In a seminal paper, Feldman and Micali (STOC '88) show an $n$-party Byzantine agreement protocol tolerating $t < n/3$ malicious parties that runs in expected constant rounds. Here, we show an expected constant-round protocol for authenticated Byzantine agreement assuming honest majority (i.e., $t < n/2$), and relying only on the existence of a secure signature scheme and a public-key infrastructure (PKI). Combined with existing results, this gives the first expected constant-round protocol for secure computation with honest majority in a point-to-point network assuming only one-way functions and a PKI. Our key technical tool --- a new primitive we introduce called moderated VSS --- also yields a simpler proof of the Feldman-Micali result. We also show a simple technique for sequential composition of protocols without simultaneous termination (something that is inherent for Byzantine agreement protocols using $o(n)$ rounds) for the case of $t<n/2$.

At the Asiacrypt 2003 conference Billet and Gilbert introduce a block cipher, which, to quote them, has the following paradoxical traceability properties: it is computationally easy to derive many equivalent distinct descriptions of the same instance of the block cipher; but it is computationally difficult, given one or even up to $k$ of them, to recover the so-called meta-key from which they were derived, or to find any additional equivalent description, or more generally to forge any new untraceable description of the same instance of the block cipher. Their construction relies on the Isomorphism of Polynomials (IP) problem. We here show how to strengthen this construction against algebraic attacks by concealing the underlying IP problems. Our modification is such that our description of the block cipher now does not give the expected results all the time and parallel executions are used to obtain the correct value.

We propose a simple universal (that is, distribution--free) steganographic system in which covertexts with and without hidden texts are statistically indistinguishable. Moreover, the proposed steganographic system has two important properties. First, the rate of transmission of hidden information approaches the Shannon entropy of the covertext source as the size of blocks used for hidden text encoding tends to infinity. Second, if the size of the alphabet of the covertext source and its minentropy tend to infinity then the the number of bits of hidden text per letter of covertext tends to $\log(n!)/n$ where $n$ is the (fixed) size of blocks used for hidden text encoding. The proposed stegosystem uses randomization.

The security and performance of pairing based cryptography has provoked a large volume of research, in part because of the exciting new cryptographic schemes that it underpins. We re-examine how one should implement pairings over ordinary elliptic curves for various practical levels of security. We conclude, contrary to prior work, that the Tate pairing is more efficient than the Weil pairing for all such security levels. This is achieved by using efficient exponentiation techniques in the cyclotomic subgroup backed by efficient squaring routines within the same subgroup.

Web services are an important series of industry standards for adding semantics to web-based and XML-based communication, in particular among enterprises. Like the entire series, the security standards and proposals are highly modular. Combinations of several standards are put together for testing as interoperability scenarios, and these scenarios are likely to evolve into industry best practices. In the terminology of security research, the interoperability scenarios correspond to security protocols. Hence, it is desirable to analyze them for security. In this paper, we analyze the security of the new Secure WS-ReliableMessaging Scenario, the first scenario to combine security elements with elements of another quality-of-service standard. We do this both symbolically and cryptographically. The results of both analyses are positive. The discussion of actual cryptographic primitives of web services security is a novelty of independent interest in this paper.

We propose a new model for key exchange (KE) based on a combination of different types of keys. In our setting, servers exchange keys with clients, who memorize short passwords and carry (stealable) storage cards containing long (cryptographic) keys. Our setting is a generalization of that of Halevi and Krawczyk \cite{HaleviKr99} (HK), where clients have a password and the public key of the server. We point out a subtle flaw in the protocols of HK and demonstrate a practical attack on them, resulting in a full password compromise. We give a definition of security of KE in our (and thus also in the HK) setting and discuss many related subtleties. We define and discuss protection against denial of access (DoA) attacks, which is not possible in any of the previous KE models that use passwords. Finally, we give a very simple and efficient protocol satisfying all our requirements.

We develop a compositional method for proving cryptographically sound security properties of key exchange protocols, based on a symbolic logic that is interpreted over conventional runs of a protocol against a probabilistic polynomial-time attacker. Since key indistinguishability and other previous specifications of secure key exchange suffer from specific compositionality problems, we develop a suitable specification of acceptable key generation. This definition is based on a simple game played by an adversary against a key exchange protocol and a conventional challenger characterizing secure encryption (or other primitives of interest). The method is illustrated using a sample protocol.

A multicollision for a function is a set of inputs whose outputs are all identical. A. Joux showed multicollision attacks on the classical iterated hash function. He also showed how these multicollision attacks can be used to get a collision attack on a concatenated hash function. In this paper, we study multicollision attacks in a more general class of hash functions which we term ``generalized sequential hash functions''. We show that multicollision attacks exist for this class of hash functions provided that every message block is used at most twice in the computation of the message digest.

