Searching and modifying public-key encrypted data (without having the decryption key) has received a lot of attention in recent literature. In this paper we re-visit this important problem and achieve much better amortized communication-complexity bounds. Our solution resolves the main open question posed by Boneh at al., \cite{BKOS07}. First, we consider the following much simpler to state problem (which turns out to be central for the above): A server holds a copy of Alice's database that has been encrypted under Alice's public key. Alice would like to allow other users in the system to replace a bit of their choice in the server's database by communicating directly with the server, despite other users not having Alice's private key. However, Alice requires that the server should not know which bit was modified. Additionally, she requires that the modification protocol should have ``small" communication complexity (sub-linear in the database size). This task is referred to as private database modification, and is a central tool in building a more general protocol for modifying and searching over public-key encrypted data with small communication complexity. The problem was first considered by Boneh at al., \cite{BKOS07}. The protocol of \cite{BKOS07} to modify $1$ bit of an $N$-bit database has communication complexity $\mathcal{O}(\sqrt N)$. Naturally, one can ask if we can improve upon this. Unfortunately, \cite{OS08} give evidence to the contrary, showing that using current algebraic techniques, this is not possible to do. In this paper, we ask the following question: what is the communication complexity when modifying $L$ bits of an $N$-bit database? Of course, one can achieve naive communication complexity of $\mathcal{O}(L\sqrt N)$ by simply repeating the protocol of \cite{BKOS07}, $L$ times. Our main result is a private database modification protocol to modify $L$ bits of an $N$-bit database that has communication complexity $\mathcal{O}(\sqrt{NL^{1+\alpha}}\textrm{poly-log~} N)$, where $0<\alpha<1$ is a constant. (We remark that in contrast with recent work of Lipmaa \cite{L08} on the same topic, our database size {\em does not grow} with every update, and stays exactly the same size.) As sample corollaries to our main result, we obtain the following: \begin{itemize} \item First, we apply our private database modification protocol to answer the main open question of \cite{BKOS07}. More specifically, we construct a public key encryption scheme supporting PIR queries that allows every message to have a non-constant number of keywords associated with it. \item Second, we show that one can apply our techniques to obtain more efficient communication complexity when parties wish to increment or decrement multiple cryptographic counters (formalized by Katz at al. ~\cite{KMO01}). \end{itemize} We believe that ``public-key encrypted'' amortized database modification is an important cryptographic primitive in it's own right and will be a useful in other applications.

Galbraith, Lin and Scott recently constructed efficiently-computable endomorphisms for a large family of elliptic curves defined over F_{q^2} and showed, in the case where q is prime, that the Gallant-Lambert-Vanstone point multiplication method for these curves is significantly faster than point multiplication for general elliptic curves over prime fields. In this paper, we investigate the potential benefits of using Galbraith-Lin-Scott elliptic curves in the case where q is a power of 2. The analysis differs from the q prime case because of several factors, including the availability of the point halving strategy for elliptic curves over binary fields. Our analysis and implementations show that Galbraith-Lin-Scott offers significant acceleration for curves over binary fields, in both doubling- and halving-based approaches. Experimentally, the acceleration surpasses that reported for prime fields (for the platform in common), a somewhat counterintuitive result given the relative costs of point addition and doubling in each case.

We consider RSA with $N = pq$, $q < p < 2q$, public encryption exponent $e$ and private decryption exponent $d$. Boneh and Durfee (Eurocrypt 1999, IEEE-IT 2000) used Coppersmith's method (Journal of Cryptology, 1997) to factorize $N$ using $e$ when $d < N^{0.292}$, the {\sf theoretical bound}. Related works have also been presented by Blömer and May (CaLC 2001). However, the {\sf experimental bound} for $d$ that has been reached so far is only $N^{0.280}$ for 1000 bits $N$ (the upper bound on $d$ less for higher number of bits). The basic idea relied on LLL algorithm, but the experimental bounds were constrained by large lattice dimensions. In this paper we present {\sf theoretical results} as well as {\sf experimental evidences} to {\sf extend the bound of} $d$ for which RSA is weak. This requires the knowledge of a few most significant bits of $p$ (alternatively these bits need to be searched exhaustively). We provide experimental results to highlight that the problem can be solved with low lattice dimensions in practice. Our strategy outperforms the existing experimental results by increasing the bounds of $d$. We provide clear evidence that RSA, with $d$ of the order of $N^{0.3}$ for 1000 bit $N$, can be cryptanalysed in practice from the knowledge of $N, e$.

