black-box traitor tracing'', the setting  where the tracer only accesses the decryption box in input/output queries/responses. For the first time here we provide a modeling of black-box traitor tracing that takes into account adversarially chosen plaintext distributions, a security notion we call {\em semantic black-box traceability}. In order to facilitate the design of schemes with semantic black-box traceability we introduce as part of our modular design approach a simpler notion called semantic user separability and we show that  this notion implies semantic black-box traceability. In the multi-user setting our constructions also demonstrate how one can derive public-key traitor tracing by reducing the required ``marking assumption'' of collusion-secure codes to cryptographic hardness assumptions.

The integer addition is often applied in ciphers as a cryptographic means. In this paper we will present some results about the linear approximating for the integer addition.

A random system is the abstraction of the input-output behavior of any kind of discrete system, in particular cryptographic systems. Many aspects of cryptographic security analyses and proofs can be seen as the proof that a certain random system (e.g. a block cipher) is indistinguishable from an ideal system (e.g. a random permutation), for different types of distinguishers. This paper presents a new generic approach to proving upper bounds on the distinguishing advantage of a combined system, assuming upper bounds of various types on the component systems. For a general type of combination operation of systems (including the combination of functions or the cascade of permutations), we prove two amplification theorems. The first is a direct-product theorem, similar in spirit to the XOR-Lemma: The distinguishing advantage (or security) of the combination of two (possibly stateful) systems is twice the product of the individual distinguishing advantages, which is optimal. The second theorem states that the combination of systems is secure against some strong class of distinguishers, assuming only that the components are secure against some weaker class of attacks. As a corollary we obtain tight bounds on the adaptive security of the cascade and parallel composition of non-adaptively (or only random-query) secure component systems. A key technical tool of the paper is to show a tight two-way correspondence, previously only known to hold in one direction, between the distinguishing advantage of two systems and the probability of provoking an appropriately defined event on one of the systems.

Two settings are typically considered for secure multiparty computation, depending on whether or not a majority of the parties are assumed to be honest. Protocols designed under this assumption provide full security (and, in particular, guarantee output delivery and fairness) when this assumption is correct; however, if half or more of the parties are dishonest then security is completely compromised. On the other hand, protocols tolerating arbitrarily-many faults do not provide fairness or guaranteed output delivery even if only a single party is dishonest. It is natural to wonder whether it is possible to achieve the ''best of both worlds''; namely, a single protocol that simultaneously achieves the best possible security in both the above settings. Ishai, et al. (Crypto 2006) recently addressed this question, and ruled out constant-round protocols of this type. As our main result, we completely settle the question by ruling out protocols using any (expected) polynomial number of rounds. Given this stark negative result, we ask what can be achieved if we are willing to assume simultaneous message transmission (or, equivalently, a non-rushing adversary). In this setting, we show that impossibility still holds for logarithmic-round protocols. We also show, for any polynomial $p$, a protocol (whose round complexity depends on $p$) that can be simulated to within closeness $O(1/p)$.

We create a credential system that lets a user anonymously authenticate at most $n$ times in a single time period. A user withdraws a dispenser of $n$ e-tokens. She shows an e-token to a verifier to authenticate herself; each e-token can be used only once, however, the dispenser automatically refreshes every time period. The only prior solution to this problem, due to Damgård et al.~[DDP05], uses protocols that are a factor of $k$ slower for the user and verifier, where $k$ is the security parameter. Damgård et al. also only support one authentication per time period, while we support $n$. Because our construction is based on e-cash, we can use existing techniques to identify a cheating user, trace all of her e-tokens, and revoke her dispensers. We also offer a new anonymity service: glitch protection for basically honest users who (occasionally) reuse e-tokens. The verifier can always recognize a reused e-token; however, we preserve the anonymity of users who do not reuse e-tokens too often.

Yap, Heng and Goi propose an efficient certificateless signature scheme based on the intractability of the computational Diffie-Hellman problem, and prove that the scheme is secure in the random oracle model. This paper shows that their certificateless signature scheme is vulnerable to key replacement attacks, where an adversary who replaces the public key of a signer can forge valid signatures on any messages for that signer without knowing the signer's private key.

Modular design is a common approach for dealing with complex tasks in modern cryptology. The critical of this approach is that designing a secure hybrid protocol. In this paper, we study password-based key exchange in the three-party setting within the UC framework and design a hybrid protocol that UC-securely realizes such task. That is, we firstly define an appropriate ideal functionality F3-pwKE for password-based three-party key exchange. Next we partition the task into two sub-tasks, three-party key distribution and password-based two-party key exchange, and propose relevant two ideal functionalities, F3-KD, FpwKE. Finally, we present a (F3-KD, FpwKE) -hybrid protocol for password-based three-party key exchange that is proved to be UC-secure with respect to non- adaptive party corruption.

Differential and linear attacks are the most widely used cryptanalytic tools to evaluate the security of symmetric-key cryptography. Since the introduction of differential and linear attacks in the early 1990's, various variants of these attacks have been proposed such as the truncated differential attack, the impossible differential attack, the square attack, the boomerang attack, the rectangle attack, the differential-linear attack, the multiple linear attack, the nonlinear attack and the bilinear attack. One of the other widely used cryptanalytic tools is the related-key attack. Unlike the differential and linear attacks, this attack is based on the assumption that the cryptanalyst can obtain plaintext and ciphertext pairs by using different, but related keys. This thesis provides several new combined differential, linear and related-key attacks, and shows their applications to block ciphers, hash functions in encryption mode and message authentication code (MAC) algorithms. The first part of this thesis introduces how to combine the differential-style, linear-style and related-key attacks: we combine them to devise the differential-nonlinear attack, the square-(non)linear attack, the related-key differential-(non)linear attack, the related-key boomerang attack and the related-key rectangle attack. The second part of this thesis presents some applications of the combined attacks to exiting symmetric-key cryptography. Firstly, we present their applications to the block ciphers SHACAL-1, SHACAL-2 and AES. In particular, we show that the differential-nonlinear attack is applicable to 32-round SHACAL-2, which leads to the best known attack on SHACAL-2 that uses a single key. We also show that the related-key rectangle attack is applicable to the full SHACAL-1, 42-round SHACAL-2 and 10-round AES-192, which lead to the first known attack on the full SHACAL-1 and the best known attacks on SHACAL-2 and AES-192 that use related keys. Secondly, we exploit the related-key boomerang attack to present practical distinguishing attacks on the cryptographic hash functions MD4, MD5 and HAVAL in encryption mode. Thirdly, we show that the related-key rectangle attack can be used to distinguish instantiated HMAC and NMAC from HMAC and NMAC with a random function.