Radio-Frequency Identifier (RFID) technology, using the ISO-14443 standard, is becoming increasingly popular, with applications like credit-cards, national-ID cards, E-passports, and physical access control. The security of such applications is clearly critical. A key feature of RFID-based systems is their very short range: Typical systems are designed to operate at a range of 5-10cm. Despite this very short nominal range, Kfir and Wool predicted that a rogue device can communicate with an ISO-14443 RFID tag from a distance of 40-50cm, based on modeling and simulations. Moreover, they claimed that such a device can be made portable, with low power requirements, and can be built very cheaply. Such a device can be used as a stand-alone RFID skimmer, to surreptitiously read the contents of simple RFID tags. The same device can be as the ``leech'' part of a relay-attack system, by which an attacker can make purchases using a victim's RFID-enhanced credit card---despite any cryptographic protocols that may be used. In this study we show that the modeling predictions are quite accurate. We show how to build a portable, extended-range RFID skimmer, using only electronics hobbyist supplies and tools. Our skimmer is able to read ISO-14443 tags from a distance of ~25cm, uses a lightweight 40cm-diameter copper-tube antenna, is powered by a 12V battery---and requires a budget of ~$100. We believe that, with some more effort, we can reach ranges of ~35cm, using the same skills, tools, and budget. We conclude that (a) ISO-14443 RFID tags can be skimmed from a distance that does not require the attacker to touch the victim; (b) Simple RFID tags, that respond to any reader, are immediately vulnerable to skimming; and (c) We are about half-way toward a full-blown implementation of a relay-attack.

The paper analyzes a new public key cryptosystem whose security is based on a matrix version of the discrete logarithm problem over an elliptic curve. It is shown that the complexity of solving the underlying problem for the proposed system is dominated by the complexity of solving a fixed number of discrete logarithm problems in the group of an elliptic curve. Using an adapted Pollard rho algorithm it is shown that this problem is essentially as hard as solving one discrete logarithm problem in the group of an elliptic curve.

Hardware side channel vulnerabilities have been studied for many years in embedded silicon-security arena including SmartCards, SetTop-boxes, etc. However, because various recent security activities have goals of improving the software isolation properties of PC platforms, software side channels have become a subject of interest. Recent publications discussed cache-based software side channel vulnerabilities of AES and RSA. Thus, following the classical approach --- a new side channel vulnerability opens a new mitigation research path --- this paper starts to investigate efficient mitigations to protect AES-software against side channel vulnerabilities. First, we will present several mitigation strategies to harden existing AES software against cache-based software side channel attacks and analyze their theoretical protection. Then, we will present a %thorough performance and security evaluation of our mitigation strategies. For ease of evaluation we measured the performance of our code against the performance of the openSSL AES implementation. In addition, we also analyzed our code under various existing attacks. Depending on the level of the required side channel protection, the measured performance loss of our mitigations strategies versus openSSL (respectively best assembler) varies between factors of 1.35 (2.66) and 2.85 (5.83).

We proposed the concept, piece in hand (soldiers in hand) matrix and have developed the framework based on the concept so far. The piece in hand matrix is a general concept which can be applicable to any type of multivariate public key cryptosystems to enhance their security. In this paper, we make improvements in the PH matrix method as follows. (i) In the PH matrix method, an arbitrary number of additional variables can be introduced to the random polynomial term in the public key, which is eliminated by the multiplication of the PH matrix to the public key in the decryption. Thus these additional variables enables the public key to have more than one solution, and therefore increases the difficulty to solve the public key. We show, in an experimental manner, that the PH matrix method improved in this way is secure even against the Gröbner basis attack. (ii) In the nonlinear PH matrix method proposed previously, the degree of polynomials in the public key is more than two, and this may cause an undesirable increase in the length of the public key. In this paper, we propose a nonlinear PH matrix method, where the degree of the public key is kept the same as the degree of the public key of the original cryptosystem, which is normally two.

Recently several researchers and practitioners have begun to address the problem of secure device pairing or how to set up secure communication between two devices without the assistance of a trusted third party. McCune, et al. [12] proposed Seeing-is-Believing (SiB), a system which uses a visual channel. The SiB visual channel consists of one device displaying the hash of its public key in the form of a two-dimensional barcode, and the other device reading this information using a photo camera. Strong mutual authentication in SiB requires running two separate unilateral authentication steps. In this paper, we show how strong mutual authentication can be achieved even with a unidirectional visual channel, where SiB could provide only a weaker property termed as presence. This could help reduce the SiB execution time and improve usability. By adopting recently proposed improved pairing protocols, we propose how visual channel authentication can be used even on devices that have very limited displaying capabilities, all the way down to a device whose display consists of a cheap single light-source, such as an LED. We also describe a new video codec that may be used to improve execution time of pairing in limited display devices, and can be used for other applications besides pairing.

NLS is one of the stream ciphers submitted to the eSTREAM project. We present a distinguishing attack on NLS by Crossword Puzzle (CP) attack method which is newly introduced in this paper. We build the distinguisher by using linear approximations of both the non-linear feedback shift register (NFSR) and the nonlinear filter function (NLF). Since the bias of the distinguisher depends on the $Konst$ value, which is a key-dependent word, we present the graph showing how the bias of distinguisher vary with $Konst$. In result, we estimate the average bias to be around $O(2^{-30})$. Therefore, we claim that NLS is distinguishable from truly random cipher after observing $O(2^{60})$ keystream words on the average. The experiments also show that our distinguishing attack is successful on $90.3\%$ of $Konst$ among $2^{32}$ possible values.