Ring signature was proposed to keep signer's anonymity when it signs messages on behalf of a ``ring" of possible signers. In this paper, we propose a novel notion of ring signature which is called attribute-based ring signature. In this kind of signature, it allows the signer to sign message with its attributes from attribute center. All users that possess of these attributes form a ring. The identity of signer is kept anonymous in this ring. Furthermore, anyone out of this ring could not forge the signature on behalf of the ring. Two constructions of attribute-based ring signature are also presented in this paper. The first scheme is proved to be secure in the random oracle model, with large universal attributes. We also present another scheme in order to avoid the random oracle model. It does not rely on non-standard hardness assumption or random oracle model. Both schemes in this paper are based on standard computational Diffie-Hellman assumption.

Traitor tracing schemes are cryptographically secure broadcast methods that allow identification of conspirators: if a pirate key is generated by $k$ traitors out of a static set of $\ell$ legitimate users, then all traitors can be identified given the pirate key. In this paper we address three practicality and security issues of the Boneh-Franklin traitor-tracing scheme. In the first place, without changing the original scheme, we modify its tracing procedure in the non-black-box model such that it allows identification of $k$ traitors in time $\tilde{O}(k^2)$, as opposed to the original tracing complexity $\tilde{O}(\ell)$. This new tracing procedure works independently of the nature of the Reed-Solomon code used to watermark private keys. As a consequence, in applications with billions of users it takes just a few minutes on a common desktop computer to identify large collusions. Secondly, we exhibit the lack of practical value of list-decoding algorithms to identify more than $k$ traitors. Finally, we show that $2k$ traitors can derive the keys of all legitimate users and we propose a fix to this security issue.

We present the first hierarchical identity based encryption (HIBE) system that has full security for more than a constant number of levels. In all prior HIBE systems in the literature, the security reductions suffered from exponential degradation in the depth of the hierarchy, so these systems were only proven fully secure for identity hierarchies of constant depth. (For deep hierarchies, previous work could only prove the weaker notion of selective-ID security.) In contrast, we offer a tight proof of security, regardless of the number of levels; hence our system is secure for polynomially many levels. Our result can very roughly be viewed as an application of Boyen's framework for constructing HIBE systems from exponent-inversion IBE systems to a (dramatically souped-up) version of Gentry's IBE system, which has a tight reduction. In more detail, we first describe a generic transformation from ``identity based broadcast encryption with key randomization" (KR-IBBE) to a HIBE, and then construct KR-IBBE by modifying a recent construction of IBBE of Gentry and Waters, which is itself an extension of Gentry's IBE system. Our hardness assumption is similar to that underlying Gentry's IBE system.

In dynamic networks with flexible memberships, group signatures and distributed signatures are an important problem. Dynamic threshold cryptosystems are best suited to realize distributed signatures in dynamic (e.g. meshed) networks. Without a group manager or a trusted third party even more flexible scenarios can be realized. Gennaro et al. showed, it is possible to dynamically increase the size of the signer group, without altering the public key. We extend this idea by removing members from the group, also without changing the public key. This is an important feature for dynamic groups, since it is very common, e.g. in meshed networks that members leave a group. Gennaro et al. used RSA and bi-variate polynomials for their scheme. In contrast, we developed a DL-based scheme that uses ideas from the field of proactive secret sharing (PSS). One advantage of our scheme is the possibility to use elliptic curve cryptography and thereby decrease the communication and computation complexity through a smaller security parameter. Our proposal is an efficient threshold cryptosystem that is able to adapt the group size in both directions. Since it is not possible to realize a non-interactive scheme with the ability to remove members (while the public key stays unchanged), we realized an interactive scheme whose communication efficency is highly optimized to compete with non-interactive schemes. Our contribution also includes a security proof for our threshold scheme.