Following the work of Al-Riyami et al. we define the notion of key encapsulation mechanism supporting cryptographic workflow (WF-KEM) and prove a KEM-DEM composition theorem which extends the notion of hybrid encryption to cryptographic workflow. We then generically construct a WF-KEM from an identity-based encryption (IBE) scheme and a secret sharing scheme. Chosen ciphertext security is achieved using one-time signatures. Adding a public-key encryption scheme we are able to modify the construction to obtain escrow-freeness. We prove all our constructions secure in the standard model.

We give a unified account of classical secret-sharing goals from a modern cryptographic vantage. Our treatment encompasses perfect, statistical, and computational secret sharing; static and dynamic adversaries; schemes with or without robustness; schemes where a participant recovers the secret and those where an external party does so. We then show that Krawczyk's 1993 protocol for robust computational secret sharing (RCSS) need not be secure, even in the random-oracle model and for threshold schemes, if the encryption primitive it uses satisfies only one-query indistinguishability (ind1), the only notion Krawczyk defines. Nonetheless, we show that the protocol is secure (in the random-oracle model, for threshold schemes) if the encryption scheme also satisfies one-query key-unrecoverability (key1). Since practical encryption schemes are ind1+key1 secure, our result effectively shows that Krawczyk's RCSS protocol is sound (in the random-oracle model, for threshold schemes). Finally, we prove the security for a variant of Krawczyk's protocol, in the standard model and for arbitrary access structures, assuming ind1 encryption and a statistically-hiding, weakly-binding commitment scheme.

Protocols proven secure in universally composable models remain secure under concurrent and modular composition, and may be easily plugged into more complex protocols without having their security re-assessed with each new use. Recently, a universally composable framework has been proposed for Radio-Frequency Identification (RFID) authentication protocols, that simultaneously provides for availability, anonymity, and authenticity. In this paper we extend that framework to support key-compromise and forward-security issues. We also introduce new, provably secure, and highly practical protocols for anonymous authentication and key-exchange by RFID devices. The new protocols are lightweight, requiring only a pseudo-random bit generator. The new protocols satisfy forward-secure anonymity, authenticity, and availability requirements in the Universal Composability model. The proof exploits pseudo-randomness in the standard model.

We address the question of whether or not semantically secure public-key encryption primitives imply the existence of chosen ciphertext attack (CCA) secure primitives. We show a black-box separation, using the methodology introduced by Impagliazzo and Rudich, for a large non-trivial class of constructions. In particular, we show that if the proposed CCA construction's decryption algorithm does not query the semantically secure primitive's encryption algorithm, then the proposed construction cannot be CCA secure

We present the first provably secure ID-based key agreement protocol, inspired by the ID-based encryption scheme of Gentry, in the standard (non-random-oracle) model. We show how this key agreement can be used in either escrowed or escrowless mode. We also give a protocol which enables users of separate private key generators to agree on a shared secret key. All our proposed protocols have comparable performance to all known protocols that are proven secure in the random oracle model.

We exhibit an infinite class of almost perfect nonlinear quadratic binomials from $\mathbb{F}_{2^n}$ to $\mathbb{F}_{2^n}$ ($n\geq 12$, $n$ divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function and to any Kasami function. It means that for $n$ even they are CCZ-inequivalent to any known APN function, and in particular for $n=12,24$, they are therefore CCZ-inequivalent to any power function. It is also proven that, except in particular cases, the Gold mappings are CCZ-inequivalent to the Kasami and Welch functions.

We demonstrate an \emph{average-case} problem which is as hard as finding $\gamma(n)$-approximate shortest vectors in certain $n$-dimensional lattices in the \emph{worst case}, where $\gamma(n) = O(\sqrt{\log n})$. The previously best known factor for any class of lattices was $\gamma(n) = \tilde{O}(n)$. To obtain our results, we focus on families of lattices having special algebraic structure. Specifically, we consider lattices that correspond to \emph{ideals} in the ring of integers of an algebraic number field. The worst-case assumption we rely on is that in some $\ell_p$ length, it is hard to find approximate shortest vectors in these lattices, under an appropriate form of preprocessing of the number field. Our results build upon prior works by Micciancio (FOCS 2002), Peikert and Rosen (TCC 2006), and Lyubashevsky and Micciancio (ICALP 2006). For the connection factors $\gamma(n)$ we achieve, the corresponding \emph{decisional} promise problems on ideal lattices are \emph{not} known to be NP-hard; in fact, they are in P. However, the \emph{search} approximation problems still appear to be very hard. Indeed, ideal lattices are well-studied objects in computational number theory, and the best known algorithms for them seem to perform \emph{no better} than the best known algorithms for general lattices. To obtain the best possible connection factor, we instantiate our constructions with infinite families of number fields having constant \emph{root discriminant}. Such families are known to exist and are computable, though no efficient construction is yet known. Our work motivates the search for such constructions. Even constructions of number fields having root discriminant up to $O(n^{2/3-\epsilon})$ would yield connection factors better than the current best of~$\tilde{O}(n)$.

Task-specific groups are often formed in an ad-hoc manner within big structures, like companies. Take the following typical scenario: A high rank manager decides that a task force group for some project needs to be built. This order is passed down the hierarchy where it finally reaches a manager who calls some employees to form a group. The members should communicate in a secure way and for efficiency reasons symmetric systems are the common choice. To establish joint secret keys for groups, group key exchange (GKE) protocols were developed. If the users are part of e.g. a Public Key Infrastructure (PKI), which is usually the case within a company or a small network, it is possible to achieve authenticated GKE by modifying the protocol and particularly by including signatures. In this paper we recall a GKE due to Burmester and Desmedt which needs only $O(\log n)$ communication and computation complexity per user, rather than $O(n)$ as in the more well-known Burmester-Desmedt protocol, and runs in a constant number of rounds. To achieve authenticated GKE one can apply compilers, however, the existing ones would need $O(n)$ computation and communication thereby mitigating the advantages of the faster protocol. Our contribution is to extend an existing compiler so that it preserves the computation and communication complexity of the non-authenticated protocol. This is particularly important for tree based protocols.