In a multipartite access structure, the set of players is divided into $K$ different entities, in such a way that all players of the same entity play the same role in the structure. Not many results are known about these structures, when $K \geq 3$. Even if the total characterization of ideal multipartite access structures seems a very ambitious goal, we take a first step in this direction. On the one hand, we detect some conditions that directly imply that a multipartite structure cannot be ideal. On the other hand, we prove that three wide families of multipartite access structures are ideal. We believe that the techniques employed in these proofs are so general that they could be used to prove in the future more general results related to the characterization of ideal multipartite access structures.

We describe a faithful embedding of the Dolev-Yao model of Backes, Pfitzmann, and Waidner (CCS 2003) in the theorem prover Isabelle/HOL. This model is cryptographically sound in the strong sense of reactive simulatability/UC, which essentially entails the preservation of arbitrary security properties under active attacks and in arbitrary protocol environments. The main challenge in designing a practical formalization of this model is to cope with the complexity of providing such strong soundness guarantees. We reduce this complexity by abstracting the model into a sound, light-weight formalization that enables both concise property specifications and efficient application of our proof strategies and their supporting proof tools. This yields the first tool-supported framework for symbolically verifying security protocols that enjoys the strong cryptographic soundness guarantees provided by reactive simulatability/UC. As a proof of concept, we have proved the security of the Needham-Schroeder-Lowe protocol using our framework.

Since Diffie-Hellman \cite{DH76}, many secure systems, based on discrete logarithm or Diffie-Hellman assumption in $\mathbb{Z}_p$, were introduced in the literature. In this work, we investigate the possibility to construct efficient primitives from exponentiation techniques over $\mathbb{Z}_p$. Consequently, we propose a new pseudorandom generator, where its security is proven under the decisional Diffie-Hellman assumption. Our generator is the most efficient among all generators from $\mathbb{Z}_p^*$ that are provably secure under standard assumptions. If an appropriate precomputation is allowed, our generator can produce $O(\log\log p)$ bits per modular multiplication. This is the best possible result in the literature (even improved by such a precomputation as well). Interestingly, our generator is the first provably secure under a decisional assumption and might be instructive for discovering potentially more efficient generators in the future. Our second result is a new family of universally collision resistant hash family (CRHF). Our CRHF is provably secure under the discrete log assumption and is more efficient than all previous CRHFs that are provably secure under standard assumptions (especially without a random oracle). This result is important, especially when the unproven hash functions (e.g., MD4, MD5, SHA-1) were broken by Wang et al. \cite{W+05,WY05,WYY05}.

We construct the first fully collusion resistant tracing traitors system with sublinear size ciphertexts and constant size private keys. More precisely, let $N$ be the total number of users. Our system generates ciphertexts of size $O(\sqrt{N})$ and private keys of size $O(1)$. We build our system by first building a simpler primitive called private linear broadcast encryption (PLBE). We then show that any PLBE gives a tracing traitors system with the same parameters. Our system uses bilinear maps in groups of composite order.

We introduce the notion of Linear Integer Secret-Sharing (LISS) schemes, and show constructions of such schemes for any access structure. We show that any LISS scheme can be used to build a secure distributed protocol for exponentiation in any group. This implies, for instance, distributed RSA protocols for arbitrary access structures and with arbitrary public exponents.

HMAC was proved by Bellare, Canetti and Krawczyk [2] to be a PRF assuming that (1) the underlying compression function is a PRF, and (2) the iterated hash function is weakly collision-resistant. However, recent attacks show that assumption (2) is false for MD5 and SHA-1, removing the proof-based support for HMAC in these cases. This paper proves that HMAC is a PRF under the sole assumption that the compression function is a PRF. This recovers a proof based guarantee since no known attacks compromise the pseudorandomness of the compression function, and it also helps explain the resistance-to-attack that HMAC has shown even when implemented with hash functions whose (weak) collision resistance is compromised. We also show that an even weaker-than-PRF condition on the compression function, namely that it is a privacy-preserving MAC, suffices to establish HMAC is a MAC as long as the hash function meets the very weak requirement of being computationally almost universal, where again the value lies in the fact that known attacks do not invalidate the assumptions made.

We consider the problem of efficiently generating sequences in hardware for use in certain cryptographic algorithms. The conventional method of doing this is to use a counter. We show that sequences generated by linear feedback shift registers (LFSRs) can be tailored to suit the appropriate algorithms. For hardware implementation, this reduces both time and chip area. As a result, we are able to suggest improvements to the design of DES Cracker built by the Electronic Frontier Foundation in 1998; provide an efficient strategy for generating start points in time-memory trade/off attacks; and present an improved parallel hardware implementation of a variant of the counter mode of operation of a block cipher.