Every public-key encryption scheme has to incorporate a certain amount of randomness into its ciphertexts to provide semantic security against chosen ciphertext attacks (IND-CCA). The difference between the length of a ciphertext and the embedded message is called the ciphertext overhead. While a generic brute-force adversary running in $2^t$ steps gives a theoretical lower bound of $t$ bits on the ciphertext overhead for IND-CPA security, the best known IND-CCA secure schemes demand roughly $2 t$ bits even in the random oracle model. Is the $t$-bit gap essential for achieving IND-CCA security? We close the gap by proposing an IND-CCA secure scheme whose ciphertext overhead matches the generic lower bound up to a small constant. Our scheme uses a variation of a four-round Feistel network in the random oracle model and hence belongs to the family of OAEP-based schemes. Maybe of independent interest is a new efficient method to encrypt long messages exceeding the length of the permutation while retaining the minimal overhead.

We present efficiently computable homomorphisms of the groups $G_2$ and $G_T$ for pairings $G_1 \times G_2 \rightarrow G_T$. This allows exponentiation in $G_2$ and $G_T$ to be accelerated using the Gallant-Lambert-Vanstone method.

Signcryption is a cryptographic primitive that aims at providing confidentiality and authentication simultaneously. Recently in May 2008, a scheme for identity based threshold signcryption was proposed by Fagen Li and Yong Yu. They have proved the confidentiality of their scheme and have also claimed the unforgeability without providing satisfactory proof. In this paper, we show that in their signcryption scheme the secret key of the sender is exposed(total break) to the clerk during sincryption and hence insecure in the presence of malicious clerks. Further, we propose a corrected version of the scheme and formally prove its security under the existing security model for signcryption.

At ACISP 2004, Huang and Wang first introduced the concept of convertible nominative signatures and also proposed a concrete scheme. However, it was pointed out by many works that Huang-Wang's scheme is in fact not a nominative signature. In this paper, we first present a security model for convertible nominative signatures. The properties of Unforgeability, Invisibility, Non-impersonation and Non-repudiation in the setting of convertible nominative signatures are defined formally. Then we modify Huang-Wang's scheme into a secure one. Formal proofs are provided to show that the modified Huang-Wang's scheme satisfies all the security properties under some conventional assumptions in the random oracle model.

This paper presents several improvements to Stern's attack on the McEliece cryptosystem and achieves results considerably better than Canteaut et al. This paper shows that the system with the originally proposed parameters can be broken in just 1400 days by a single 2.4GHz Core 2 Quad CPU,or 7 days by a cluster of 200 CPUs. This attack has been implemented and is now in progress. This paper proposes new parameters for the McEliece and Niederreiter cryptosystems achieving standard levels of security against all known attacks. The new parameters take account of the improved attack; the recent introduction of list decoding for binary Goppa codes; and the possibility of choosing code lengths that are not a power of 2. The resulting public-key sizes are considerably smaller than previous parameter choices for the same level of security.

Modular exponentiation in an abelian group is one of the most frequently used mathematical primitives in modern cryptography. {\em Batch verification} is to verify many exponentiations simultaneously. We propose two fast batch verification algorithms. The first one makes use of exponents with small weight, called {\em sparse exponents}, which is asymptotically 10 times faster than the individual verification and twice faster than the previous works without security loss. The second one is applied only to elliptic curves defined over small finite fields. Using sparse Frobenius expansion with small integer coefficients, we propose a complex exponent test which is four times faster than the previous works. For example, each exponentiation in one batch requires asymptotically 9 elliptic curve additions in some elliptic curves for $2^{80}$ security.

We construct a new public key encryption based on two assumptions: 1) One can obtain a pseudorandom generator with small locality by connecting the outputs to the inputs using any sufficiently good unbalanced expander. 2) It is hard to distinguish between a random graph that is such an expander and a random graph where a (planted) random logarithmic-sized subset S of the outputs is connected to fewer than |S| inputs. The validity and strength of the assumptions raise interesting new algorithmic and pseudorandomness questions, and we explore their relation to the current state-of-art.