In this paper, we will show that the certificateless signature scheme recently proposed by Yap, Heng and Goi at EUC Workshops 2006 is insecure against a key replacement attack. Our attack shows that anyone who replaces a signer's public key can forge valid signatures for that signer without knowledge of the signer's private key.

Kim {\em et al}. \cite{KiBiPrHo06} and Contini {\em et al}. \cite{CoYi06} studied on the security of HMAC and NMAC based on HAVAL, MD4, MD5, SHA-0 and SHA-1. Especially, they considered the distinguishing attacks. However, they did not describe generic distinguishing attacks on NMAC and HMAC. In this paper, we describe the generic distinguishers to distinguish NMAC and HMAC with the birthday attack complexity and we prove the security bound when the underlying compression function is the random oracle.

On the basis of BB short signature scheme, this paper derives a new signature scheme, from which we construct a new kind of group signature scheme. The security of the new group signature scheme is based on the q-Strong Diffie-Hellman assumption and the Decisional Diffie-Hellman assumption in the random oracle model. The length of the new group signature is a little longer than that of BBS short group signature. However, in the new group signature scheme, giving certificates and private keys to group members do not need any third trusted party, while in BBS short group signature scheme it does need.

This paper constructs a new group blind signature scheme on the basis of CZK group signature scheme. The security of the new scheme is under the computational Diffie-Hellman problem in the random oracle model. In our scheme, to blind the group signature of CZK only adds the computation of modular addition; while the scheme in LR98 adds the computation of double discreet logarithm, root of the discreet logarithm and random permutation in order to blind the group signature of CS97. As far as the computation complexity is concerned, our scheme is more efficient than LR98.

This paper presents some properties of he deterministic random bit generator ISAAC (FSE'96), contradicting several statements of its introducing article. In particular, it characterizes huge subsets of internal states which induce a strongly non-uniform distribution in the $8\,192$ first bits produced. A previous attack on ISAAC presented at Asiacrypt'06 by Paul and Preneel is demonstrated to be non relevant, since relies on an erroneous algorithm. Finally, a modification of the algorithm is proposed to fix the weaknesses discovered.

In \cite{BCS96}, the concept of zigzag function was introduced in relation with oblivious transfer \cite{R84}. This subject has later been studied in \cite{S99,DS01,CFW01}. The definition of zigzag functions has been generalized to $s$-zigzag functions for $2\leq s\leq n$. It turns out that zigzag functions are also interesting combinatorial objects, thanks to their relation with self-intersecting codes and orthogonal arrays \cite{BCS96,S99}. The aim of this work is to formulate these objects with respect to a new metric following the approach proposed in \cite{BNNP} and to investigate the properties of the generalized zigzag functions and related concepts.

We give a construction of statistically-hiding commitment schemes (ones where the hiding property holds information theoretically), based on the minimal cryptographic assumption that one-way functions exist. Our construction employs two-phase commitment schemes, recently constructed by Nguyen, Ong and Vadhan (FOCS `06), and universal one-way hash functions introduced and constructed by Naor and Yung (STOC `89) and Rompel (STOC `90).

We describe a method for enumerating all essentially different executions possible for a cryptographic protocol. We call them the shapes of the protocol. Naturally occurring protocols have only finitely many, indeed very few shapes. Authentication and secrecy properties are easy to determine from them, as are attacks and anomalies. CPSA, our Cryptographic Protocol Shape Analyzer, implements the method. In searching for shapes, CPSA starts with some initial behavior, and discovers what shapes are compatible with it. Normally, the initial behavior is the point of view of one participant. The analysis reveals what the other principals must have done, given this participant's view. The search is complete, i.e. every shape can in fact be found in a finite number of steps. The steps in question are applications of two authentication tests, fundamental patterns for protocol analysis and heuristics for protocol design. We have formulated the authentication tests in a new, stronger form, and proved completeness for a search algorithm based on them.

In this correspondence, construction of balanced Boolean functions with maximum possible algebraic (annihilator) immunity (AI) is studied with an additional property which is necessary to resist fast algebraic attack. The additional property considered here is, given an $n$-variable ($n$ even) balanced function $f$ with maximum possible AI $\frac{n}{2}$, and given two $n$-variable Boolean functions $g, h$ such that $fg = h$, if $\deg(h) = \frac{n}{2}$, then $\deg(g)$ must be greater than or equal to $\frac{n}{2}$. Our results can also be used to present theoretical construction of resilient Boolean functions having maximum possible AI.

Authentication codes provide message integrity guarantees in an information theoretic sense within a symmetric key setting. Information theoretic bounds on the success probability of an adversary who has access to previously authenticated messages have been derived by Simmons and Rosenbaum, among others. In this paper we consider a strong attack scenario where the adversary is adaptive and has access to authentication and verification oracles. We derive information theoretic bounds on the success probability of the adversary and on the key size of the code. This brings the study of unconditionally secure authentication systems on a par with the study of computationally secure ones. We characterize the codes that meet these bounds and compare our result with the earlier ones.

Cryptographic protocols are often designed and analyzed under some trusted setup assumptions, namely in settings where the participants have access to global information that is trusted to have some basic security properties. However, current modeling of security in the presence of such setup falls short of providing the expected security guarantees. A quintessential example of this phenomenon is the deniability concern: there exist natural protocols that meet the strongest known composable security notions, and are still vulnerable to bad interactions with rogue protocols that use the same setup. We extend the notion of universally composable (UC) security in a way that re-establishes its original intuitive guarantee even for protocols that use globally available setup. The new formulation prevents bad interactions even with adaptively chosen protocols that use the same setup. In particular, it guarantees deniability. While for protocols that use no setup the proposed requirements are the same as in traditional UC security, for protocols that use global setup the proposed requirements are significantly stronger. In fact, realizing Zero Knowledge or commitment becomes provably impossible, even in the Common Reference String model. Still, we propose reasonable alternative setup assumptions and protocols that allow realizing practically any cryptographic task under standard hardness assumptions even against adaptive corruptions.