(Revision of Sept. 2004 of a journal submission from Dec. 2000.) Certified mail is the fair exchange of a message for a receipt, i.e., the recipient gets the message if and only if the sender gets a receipt. It is an important primitive for electronic commerce and other atomicity services. Certified-mail protocols are known in the literature, but there was no rigorous definition yet, in particular for optimistic protocols and for many interleaved executions. We provide such a definition via an ideal system and show that a specific real certified-mail protocol is as secure as this ideal system in the sense of reactive simulatability in the standard model of cryptography and under standard assumptions. As certified mail without any third party is not practical, we consider optimistic protocols, which involve a third party only if one party tries to cheat. The real protocol resembles prior protocols, but we had to use a different cryptographic primitive to achieve simulatability. The communication model is synchronous. This proof first demonstrated that a cryptographic multi-step protocol can fulfil a general definition of reactive simulatability enabling concurrent composition. We also first showed how formal-method style reasoning can be applied over the ideal system in a cryptographically sound way. Moreover, the treatment of multiple protocol runs and their modular proof in spite of the use of common cryptographic primitives for all runs can be seen as a first example of what is now known as joint-state composition.

In a variety of group-oriented applications cryptographic primitives like group signatures or ring signatures are valuable methods to achieve anonymity of group members. However, in their classical form, these schemes cannot be deployed for applications that simultaneously require (i) to avoid centralized management authority like group manager and (ii) the signer to be anonymous only against non-members while group members have rights to trace and identify the signer. The idea of recently introduced {\it democratic group signatures} is to provide these properties. Based on this idea we introduce a group-oriented signature scheme that allows the group members to trace the identity of any other group member who issued a signature while non-members are only able to link the signatures issued by the same signer without tracing. For this purpose the signature scheme assigns to every group member a unique pseudonym that can be used by any non-member verifier to communicate with the anonymous signer from the group. We present several group-oriented application scenarios where this kind of linkability is essential. We propose a concrete linkable democratic group signature scheme for two-parties, prove its security in the random oracle model, and describe how to modularly extend it to the multi-party case.

In this paper we study the probability of differentials and characteristics over 2 rounds of the AES with the objective to understand how the components of the AES round transformation interact. We extend and correct the analysis of the differential properties of the multiplicative inverse in GF($2^n$). We show that AES has characteristics with a fixed-key probability that is many times larger than the EDP. For instance, in the case of 2-round AES, we measured factors up to $2^{100}$. We study the number of characteristics with EDP $>0$ whose probability adds up to the probability of a differential and derive formulas that allow to produce a close estimate of this number for any differential. We show how the properties discovered in our study can be used to explain the values of the differentials with the largest EDP values and to construct new distinguishers using truncated differentials.

We present the Zhuang-Zi algorithm, a new method for solving multivariate polynomial equations over a finite field. We describe the algorithm and present examples, some of which cannot be solved with the fastest known algorithms.

This paper takes UMAC --- a message authentication algorithm (MAC) optimized for performance on 32-bit architectures --- as its starting point, and adapts its strategies for optimum performance on 64-bit architectures. The resulting MAC, called UMAC8, achieves per message forgery probabilities of about $2^{-60}$ and $2^{-120}$ for tags of length 64 and 128 bits. The UMAC strategies are discussed at length and adapted for 64-bit environments, but are also modified to address several UMAC shortcomings, particularly key-agility and susceptibility to timing attacks. UMAC achieved peak throughput rates, when generating 64-bit tags, of 1.0 CPU cycle per byte of message authenticated, while UMAC8 achieves 0.5 cycles per byte.

Vector Stream Cipher (VSC) is a stream cipher designed by ChaosWare and patented by NICT (formerly CRL), Japanese patents 3030341 and 3455758, US patent 6,668,265. VSC is recommended by the Softbank Technology Corporation for use in high bandwidth and high security applications. In this paper we present a practical attack instantly recovering the entire secret key of the high-speed single-round VSC variants with only 4 known subsequent plaintext blocks showing how all single-round VSC variants can be trivially broken due to their simple algebraic nature. The algorithm presented in this paper cannot break the 8-round VSC, but it can be easily adapted to any particular high-speed single-round VSC variant and extended to break some of the multiple-round VSC variants with very little effort and it may help accelerate other attacks.

In this contribution, we derive a novel parallel formulation of the standard Itoh-Tsujii algorithm for multiplicative inverse computation over GF($2^m$). The main building blocks used by our algorithm are: field multiplication, field squaring and field square root operators. It achieves its best performance when using a special class of irreducible trinomials, namely, $P(X) = X^m + X^k + 1$, with $m$ and $k$ odd numbers and when implemented in hardware platforms. Under these conditions, our experimental results show that our parallel version of the Itoh-Tsujii algorithm yields a speedup of about 30% when compared with the standard version of it. Implemented in a Virtex 3200E FPGA device, our design is able to compute multiplicative inversion over GF($2^193$) after 20 clock cycles in about $0.94\mu$S.

We describe a new and practical identity-based key encapsulation mechanism that is secure in the standard model against chosen-ciphertext (CCA2) attacks. Since our construction is direct and not based on hierarchical identity-based encryption, it is more efficient than all previously proposed schemes. Furthermore, we give the first chosen-ciphertext secure identity-based key encapsulation mechanism with threshold key delegation and decryption in the standard model.