Proxy signature schemes allow a proxy signer to generate proxy signatures on behalf of an original signer. Mambo et al. first introduced the notion of proxy signature and a lot of research work can be found on this topic nowadays. Recently, many identity based proxy signature schemes were proposed. However, some schemes are vulnerable to proxy key exposure attack. In this paper, we propose a security model for identity based proxy signature schemes. Then an efficient scheme from pairings is presented. The presented scheme is provably secure in the random oracle model. In particular, the new scheme is secure against proxy key exposure attack.

In this note, we describe a correction to the cryptosystem proposed by the authors in "Efficient and Secure Comparison for On-Line Auctions". Although the correction is small and does not affect the performance of the protocols proposed in that paper, it is necessary as the cryptosystem is not secure without it.

LSBS-RSA denotes an RSA system with modulus primes, p and q, sharing a large number of least significant bits. In ISC 2007, Zhao and Qi analyzed the security of short exponent LSBS-RSA. They claimed that short exponent LSBS-RSA is much more vulnerable to the lattice attack than the standard RSA. In this paper, we point out that there exist some errors in the calculation of Zhao & Qi's attack. After re-calculating, the result shows that their attack is unable for attacking RSA with primes sharing bits. Consequently, we give a revised version to make their attack feasible. We also propose a new method to further extend the security boundary, compared with the revised version. The proposed attack also supports the result of analogue Fermat factoring on LSBS-RSA, which claims that p and q cannot share more than (n/4) least significant bits, where n is the bit-length of pq. In conclusion, it is a trade-off between the number of sharing bits and the security level in LSBS-RSA. One should be more careful when using LSBS-RSA with short exponents.

To construct a suitable and secure proxy re-signature scheme is not an easy job, up to now, there exist only three schemes, one is proposed by Blaze et al. at EUROCRYPT 1998, and the others are proposed by Ateniese and Hohenbergerat ACM CCS 2005. However, none of these schemes is proved in the standard model (i.e., do not rely on the random oracle heuristic). In this paper, based on Waters' approach, we first propose a multi-use bidirectional proxy re-signature scheme, denoted as $S_{mb}$, which is existentially unforgeable in the standard model. And then, we extend $S_{mb}$ to be a multi-use bidirectional ID-based proxy re-signature scheme, denoted by $S_{id-mb}$, which is also existentially unforgeable in the standard model. Both of these two proposed schemes are computationally efficient, and their security bases on the Computational Diffie-Hellman (CDH) assumption.

In this paper,we construct two veriable attribute-based encryption(VABE)schemes.One is with a single authority,and the other is with multi authorities.Not only our schemes are proved secure as the previous ABE schemes,they also provide a verication property.Adding the verication property has a few advantages:first,it allows the user to immediately check the correctness of the keys,if not,he only needs the authority to resend the corresponding shares,especially,in multi-authoritycase,if the key does not pass the check,the user only needs to ask the particular authority to resend its own part,without need to go to all the authorities,this saves a lot of time when error appears;second,if the keys pass the verication but the user still does not rightly decrypt out the message,something might be wrong with the attributes or ciphertexts,then,the user has to contact with the encryptor.We formalize the notion of VABE and prove our schemes in our model.

Predicate encryption is a new paradigm generalizing, among other things, identity-based encryption. In a predicate encryption scheme, secret keys correspond to predicates and ciphertexts are associated with attributes; the secret key SK_f corresponding to the predicate f can be used to decrypt a ciphertext associated with attribute I if and only if f(I)=1. Constructions of such schemes are currently known for relatively few classes of predicates. We construct such a scheme for predicates corresponding to the evaluation of inner products over N (for some large integer N). This, in turn, enables constructions in which predicates correspond to the evaluation of disjunctions, polynomials, CNF/DNF formulae, or threshold predicates (among others). Besides serving as what we feel is a significant step forward in the theory of predicate encryption, our results lead to a number of applications that are interesting in their own right.