Recently Tate pairing and its variations are attracted in cryptography. Their operations consist of a main iteration loop and a final exponentiation. The final exponentiation is necessary for generating a unique value of the bilinear pairing in the extension fields. The speed of the main loop has become fast by the recent improvements, e.g., the Duursma-Lee algorithm and $\eta_T$ pairing. In this paper we discuss how to enhance the speed of the final exponentiation of the $\eta_T$ pairing in the extension field ${\mathbb F}_{3^{6n}}$. Indeed, we propose some efficient algorithms using the torus $T_2({\mathbb F}_{3^{3n}})$ that can efficiently compute an inversion and a powering by $3^{n}+1$. Consequently, the total processing cost of computing the $\eta_T$ pairing can be reduced by 17% for n=97.

The informal goal of a watermarking scheme is to ``mark'' a digital object, such as a picture or video, in such a way that it is difficult for an adversary to remove the mark without destroying the content of the object. Although there has been considerable work proposing and breaking watermarking schemes, there has been little attention given to the formal security goals of such a scheme. In this work, we provide a new complexity-theoretic definition of security for watermarking schemes. We describe some shortcomings of previous attempts at defining watermarking security, and show that security under our definition also implies security under previous definitions. We also propose two weaker security conditions that seem to capture the security goals of practice-oriented work on watermarking and show how schemes satisfying these weaker goals can be strengthened to satisfy our definition.

A new invariant of the set of $n$-variable Boolean functions with respect to the action of $AGL(n,2)$ is studied. Application of this invariant to prove affine nonequivalence of two Boolean functions is outlined. The value of this invariant is computed for $PS_{ap}$ type bent functions.

We exhibit an infinite class of almost perfect nonlinear quadratic binomials from $\mathbb{F}_{2^{n}}$ to $\mathbb{F}_{2^{n}}$ with $n=4k$ and $k$ odd. We prove that these functions are CCZ-inequivalent to known APN power functions when $k\ne 1$. In particular it means that for $n=12,20,28$, they are CCZ-inequivalent to any power function.

Pairing based cryptography is a new public key cryptographic scheme. An elliptic curve suitable for pairing based cryptography is called a ``pairing-friendly'' elliptic curve. After Mitsunari, Sakai and Kasahara's traitor tracing scheme and Boneh and Boyen's short signature scheme, many protocols based on pairing-related problems such as the $q$-weak Diffie-Hellman problem have been proposed. In Eurocrypt 2006, Cheon proposed a new efficient algorithm to solve pairing-related problems and recently the complexity of Cheon's algorithm has been improved by Kozaki, Kutsuma and Matsuo. Due to these two works, an influence of Cheon's algorithm should be considered when we construct a suitable curves for the use of a protocol based on a pairing-related problem. Among known methods for constructing pairing-friendly elliptic curves, ones using cyclotomic polynomials such as the Brezing-Weng method and the Freeman-Scott-Teske method are affected by Cheon's algorithm. In this paper, we study how to reduce a security loss of a cyclotomic family by Cheon's algorithm. The proposed method constructs many pairing-friendly elliptic curves with small security loss by Cheon's algorithm suitable for protocols based on pairing-related problems.

In this paper, we demonstrate that the construction proposed by Lan Nguyen at CT-RSA'05 does lead to a cryptographic accumulator which is not collision resistant.

Sorry for the absence. But I want revise this part after anoymous review!

The transmission of voice communications as datagram packets over IP networks, commonly known as Voice-over-IP (VoIP) telephony, is rapidly gaining wide acceptance. With private phone conversations being conducted on insecure public networks, security of VoIP communications is increasingly important. We present a structured security analysis of the VoIP protocol stack, which consists of signaling (SIP), session description (SDP), key establishment (SDES, MIKEY, and ZRTP) and secure media transport (SRTP) protocols. Using a combination of manual and tool-supported formal analysis, we uncover several design flaws and attacks, most of which are caused by subtle inconsistencies between the assumptions that protocols at different layers of the VoIP stack make about each other. The most serious attack is a replay attack on SDES, which causes SRTP to repeat the keystream used for media encryption, thus completely breaking transport-layer security. We also demonstrate a man-in-the-middle attack on ZRTP, which allows the attacker to convince the communicating parties that they have lost their shared secret. If they are using VoIP devices without displays and thus cannot execute the ``human authentication'' procedure, they are forced to communicate insecurely, or not communicate at all, i.e., this becomes a denial of service attack. Finally, we show that the key derivation process used in MIKEY cannot be used to prove security of the derived key in the standard cryptographic model for secure key exchange.

This paper presents a very simple and efficient adaptively-sound perfect NIZK argument system for any NP-language. In contrust to recently proposed schemes by Groth, Ostrovsky and Sahai, our scheme does not pose any restriction on the statements to be proven. Besides, it enjoys a number of desirable properties: it allows to re-use the common reference string (CRS), it can handle arithmetic circuits, and the CRS can be set-up very efficiently without the need for an honest party. We then show an application of our techniques in constructing efficient NIZK schemes for proving arithmetic relations among committed secrets, whereas previous methods required expensive generic NP-reductions. The security of the proposed schemes is based on a strong non-standard assumption, an extended version of the so-called Knowledge-of-Exponent Assumption (KEA) over bilinear groups. We give some justification for using such an assumption by showing that the commonly-used approach for proving NIZK arguments sound does not allow for adaptively-sound statistical NIZK arguments (unless NP is in P/poly). Furthermore, we show that the assumption used in our construction holds with respect to generic adversaries that do not exploit the specific representation of the group elements. We also discuss how to avoid the non-standard assumption in a pre-processing model.

Algorithmic progress and future technological advances threaten today's cryptographic protocols. This may allow adversaries to break a protocol retrospectively by breaking the underlying complexity assumptions long after the execution of the protocol. Long-term secure protocols, protocols that after the end of the execution do not reveal any information to a then possibly unlimited adversary, could meet this threat. On the other hand, in many applications, it is necessary that a protocol is secure not only when executed alone, but within arbitrary contexts. The established notion of universal composability (UC) captures this requirement. This is the first paper to study protocols which are simultaneously long-term secure and universally composable. We show that the usual set-up assumptions used for UC protocols (e.g., a common reference string) are not sufficient to achieve long-term secure and composable protocols for commitments or zero-knowledge protocols. We give practical alternatives (e.g., signature cards) to these usual setup-assumptions and show that these enable the implementation of the important primitives commitment and zero-knowledge protocols.