This paper aims at introducing generalized Jacobians as a new candidate for discrete logarithm (DL) based cryptography. The motivation for this work came from the observation that several practical DL-based cryptosystems, such as ElGamal, the Elliptic and Hyperelliptic Curve Cryptosystems, XTR, LUC as well as CEILIDH can all naturally be reinterpreted in terms of generalized Jacobians. However, usual Jacobians and algebraic tori are thus far the only generalized Jacobians implicitly utilized in cryptography. In order to go one step further, we here study the simplest nontrivial generalized Jacobians of an elliptic curve. In this first of a series of articles, we obtain explicit formulae allowing to efficiently perform arithmetic operations in these groups. This work is part of our doctoral dissertation, where security aspects are considered in depth. As a result, these groups thus provide the first concrete example of semi-abelian varieties suitable for DL-based cryptography.

Given a Boolean function $f$ on $n$-variables, we find a reduced set of homogeneous linear equations by solving which one can decide whether there exist annihilators at degree $d$ or not. Using our method the size of the associated matrix becomes $\nu_f \times (\sum_{i=0}^{d} \binom{n}{i} - \mu_f)$, where, $\nu_f = |\{x | wt(x) > d, f(x) = 1\}|$ and $\mu_f = |\{x | wt(x) \leq d, f(x) = 1\}|$ and the time required to construct the matrix is same as the size of the matrix. This is a preprocessing step before the exact solution strategy (to decide on the existence of the annihilators) that requires to solve the set of homogeneous linear equations (basically to calculate the rank) and this can be improved when the number of variables and the number of equations are minimized. As the linear transformation on the input variables of the Boolean function keeps the degree of the annihilators invariant, our preprocessing step can be more efficiently applied if one can find an affine transformation over $f(x)$ to get $h(x) = f(Bx+b)$ such that $\mu_h = |\{x | h(x) = 1, wt(x) \leq d\}|$ is maximized (and in turn $\nu_h$ is minimized too). We present an efficient heuristic towards this. Our study also shows for what kind of Boolean functions the asymptotic reduction in the size of the matrix is possible and when the reduction is not asymptotic but constant.

Kurosawa-Desmedt encryption scheme is a variation of Cramer-Shoup encryption schemes, which are the first practical schemes secure against adaptive chosen ciphertext attack in standard model. We introduce a variant of Kurosawa-Desmedt encryption scheme, which is not only secure against adaptive chosen ciphertext attack but also slightly more efficient than the original version.

We improve on the best known cryptanalysis of the stream cipher Py by using a hidden Markov model for the carry bits in addition operations where a certain distinguishing event takes place, and constructing from it an "optimal distinguisher" for the bias in the output bits which makes more use of the information available. We provide a general means to efficiently measure the efficacy of such a hidden Markov model based distinguisher, and show that our attack improves on the previous distinguisher by a factor of 2^16 in the number of samples needed. Given 2^72 bytes of output we can distinguish Py from random with advantage greater than 1/2, or given only a single stream of 2^64 bytes we have advantage 0.03.

Authenticated encryption schemes used in order to send one message to one recipient have received considerable attention in the last years. We investigate the case of schemes, we call authenticated $\mathtt{1{\to}n}$ schemes, that allow one to encrypt efficiently in a public-key setting a message for several, say $n$, recipients in an authenticated manner. We propose formal security definitions for such schemes that work also for $n=1$ and which are stronger and/or more general than those currently proposed. We then present a flexible mode of operation that transforms any $\mathtt{1{\to}1}$ authenticated encryption scheme working on small messages into a $\mathtt{1{\to}n}$ authenticated encryption scheme working on longer messages. We show that it allows the construction of efficient $\mathtt{1{\to}n}$ schemes that are proved secure for the strongest security notion.

Recently Manik et al. [13] proposed a novel remote user authentication scheme using bilinear pairings. Chou et al. [14] identified a weakness in Manik et al.’s scheme and made an improvement. In this paper, we show that both Manik et al.’s and Chou et al.’s schemes are insecure against forgery attack and replay attack.

Low degree annihilators for Boolean functions are of great interest in cryptology because of algebraic attacks on LFSR-based stream ciphers. Several polynomial algorithms for construction of low degree annihilators are introduced in this paper. The existence of such algorithms is studied for the following forms of the function representation: algebraic normal form (ANF), disjunctive normal form (DNF), conjunctive normal form (CNF), and arbitrary formula with the Boolean operations of negation, conjunction, and disjunction. For ANF and DNF of a Boolean function $f$ there exist polynomial algorithms that find the vector space $A_d (f)$ of all annihilators of degree $\leqslant d$. For CNF this problem is NP-hard. Nevertheless author introduces one polynomial algorithm that constructs some subspace of $A_d (f)$ having formula that represents $f$.

We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham. We show that our framework incorporates existing constructions for k = 3, 4, 6, and 12, and we give evidence that the method is unlikely to produce infinite families of curves with embedding degree k > 12.