The black-box extraction problem over rings has (at least) two important interpretations in cryptography: An efficient algorithm for this problem implies (i) the equivalence of computing discrete logarithms and solving the Diffie-Hellman problem and (ii) the in-existence of secure ring-homomorphic encryption schemes. In the special case of a finite field, Boneh/Lipton and Maurer/Raub showed that there exist algorithms solving the black-box extraction problem in subexponential time. It is unknown whether there exist more efficient algorithms. In this work we consider the black-box extraction problem over finite rings of characteristic $n$, where $n$ has at least two different prime factors. We provide a polynomial-time reduction from factoring $n$ to the black-box extraction problem for a large class of finite commutative unitary rings. Under the factoring assumption, this implies the in-existence of certain efficient generic reductions from computing discrete logarithms to the Diffie-Hellman problem on the one side, and might be an indicator that secure ring-homomorphic encryption schemes exist on the other side.

Abstract. The piece in hand (PH) is a general scheme which is applicable to any reasonable type of multivariate public key cryptosystems for the purpose of enhancing their security. In this paper, we propose a new class PH method called NLPHPV (NonLinear Piece in Hand Perturbation Vector) method. Although our NLPHPV uses similar perturbation vectors as is used for the previously known internal perturbation method, this new method can avoid redundant repetitions in decryption process. With properly chosen parameter sizes, NLPHPV achieves an observable gain in security from the original multivariate public key cryptosystem. We demonstrate these by both theoretical analyses and computer simulations against major known attacks and provides the concrete sizes of security parameters, with which we even expect the grater security against potential quantum attacks.

The one-up problem is defined for any group and a function from the group to integers. An instance of problem consists of two points in the group. A solution consists of another point satisfying an equation involving the group and the function. The one-up problem must be hard for the security of (EC)DSA. Heuristic arguments are given for the independence of the discrete log and one-up problems. DSA and ECDSA are conjectured to be secure if the discrete log and one-up problems are hard and the hash is collision resistant.

Akiyama and Goto have proposed a cryptosystem based on rational points on curves over function fields (stated in the equivalent form of sections of fibrations on surfaces). It is easy to construct a curve passing through a few given points, but finding the points, given only the curve, is hard. We show how to break their original cryptosystem by using algebraic points instead of rational points and discuss possibilities for changing their original system to create a secure one.

A theoretical approach for integer factoring using complex analysis is to apply Newton's method on an analytic function whose zeros, within in a certain strip, correspond to factors of a given integer. A few successful toy experiments of factoring small numbers with this approach, implemented in a naive manner that amounts to complexified trial division, show that, at least for small numbers, Newton's method finds the requisite zeros, at least some of time (factors of nearby numbers were also sometimes found). Nevertheless, some heuristic arguments predict that this approach will be infeasible for factoring numbers of the size currently used in cryptography.

In predicate encryption systems, given a capability, one can evaluate one or more predicates on the encrypted data, while all other information about the plaintext remains hidden. We consider the first such systems to permit delegation of capabilities. In a system that supports delegation, a user Alice who has a capability can delegate to Bob a more restrictive capability, which allows him to learn less about encrypted data than she did. We formally define delegation in predicate encryption systems, and propose a new security definition for delegation. In addition, we present an efficient construction supporting conjunctive queries. The security of our construction can be reduced to the general 3-party Bilinear Diffie-Hellman assumption, and the Bilinear Decisional Diffie-Hellman assumption in composite-order bilinear groups.

We propose two constructions of chosen-ciphertext secure identity-based encryption (IBE) schemes. Our schemes have a security proof in the standard model, yet they offer performance competitive with all known random-oracle based schemes. The efficiency improvement is obtained by combining modifications of the IBE schemes by Waters and Gentry with authenticated symmetric encryption.