In this paper, we formulate and realize a definition of security for three-party key distribution within the universally composable (UC) framework. That is, an appropriate ideal functionality that captures the basic security requirements of three-party key distribution is formulated. We show that UC definition of security for three-party key distribution protocol is strictly more stringent than a previous definition of security which is termed AKE-security. Finally, we present a real-life protocol that securely realizes the formulated ideal functionality with respect to non-adaptive adversaries.

In this paper, the authors give the definitions of a coprime sequence and a lever function, and describe the five algorithms and six characteristics of a prototypal public key cryptosystem which is used for encryption and signature, and based on three new problems and one existent problem: the multivariate permutation problem (MPP), the anomalous subset product problem (ASPP), the transcendental logarithm problem (TLP), and the polynomial root finding problem (PRFP). Prove by reduction that MPP, ASPP, and TLP are computationally at least equivalent to the discrete logarithm problem (DLP) in the same prime field, and meanwhile find some evidence which inclines people to believe that the new problems are harder than DLP each, namely unsolvable in DLP subexponential time. Demonstrate the correctness of the decryption and the verification, deduce the probability of a plaintext solution being nonunique is nearly zero, and analyze the exact securities of the cryptosystem against recovering a plaintext from a ciphertext, extracting a private key from a public key or a signature, and forging a signature through known signatures, public keys, and messages on the assumption that IFP, DLP, and LSSP can be solved. Studies manifest that the running times of effectual attack tasks are greater than or equal to O(2^n) so far when n = 80, 96, 112, or 128 with lg M = 696, 864, 1030, or 1216. As viewed from utility, it should be researched further how to decrease the length of a modulus and to increase the speed of the decryption.

We propose public-key cryptosystems with public key a system of polynomial equations and private key an ideal.

Among private set operations, the privacy preserving element reduction of a multiset can be an important tool for privacy enhancing technology as itself or in the combination with other private set operations. Recently, a protocol, over-threshold-set-union-protocol, for a privacy preserving element reduction method of a multiset was proposed by Kissner and Song in Crypto 2005. In this paper, we point out that there is a mathematical flaw in their polynomial representation of element reduction of a multiset and the resulting protocol error from the flaw in the polynomial representation of a multiset. We correct their polynomial representation of a multiset and propose an over-threshold-set-operation-protocol based on the corrected representation. Our over-threshold-set-operation-protocol can be combined with a privacy preserving set operation and outputs those elements appears over the predetermined threshold number times in the resulting multiset of set operation.

Recently there is a paper entitled "{\it Breaking a New Instance of TTM Cryptosystem}" by Xuyun Nie, Lei Hu, Jianyu Li, Crystal Updegrove and Jintai Ding [1] claiming a successive attack on the scheme of TTM presented in [3]. In the present article, we will show that their claim is a {\bf misunderstanding}.

We present AIE (Authenticated Interleaved Encryption), a new scheme that allows nodes of a network to exchange messages securely (i.e. encrypted and authenticated) without sharing a common key or using public key cryptography. Our scheme is well adapted to networks, such as ad hoc, overlay or sensor networks, where nodes have limited capabilities and can share only a small number of symmetric keys. It provides privacy and integrity. An eavesdropper listening to a communication is unable to decrypt it and modify it without being detected. We show that our proposal can be used in wireless sensor networks to send encrypted packets to very dynamic sets of nodes without having to establish and maintain group keys. These sets of nodes can be explicitly specified by the source or can be specified by the network according to some criteria, such as their location, proximity to an object, temperature range. As a result, a node can, for example, send encrypted data to all the nodes within a given geographical area, without having to identify the destination nodes in advance. Finally we show that our proposal can be used to implement a secure and scalable aggregation scheme for wireless sensor networks.

We discuss the underlying mathematics that causes the embedding degree of a curve of any genus to not necessarily correspond to the minimal embedding field, and hence why it may fail to capture the security of a pairing-based cryptosystem. Let $C$ be a curve of genus $g$ defined over a finite field $\F_q$, where $q=p^m$ for a prime $p$. The Jacobian of the curve is an abelian variety, $J_C(\F_q)$, of dimension $g$ defined over $\F_q$. For some prime $N$, coprime to $p$, the embedding degree of $J_C(\F_q)[N]$ is defined to be the smallest positive integer $k$ such that $N$ divides $q^k-1$. Hence, $\F_{q^k}^*$ contains a subgroup of order $N$. To determine the security level of a pairing-based cryptosystem, it is important to know the minimal field containing the $N$th roots of unity, since the discrete logarithm problem can be transported from the curve to this field, where one can perform index calculus. We show that it is possible to have a dramatic (unbounded) difference between the size of the field given by the embedding degree, $\F_{p^{mk}}$, and the minimal embedding field that contains the $N$th roots of unity, $\F_{p^d}$, where $d\mid mk$. The embedding degree has utility as it indicates the field one must work over to compute the pairing, while a security parameter should indicate the minimal field containing the embedding. We discuss a way of measuring the difference between the size of the two fields and we advocate the use of two separate parameters. We offer a possible security parameter, $k'=\frac{\ord_Np}{g}$, and we present examples of elliptic curves and genus 2 curves which highlight the difference between them. While our observation provides a proper theoretical understanding of minimal embedding fields in pairing-based cryptography, it is unlikely to affect curves used in practice, as a discrepancy may only occur when $q$ is non-prime. Nevertheless, it is an important point to keep in mind and a motivation to recognize two separate parameters when describing a pairing-based cryptosystem.

We give a complexity-theoretic characterization of the class of problems in NP having zero-knowledge argument systems. This characterization is symmetric in its treatment of the zero knowledge and the soundness conditions, and thus we deduce that the class of problems in NP intersect coNP having zero-knowledge arguments is closed under complement. Furthermore, we show that a problem in NP has a *statistical* zero-knowledge argument system if and only if its complement has a computational zero-knowledge *proof* system. What is novel about these results is that they are *unconditional*, i.e., do not rely on unproven complexity assumptions such as the existence of one-way functions. Our characterization of zero-knowledge arguments also enables us to prove a variety of other unconditional results about the class of problems in NP having zero-knowledge arguments, such as equivalences between honest-verifier and malicious-verifier zero knowledge, private coins and public coins, inefficient provers and efficient provers, and non-black-box simulation and black-box simulation. Previously, such results were only known unconditionally for zero-knowledge *proof systems*, or under the assumption that one-way functions exist for zero-knowledge argument systems.