This paper presents a practical digital signature scheme to be used in conjunction with network coding. Our scheme simultaneously provides authentication and detects malicious nodes that intentionally corrupt content on the network. The homomorphic property of the signatures allows nodes to sign any linear comination of the incoming packets without contacting the signing authority, but it is computationally infeasible for a node to sign a linear combination of the packets without disclosing what linear combination was used in the generation of the packet. Furthermore, we prove that the signature scheme is secure under well known cryptographic assumptions of the hardness of the Discrete-Log problem and the computational co-Diffie-Hellman problem on elliptic curves. Our scheme has a three-fold advantage over schemes based on homomorphic hashing: Firstly, we do not need to securely transmit hash values of the packets that the source transmits; secondly, since our scheme is based on elliptic curves, smaller security parameters suffice and this translates to improved efficiency since the bit lengths involved are smaller; finally, our scheme provides authentication of the data in addition to detecting pollution of packets.

Abstract. We show two ways of recovering all matching documents, in the Ostrovsky et al. Private Search [3], while requiring considerably shorter buffers. Both schemes rely on the fact that documents colliding in a buffer position provide the sum of their plaintexts. Efficient decoding algorithms can make use of this property to recover documents never present alone in a buffer position.

We propose an efficient anonymous authentication scheme which might be deployed in the setting of trusted computing platform. Our construction implements features such as total anonymity, variable anonymity, and rogue TPM tagging. The new scheme is significantly simpler, and more efficient than the current solution that has been adopted in the standard specification. We have proved the new scheme is secure under the strong RSA assumption, and the decisional Diffie-Hellman assumption.

We propose constructing provable collision resistant hash functions from expander graphs. As examples, we investigate two specific families of optimal expander graphs for provable hash function constructions: the families of Ramanujan graphs constructed by Lubotzky-Phillips-Sarnak and Pizer respectively. When the hash function is constructed from one of Pizer's Ramanujan graphs, (the set of supersingular elliptic curves over ${\FF}_{p^2}$ with $\ell$-isogenies, $\ell$ a prime different from $p$), then collision resistance follows from hardness of computing isogenies between supersingular elliptic curves. We estimate the cost per bit to compute these hash functions, and we implement our hash function for several members of the LPS graph family and give actual timings.

When communicating over a noisy channel, it is typically much easier to deal with random, independent errors with a known distribution than with adversarial errors. This paper looks at how one can use schemes designed for random errors in an adversarial context, at the cost of relatively few additional random bits and without using unproven computational assumptions. The basic approach is to permute the positions of a bit string using a permutation drawn from a $t$-wise independent family, where $t=o(n)$. This leads to two new results: 1. We construct *computationally efficient* information reconciliation protocols correcting $pn$ adversarial binary Hamming errors with optimal communication and entropy loss $n(h(p)+o(1))$ bits, where $n$ is the length of the strings and $h()$ is the binary entropy function. Information reconciliation protocols are important tools for dealing with noisy secrets in cryptography; they are also used to synchronize remote copies of large files. 2. We improve the randomness complexity (key length) of efficiently decodable capacity-approaching "private codes" from $\Theta(n\log n)$ to $n+o(n)$. We also present a simplified proof of an existential result on private codes due to Langberg (FOCS '04).

Since stream ciphers have the reputation to be inefficient in software applications the new stream cipher Hermes8 has been developed. It is based on a 8-bit-architecture and an algorithm with low complexity. The two versions presented here are Hermes8-80 with 23 byte state and 10 byte key and furthermore Hermes8-128 with 37 byte state and 16 byte key. Both are suited to run efficiently on 8-bit micro computers and dedicated hardware (e.g. for embedded systems). The estimated performance is up to one encrypted byte per 118 CPU cycles and one encrypted byte per nine cycles in hardware. The clarity and low complexity of the design supports cryptanalytic methods. The 8x8 sized S-BOX provides the non-linear function needed for proper confusion. Hermes8 uses the well-established AES S-BOX, but works also excellent with well-designed random S-BOXes. Hermes8 withstands so far several attacks by means of statistical tests, e.g. the Strict Avalanche Criterion and FIPS 140-2 are met successfully.

It has been noted recently that algebraic (annihilator) immunity alone does not provide sufficient resistance against algebraic attacks. In this regard, given a Boolean function $f$, just checking the minimum degree annihilators of $f, 1+f$ is not enough and one should check the relationsips of the form $fg = h$, and a function $f$, even if it has very good algebraic immunity, is not necessarily good against fast algebraic attack, if degree of $g$ becomes very low when degree of $h$ is equal to or little greater than the algebraic immunity of $f$. In this paper we theoretically study the two currently known constructions having maximum possible algebraic immunity from this viewpoint. To the end, we also experimentally study some cryptographically significant functions having good algebraic immunity.

We construct a reasonably efficient threshold and proactive pseudo-random permutation (PRP). Our protocol needs only O(1) communication rounds. It tolerates up to (n-1)/2 of n dishonest servers in the semi-honest environment. Many protocols that use PRPs (e.g., a CBC block cipher mode) can now be translated into the distributed setting. Our main technique for constructing invertible threshold PRPs is a distributed Luby-Rackoff construction where both the secret keys *and* the input are shared among the servers. We also present protocols for obliviously computing pseudo-random functions by Naor-Reingold and Dodis-Yampolskiy with shared input and keys.