Parallel FFT-Hashing was designed by C. P. Schnorr and S. Vaudenay in 1993. The function is a simple and light weight hash algorithm with 128-bit digest. Its basic component is a multi-permutation which helps in proving its resistance to collision attacks. % In this work we show a preimage attack on Parallel FFT-Hashing with complexity $2^{t+64}+2^{128-t}$ and memory $2^{t}$ which is less than the generic complexity $2^{128}$. When $t=32$, we can find a preimage with complexity $2^{97}$ and memory $2^{32}$. Our method can be described as ``disseminative-meet-in-the-middle-attack'' we actually use the properties of multi-permutation (helpful against collision attack) to our advantage in the attack. Overall, this type of attack (beating the generic one) demonstrates that the structure of Parallel FFT-Hashing has some weaknesses when preimage attack is considered. To the best of our knowledge, this is the first attack on Parallel FFT-Hashing.

CellHash \cite{DaGoVa91} and SubHash \cite{DaGoVa92} were suggested by J. Daemen, R. Govaerts and J. Vandewalle in 1991 and 1992. SubHash is an improved version from CellHash. They have 257-bit internal state and 256-bit hash output. In this paper, we show a preimage attack on CellHash (SubHash) with the complexity $2^{129+t}$ and the memory $2^{128-t}$ for any $t$ (with the complexity about $2^{242}$ and the memory size $2^{17}$). Even though we modify them in a famous way, we show that we can find a preimage on the modified CellHash (the modified SubHash) with the complexity $2^{200}$ and the memory size $2^{59}$ (with the complexity about $2^{242}$ and the memory size $2^{17}$).

In this paper, we suggest a preimage attack on Hashing with Polynomials \cite{Shpilrain06b}. The algorithm has $n$-bit hash output and $n$-bit intermediate state. (for example, $n=163$). The algorithm is very simple and light so that it can be implement in low memory environment. Our attack is based on the meet-in-the-middle attack. We show that we can find a preimage with the time complexity $2^{n-t}+2^{t}*(n+1/33)$ and the memory $2^{t}$ even though the recursive formula $H$ uses any \textsf{f} whose each term's degree in terms of \textsf{x} is $2^a$ for a non-negative integer $a$. We recommend that hash functions such as Hashing with Polynomials should have the intermediate state size at least two times bigger than the output size.

In [3] the authors give the first mathematical formalization of an unconditionally secure commitment scheme. Their construction has some similarities to one used to build authentication codes, so they raise the question whether there is some relation between commitment schemes and authentication schemes. They conjecture that authentication schemes with arbitration can be used, but they stress that the information flows are different. In this paper, we show that there is indeed a relation between unconditionally secure commitment schemes and unconditionally secure authentication schemes, and that an unconditionally secure commitment scheme can be built from such an authentication scheme and an unconditionally secure cipher system. This parallel is then used to analyse a new attack against commitment schemes that is the counterpart of the impersonation attack in an authentication system. To investigate the opposite direction, we start by defining an optimal commitment system and showing that this must be a resolvable design commitment scheme as proposed in the aforementioned paper. Then, a proof is given that the resolvable design commitment schemes are a composition of an authentication system and a cipher system and the conclusion follows that this is the case for all optimal commitment systems. We prove that there is a commitment scheme based on Galois Fields that uses the One-Time Pad as the cipher system, which to our knowledge is new in the literature. The main technique in the proof is the construction of an appropriate design for any n, originating an authentication system that is perfectly secure against deception attacks of levels 0 and 1. The commitment scheme here proposed uses only very simple operations and can be very efficiently implemented both in hardware and software. Finally, we give a brief look at the possibility of building commitment schemes from other primitives.

In this paper, we will propose a MAC with two versions, which is called LAMA. The proposal MAC has the input size of 128 bits and 256 bits in the versions 1, 2 respectively, and output size of 128 bits. There have not been found a attack better than the exhaustive search attack for the MAC, and it has a fast implementations in about 5 cycles/byte in the both versions.

In this paper, we propose a generic construction of chosen-ciphertext secure cryptosystems against adversaries with a bounded number of decrytion queries from arbitrary semantically secure encryption in a black box manner. Our construction is not only an alternative to the previously known technique, i.e. the Naor-Yung paradigm, but also has some interesting properties. Especially, (1) it does not require non-interactive zero-knowledge proof, and (2) its component ciphertexts can be compressed into only one if the underlying encryption has a certain homomorphic property. Consequently, when applying our construction to the ElGamal encryption, ciphertext overhead of the resulting scheme will be only one group element which is considered optimal since it is the same as the original ElGamal. Disadvantages to previous schemes are that the upper bound of the number of decryption queries (e.g. 2^{30}) has to be known before set-up phase, and the size of public key is large.

The common random string model permits the construction of cryptographic protocols that are provably impossible to realize in the standard model. In this model, a trusted party generates a random string and gives it to all parties in the protocol. However, the introduction of such a third party should set alarm bells going off: Who is this trusted party? Why should we trust that the string is random? Even if the string is uniformly random, how do we know it does not leak private information to the trusted party? The very point of doing cryptography in the first place is to prevent us from trusting the wrong people with our secrets. In this paper, we propose the more realistic multi-string model. Instead of having one trusted authority, we have several authorities that generate random strings. We do not trust any single authority, we only assume a majority of them generate the random string honestly. We demonstrate the use of this model for two fundamental cryptographic taks. We define non-interactive zero-knowledge in the multi-string model and construct NIZK proofs in the multi-string model. We also consider multi-party computation and show that any functionality can be securely realized in the multi-string model.

Wang and Yu showed that MD5 was not collision-resistant, but it is known that their sufficient conditions for finding a collision of MD5 includes some mistakes. In this paper, we examine the sufficient conditions by computer simulation. We show that the Wang-Yu conditions include 16 unnecessary conditions for making a collision. Sasaki et al. claimed that modifying one condition made it possible to remove eleven conditions. However, the result of our computer simulation shows that their conditions does not make a collision.

In the universal composability framework, we define an ideal functionality for blind signatures, as an alternative to a functionality recently proposed by Fischlin. Fischlin proves that his functionality cannot be realized in the plain model, but this result does not apply to our functionality. We show that our functionality is realized in the plain model by a blind signature protocol if and only if the corresponding blind signature scheme is secure with respect to blindness and non-forgeability, as defined by Juels, Luby and Ostrovsky.

We present and analyze the F5 algorithm for computing Groebner bases. On the practical side, we correct minor errors in Faugere's pseudo code, and report our experiences implementing the -- to our knowledge -- first working public version of F5. While not designed for efficiency, it will doubtless be useful to anybody implementing or experimenting with F5. In addition, we list some experimental results, hinting that the version of F5 presented in Faugere's original paper can be considered as more or less naive, and that Faugere's actual implementations are a lot more sophisticated. We also suggest further improvements to the F5 algorithm and point out some problems we encountered when attempting to merge F4 and F5 to an "F4.5" algorithm. On the theoretical side, we slightly refine Faugere's theorem that it suffices to consider all normalized critical pairs, and give the first full proof, completing his sketches. We strive to present a more accessible account of the termination and correctness proofs of F5. Unfortunately, we still rely on a conjecture about the correctness of certain optimizations. Finally, we suggest directions of future research on F5.

Significant progress in the design of special purpose hardware for supporting the Number Field Sieve (NFS) has been made. From a practical cryptanalytic point of view, however, none of the published proposals for coping with the sieving step is satisfying. Even for the best known designs, the technological obstacles faced for the parameters expected for a 1024-bit RSA modulus are significant. Below we present a new hardware design for implementing the sieving step. The suggested chips are of moderate size and the inter-chip communication does not seem unrealistic. According to our preliminary analysis of the 1024-bit case, we expect the new design to be about 2 to 3.5 times slower than TWIRL (a wafer-scale design). Due to the more moderate technological requirements, however, from a practical cryptanalytic point of view the new design seems to be no less attractive than TWIRL.

In spite of growing importance of AES, the Data Encryption Standard is by no means obsolete. DES has never been broken from the practical point of view. The triple DES is believed very secure, is widely used, especially in the financial sector, and should remain so for many many years to come. In addition, some doubts have been risen whether its replacement AES is secure, given the extreme level of ``algebraic vulnerability'' of the AES S-boxes (their low I/O degree and exceptionally large number of quadratic I/O equations). Is DES secure from the point of view of algebraic cryptanalysis, a new very fast-growing area of research? We do not really hope to break it, but just to advance the field of cryptanalysis. At a first glance, DES seems to be a very poor target - as there is (apparently) no strong algebraic structure of any kind in DES. However Courtois and Pieprzyk showed that ``small'' S-boxes always have a low I/O degree (cubic for DES as we show). In addition, due to their low gate count requirements, by introducing additional variables, we can always get an extremely sparse system of quadratic equations. To assess the algebraic vulnerabilities is the easy part, that may appear unproductive. In this paper we demonstrate that in this way, several interesting attacks on a real-life ``industrial'' block cipher can be found. One of our attacks is the fastest known algebraic attack on 6 rounds of DES. Yet, it requires only ONE SINGLE known plaintext (instead of a very large quantity) which is quite interesting in itself. Though (on a PC) we recover the key for only six rounds, in a much weaker sense we can also attack 12 rounds of DES. These results are very interesting because DES is known to be a very robust cipher, and our methods are very generic. They can be applied to DES with modified S-boxes and potentially other reduced-round block ciphers.

This note discusses the complexity evaluation of cryptanalytic attacks, with the example of exhaustive key search, illustrated with several ciphers from the eSTREAM project. A measure is proposed to evaluate the effective computational cost of cryptanalytic algorithms, based on the observation that the standard one is not precise enough.

In this paper we show a general transformation from any honest verifier statistical zero-knowledge argument to a concurrent statistical zero-knowledge argument. Our transformation relies only on the existence of one-way functions. It is known that the existence of zero-knowledge systems for any non-trivial language implies one way functions. Hence our transformation \emph{unconditionally} shows that concurrent statistical zero-knowledge arguments for a non-trivial language exist if and only if standalone secure statistical zero-knowledge arguments for that language exist. Further, applying our transformation to the recent statistical zero-knowledge argument system of Nguyen et al (STOC'06) yields the first concurrent statistical zero-knowledge argument system for all languages in \textbf{NP} from any one way function.

We point out that the seemingly strong pseudorandom oracle preserving (PRO-Pr) property of hash function domain-extension transforms defined and implemented by Coron et. al. [12] can actually weaken our guarantees on the hash function, in particular producing a hash function that fails to be even collision-resistant (CR) even though the compression function to which the transform is applied is CR. Not only is this true in general, but we show that all the transforms presented in [12] have this weakness. We suggest that the appropriate goal of a domain extension transform for the next generation of hash functions is to be multi-property preserving, namely that one should have a single transform that is simultaneously at least collision-resistance preserving, pseudorandom function preserving and PRO-Pr. We present an efficient new transform that is proven to be multi-property preserving in this sense.

We establish rigorous foundations to the use of modular, layered design for building complex distributed systems. Layering is key to the design of the Internet and other distributed systems, hence such solid, theoretical foundations are essential, especially when considering adversarial settings, such as for security and cryptographic protocols. We define the basic concepts for modular, layered design: protocols, systems, configurations, executions, and models, and three relations: indistinguishability (between two systems), satisfaction (of a model by a system), and realization (by protocol, of one model over another model). We prove several basic properties, including the {\em layering lemma} and the {\em indistinguishability lemma}. The indistinguishability lemma shows that if two systems \Gamma_L, \Gamma_R are indistinguishable, and \Gamma_L satisfies some model M, then \Gamma_R also satisfies M. The layering lemma shows that given protocols {\pi_i}^u_{i=1}, if every protocol \pi_i realizes model M_i over model M_{i-1}, then the composite protocol \pi_{1||...||u} realizes model M_u over M_0. This allows specification, design and analysis of each layer independently, and combining the results to ensure properties of the complete system. Our framework is based on {\em games}, following many works in applied cryptography. This differs from existing frameworks allowing compositions of cryptographic protocols, based on {\em simulatability of ideal functionality}. Game-based models are more general and flexible than ideal functionality specifications, supporting different adversarial models and avoiding over-specification, which is essential for practical distributed systems and networks.

In a recent paper Mohassel and Franklin study the efficiency of secure two-party computation in the presence of malicious behavior. Their aim is to make classical solutions to this problem, such as zero-knowledge compilation, more efficient. The authors provide several schemes which are the most efficient to date. We propose a modification to their main scheme using expanders. Our modification asymptotically improves at least one measure of efficiency of all known schemes. We also point out an error, and improve the analysis of one of their schemes.