In CRYPTO 2005, Xiaoyun Wang, Hongbo Yu and Yiqun Lisa Yin proposed an efficient collision attack on SHA-0. Collision messages are found with complexity $2^{39}$ SHA-0 operations by using their method. Collision messages can be obtained when a message satisfying all sufficient conditions is found. In their paper, they proposed message modifications that can satisfy all sufficient conditions of step 1-20. However, they didn't propose message modifications for sufficient conditions after step 21. In this paper, we propose message modifications for sufficient conditions of step 21-23. By using our message modifications, collision messages are found with complexity $2^{36}$ SHA-0 operations.

Security and privacy in RFID systems is an important and active research area. A number of challenges arise due to the extremely limited computational, storage and communication abilities of a typical RFID tag. This paper describes a step-by-step construction of a family of simple protocols for inexpensive untraceable identification and authentication of RFID tags. This work is aimed primarily at RFID tags that are capable of performing a small number of inexpensive conventional (as opposed to public key) cryptographic operations. It also represents the first result geared for so-called {\em batch mode} of RFID scanning whereby the identification (and/or authentication) of tags is delayed. Proposed protocols involve minimal interaction between a tag and a reader and place very low computational burden on the tag. Notably, they also impose low computational load on back-end servers.

This paper provides one more step towards bridging the gap between the formal and computational approaches to cryptographic protocols. We extend the well-known Abadi-Rogaway logic with probabilistic hashes and we give precise semantic to it using Canetti's oracle hashing. Finally, we show that this interpretation is computationally sound.

In 2005, Wen et al. proposed the first provably secure three-party password-based authenticated key exchange using Weil pairings, and provided their proof in a modified Bellare-Rogaway model (BR-model). Here, we show an impersonation attack on Wen et al.¡¦s scheme and point out a main flaw of their model that allows a man-in-the-middle adversary easily violate the security.

We present a certificate-based encryption scheme which is fully secure in the standard model. Our scheme is based on the identity-based encryption scheme of Waters \cite{W05}. Although some generic constructions from IBE to CBE has been previously proposed, they use the Random Oracle heuristic or provide less practical schemes than ours. Finally, we point out that one of the existing generic constructions going from IBE to CBE is flawed.

Formal verification is getting more and more important in computer science. However the state of the art formal verification methods in cryptography are very rudimentary. This paper is one step to provide a tool box allowing the use of formal methods in every aspect of cryptography. In this paper we give a formal specification of the RSA probabilistic signature scheme (RSA-PSS) [4] which is used as algorithm for digital signatures in the PKCS #1 v2.1 standard [7]. Additionally we show the correctness of RSA-PSS. This includes the correctness of RSA, the formal treatment of SHA-1 and the correctness of the PSS encoding method. Moreover we present a proof of concept for the feasibility of verification techniques to a standard signature algorithm.

Jansen introduced a technique for building LFSRs that can be clocked a large number of times with a single simple operation. These may be useful in the construction of stream ciphers based on clock-controlled LFSRs. However, for LFSR sizes of typical interest, it appears generally hard to find such jumping LFSRs with particular desired parameters. In this note we explain a trick which we used to find the jumping LFSRs in MICKEY and MICKEY-128, and which may be useful for future applications.

We report on a man-in-the-middle attack on PKINIT, the public key extension of the widely deployed Kerberos 5 authentication protocol. This flaw allows an attacker to impersonate Kerberos administrative principals (KDC) and end-servers to a client, hence breaching the authentication guarantees of Kerberos. It also gives the attacker the keys that the KDC would normally generate to encrypt the service requests of this client, hence defeating confidentiality as well. The discovery of this attack caused the IETF to change the specification of PKINIT and Microsoft to release a security update for some Windows operating systems. We discovered this attack as part of an ongoing formal analysis of the Kerberos protocol suite, and we have formally verified several fixes to PKINIT that prevent our attack.

We present a simple algorithm for computing the arithmetic weight of an integer with respect to a given radix r>=2. The arithmetic weight of n is the minimum number of nonzero digits in any signed radix-r representation of n. This algorithm leads to a new family of minimal weight signed radix-r representations which can be constructed using a left-to-right on-line algorithm. These representations are different from the ones previously reported by Joye and Yen at PKC 2002. The idea behind our algorithm is that of choosing closest elements which was introduced by Muir and Stinson at CT-RSA 2005. Our results have applications in coding theory and in the efficient implementation of public-key cryptography.

A nominative signature scheme allows a nominator (or signer) and a nominee (or verifier) to jointly generate and publish a signature in such a way that \emph{only} the nominee can verify the signature and if necessary, \emph{only} the nominee can prove to a third party that the signature is valid. In a recent work, Huang and Wang proposed a new nominative signature scheme which, in addition to the above properties, \emph{only} allows the nominee to convert a nominative signature to a publicly verifiable one. In ACISP 2005, Susilo and Mu presented several algorithms and claimed that these algorithms can be used by the nominator to verify the validity of a published nominative signature, show to a third party that the signature is valid, and also convert the signature to a publicly verifiable one, all \emph{without} any help from the nominee. In this paper, we point out that Susilo and Mu's attacks are actually \emph{incomplete} and {\it inaccurate}. In particular, we show that there exists no efficient algorithm for a nominator to check the validity of a signature if this signature is generated by the nominator and the nominee {\it honestly} and the Decisional Diffie-Hellman Problem is hard. On the other hand, we point out that the Huang-Wang scheme is indeed {\it insecure}, since there is an attack that allows the nominator to generate valid nominative signatures alone and prove the validity of such signatures to a third party.