We investigate the security properties of "isotropic channels", broadcast media in which a receiver cannot reliably determine whether a message originated from any particular sender and a sender cannot reliably direct a message away from any particular receiver. We show that perfect isotropism implies perfect (information-theoretic) secrecy, and that asymptotically close to perfect secrecy can be achieved on any channel that provides some (bounded) uncertainty as to sender identity. We give isotropic security protocols under both passive and active adversary models, and discuss the practicality of realizing isotropic channels over various media.

In this paper we overview a large number of currently known group key exchange protocols while focusing on the protocols designed for more than three participants (for an overview of two- and three-party key exchange protocols we refer to [BM03, DB05c]). For each mentioned protocol we briefly describe the current state of security based on the original analysis as well as later results appeared in the literature. We distinguish between (i) protocols with heuristic security arguments based on informally defined security requirements and (ii) protocols that have been proven secure in one of the existing security models for group key exchange. Note, this paper continues the work started in Manulis (ePrint Rep. 2006/388) which provides an analytical survey on security requirements and currently known models for group key exchange. We emphasize that the following survey focuses on the security aspects of the protocols and does not aim to provide any efficiency comparison. The reader interested in this kind of surveys we refer to Rafaeli and Hutchison (ACM Comp. Surveys, 2003) and Amir et al. (ACM Trans. on Inf. and Syst. Sec., 2004).

The paper proposes four new ID based strong designated verifier proxy signature (SDVPS) scheme. The schemes are formed by introducing proxy in ID based SDVS, ID based in SDVPS and ID based proxy in SDVS. We have also analyzed the security of the schemes and their computation aspects.

Following an attack against exculpability, put forward at Asiacrypt'06, of ACJT's group signature, we further found Nguyen's identity escrow (group Signature) scheme did not satisfy non-frameabiliy either.

We derive a new algorithm for computing the Tate pairing on an elliptic curve over a finite field. The algorithm uses a generalisation of elliptic divisibility sequences known as elliptic nets, which are maps from $\Z^n$ to a ring that satisfy a certain recurrence relation. We explain how an elliptic net is associated to an elliptic curve and reflects its group structure. Then we give a formula for the Tate pairing in terms of values of the net. Using the recurrence relation we can calculate these values in linear time. Computing the Tate pairing is the bottleneck to efficient pairing-based cryptography. The new algorithm has time complexity comparable to Miller's algorithm, and is likely to yield to further optimisation.

Designing public key encryption schemes withstanding chosen ciphertext attacks, which is the highest security level for such schemes, is generally perceived as a delicate and intricate task, and for good reason. In the standard model, there are essentially three well-known but quite involved approaches. This state of affairs is to be contrasted with the situation for semantically secure encryption schemes, a much weaker security notion that only guarantees security in the absence of active attack but that appears to be much easier to fulfill, both conceptually and practically. Thus, the boundary between passive attack and active attack seems to make up the dividing line between which security levels are relatively easily achieved and which are not. Our contributions are two-fold. First, we show a simple, efficient black-box construction of a public key encryption scheme withstanding chosen ciphertext attack from any given semantically secure one. Our scheme is $q$-bounded in the sense that security is only guaranteed if the adversary makes at most $q$ adaptive chosen ciphertext queries. Here, $q$ is an arbitrary polynomial that is fixed in advance in the key-generation. Our work thus shows that whether or not the number of active, adversarial queries is known in advance is the dividing line, and not passive versus active attack. In recent work, Gertner, Malkin and Myers show that such black-box reductions are impossible if instead $q$ is a polynomial that only depends on the adversary. Thus, in a sense, our result appears to be the best black-box result one can hope for. Second, we give a non-blackbox reduction from bounded chosen ciphertext security to semantic security where the length of the public/secret keys and ciphertexts drops from quadratic to linear in $q$, compared to our black-box construction. This latter scheme, however, is only of theoretical interest as it uses general NP-reductions, and our blackbox construction is in fact much more practical.

Cramer and Shoup proposed the first provably secure practical public-key encryption scheme in the standard model (CS98). We find new way to construct the secure reduction in which the decryption oracle is not needed yet. Thus we get a simplified version of CS98 which is more efficient than the original scheme, and also provably secure against chosen ciphertext attack in standard model.

The ring signature allows a signer to leak secrets anonymously, without the risk of identity escrow. At the same time, the ring signature provides great flexibility: No group manager, no special setup, and the dynamics of group choice. The ring signature is, however, vulnerable to malicious or irresponsible signers in some applications, because of its anonymity. In this paper, we propose a traceable ring signature scheme. A traceable ring scheme is a ring signature except that it can restrict ``excessive'' anonymity. The traceable ring signature has a tag that consists of a list of ring members and an issue that refers to, for instance, a social affair or an election. A ring member can make any signed but anonymous opinion regarding the issue, but only once (per tag). If the member submits another signed opinion, possibly pretending to be another person who supports the first opinion, the identity of the member is immediately revealed. If the member submits the same opinion, for instance, voting ``yes'' regarding the same issue twice, everyone can see that these two are linked. The traceable ring signature can suit to many applications, such as an anonymous voting on a BBS, a dishonest whistle-blower problem, and unclonable group identification. We formalize the security definitions for this primitive and show an efficient and simple construction.

In this report we provide an analytical survey on security issues that are relevant for group key exchange (GKE) protocols. We start with the description of the security requirements that have been informally described in the literature and widely used to analyze security of earlier GKE protocols. Most of these definitions were originally stated for two-party protocols and then adapted to a group setting. These informal definitions are foundational for the later appeared formal security models for GKE protocols whose development, strengths, and weaknesses are also described and analyzed.

At Eurocrypt '06, Nguyen and Regev presented a new key-recovery attack on the Goldreich-Goldwasser-Halevi (GGH) lattice-based signature scheme: when applied to NTRUSign-251 without perturbation, the attack recovers the secret key given only 90,000 signatures. At the rump session, Whyte speculated whether the number of required signatures might be significantly decreased to say 1,000, due to the special properties of NTRU lattices. This short note shows that this is indeed the case: it turns out that as few as 400 NTRUSign-251 signatures are sufficient in practice to recover the secret key. Hence, NTRUSign without perturbation should be considered totally insecure.