Over the last 30 years the study of group key agreement has stimulated much work. And as a result of the increased popularity of ad hoc networks, some approaches for the group key establishment in such networks are proposed. However, they are either only for static group or the memory, computation and communication costs are unacceptable for ad-hoc networks. In this thesis some protocol suites from the literature (2^d-cube, 2^d-octopus, Asokan-Ginzboorg, CLIQUES, STR and TGDH) shall be discussed. We have optimized STR and TGDH by reducing the memory, communication and computation costs. The optimized version are denoted by µSTR and µTGDH respectively. Based on the protocol suites µSTR and µTGDH we present a Tree-based group key agreement Framework for Ad-hoc Networks (TFAN). TFAN is especially suitable for ad-hoc networks with limited bandwidth and devices with limited memory and computation capability. To simulate the protocols, we have implemented TFAN, µSTR and µTGDH with J2ME CDC. The TFAN API will be described in this thesis.

In this paper we describe how to efficiently implement pairing calculation on supersingular genus~2 curves over prime fields. We find that pairing calculation on supersingular genus~2 curves over prime fields is efficient and a viable candidate for practical implementation. We also show how to eliminate divisions in an efficient manner when computing the Tate pairing, and how this algorithm is useful for curves of genus greater than one.

Many cryptographic protocols secure against malicious players use specially designed cryptographic tools. Essentially, these special tools function much like less-expensive tools, but give extra `powers' to a reduction or simulation algorithm. Using these powers, cryptographers can construct a proof of security using standard techniques. However, these powers are not available to either the honest parties or the adversary. In a large class of protocols, by replacing the expensive, specially designed cryptographic tool with a corresponding less-expensive tool, we can improve the protocol's efficiency without changing the functionality available to either the adversary or the honest parties. The key motivating question we address in this paper is whether the new, `substituted' protocol is still secure. We introduce a framework for reasoning about this question. Our framework uses translators: special purpose oracles that map outputs of one cryptographic tool to corresponding outputs of a different tool. Translators are similar to, but generally weaker than, the ``angels'' of Prabhakaran and Sahai. We introduce the notion of substitution-friendly protocols and show that such protocols remain secure after substitution in our framework. We also leverage existing proofs of security; there is no need to re-prove security from scratch. We demonstrate our framework with a non-interactive non-malleable bit commitment protocol.

Worldwide symmetric encryption standards such as DES (Data Encryption Standard), AES (Advanced Encryption Standard), and EES (Escrowed Encryption Standard), have been -- and some of them still are -- extensively used to solve the problem of communication over an insecure channel, but with today's advanced technologies, they seem to not be as secure as one would like. In this paper, we propose efficient alternatives based on special classes of globally invertible cascaded convolutional transducers. The proposed symmetric encryption techniques have at least four advantages over traditional schemes based on Feistel ciphers. First, the secret key of a cascaded convolutional cryptosystem is usually much more easier to generate. Second, the encryption and decryption procedures are much simpler, and consequentially, much faster. Third, the desired security level can be obtained by just setting appropriate values for the parameters of the convolutional cryptosystem. Finally, they are much more parallelizable than symmetric encryption standards based on Feistel ciphers.

A linear $(q^d,q,t)$-perfect hash family of size $s$ in a vector space $V$ of order $q^d$ over a field $F$ of order $q$ consists of a sequence $\phi_1,\ldots,\phi_s$ of linear functions from $V$ to $F$ with the following property: for all $t$ subsets $X\subseteq V$ there exists $i\in\{1,\ldots,s\}$ such that $\phi_i$ is injective when restricted to $F$. A linear $(q^d,q,t)$-perfect hash family of minimal size $d(t-1)$ is said to be optimal. In this paper we use projective geometry techniques to completely determine the values of $q$ for which optimal linear $(q^3,q,3)$-perfect hash families exist and give constructions in these cases. We also give constructions of optimal linear $(q^2,q,5)$-perfect hash families.

In this thesis we consider homomorphic cryptosystems and their applications. Homomorphic cryptosystems allow for computations on encrypted data. We prove that the search for an algebraically homomorphic scheme can be reduced to the search of a homomorphic scheme on a special non-abelian group. Furthermore, we focus on a special application: computing with encrypted functions and data, respectively. For this application we develop an improved protocol that is efficient for functions that are computable by polynomial branching programs. Finally, we generalise the elliptic curve Paillier scheme by S. Galbraith in order to construct a threshold version of it. For this threshold scheme we develop several Sigma-protocols. Using these protocols we apply our threshold scheme on multiparty computations, electronic voting and commitment schemes.