While recent timed-release encryption (TRE) schemes are implicitly supported by a certificateless encryption (CLE) mechanism, the security models of CLE and TRE differ and there is no generic transformation from a CLE to a TRE. This paper gives a generalized model for CLE that fulfills the requirements of TRE. This model is secure against adversaries with adaptive trapdoor extraction capabilities, decryption capabilities for arbitrary public keys, and partial decryption capabilities. It also supports hierarchical identifiers. We propose a concrete scheme under our generalized model and prove it secure without random oracles, yielding the first strongly-secure security-mediated CLE and the first TRE in the standard model. In addition, our technique of partial decryption is different from the previous approach.

Confidentiality and authenticity are two of the most fundamental problems in cryptography. Many applications require both confidentiality and authenticity, and hence an efficient way to get both together was very desirable. In 1997, Zheng proposed the notion of ``signcryption'', a single primitive which provides both confidentiality and authenticity in a way that's more efficient than signing and encrypting separately. Proxy re-encryption is a primitive that allows a semi-trusted entity called the ``proxy'' to convert ciphertexts addressed to a ``delegator'' to those that can be decrypted by a ``delegatee'', by using some special information given by the delegator, called the ``rekey''. In this work, we propose the notion of signcryption with proxy re-encryption (SCPRE), and motivate the same. We define security models for SCPRE, and also propose a concrete unidirectional, non-interactive identity-based SCPRE construction. We also provide complete proofs of security for the scheme in the security models defined. We finally provide directions for further research in this area.

In this paper, we propose two new certificate-based signature (CBS) schemes with new features and advantages. The first one is very efficient as it does not require any pairing computation and its security can be proven using Discrete Logarithm assumption in the random oracle model. We also propose another scheme whose security can be proven in the standard model without random oracles. To the best of our knowledge, these are the \emph{first} CBS schemes in the literature that have such kind of features.

The Naccache-Stern (NS) knapsack cryptosystem is an original yet little-known public-key encryption scheme. In this scheme, the ciphertext is obtained by multiplying public-keys indexed by the message bits modulo a prime $p$. The cleartext is recovered by factoring the ciphertext raised to a secret power modulo $p$. NS encryption requires a multiplication per two plaintext bits on the average. Decryption is roughly as costly as an RSA decryption. However, NS features a bandwidth sublinear in $\log p$, namely $\log p/\log \log p$. As an example, for a $2048$-bit prime $p$, NS encryption features a 233-bit bandwidth for a 59-kilobyte public key size. This paper presents new NS variants achieving bandwidths {\sl linear} in $\log p$. As linear bandwidth claims a public-key of size $\log^3 p/\log \log p$, we recommend to combine our scheme with other bandwidth optimization techniques presented here. For a $2048$-bit prime $p$, we obtain figures such as 169-bit plaintext for a 10-kilobyte public key, 255-bit plaintext for a 20-kilobyte public key or a 781-bit plaintext for a 512-kilobyte public key. Encryption and decryption remain unaffected by our optimizations: As an example, the 781-bit variant requires 152 multiplications per encryption.

This paper presents a new shape for ordinary elliptic curves over fields of characteristic 2. Using the new shape, this paper presents the first complete addition formulas for binary elliptic curves, i.e., addition formulas that work for all pairs of input points, with no exceptional cases. If n >= 3 then the complete curves cover all isomorphism classes of ordinary elliptic curves over F_2^n. This paper also presents dedicated doubling formulas for these curves using 2M + 6S + 3D, where M is the cost of a field multiplication, S is the cost of a field squaring, and D is the cost of multiplying by a curve parameter. These doubling formulas are also the first complete doubling formulas in the literature, with no exceptions for the neutral element, points of order 2, etc. Finally, this paper presents complete formulas for differential addition, i.e., addition of points with known difference. A differential addition and doubling, the basic step in a Montgomery ladder, uses 5M + 4S + 2D when the known difference is given in affine form.

In this paper we study a novel computational problem called the Hidden Root Problem, which appears naturally when considering fault attacks on pairing based cryptosystems. Furthermore, a variant of this problem is one of the main obstacles for efficient pairing inversion. We present an algorithm to solve this problem over extension fields and investigate for which parameters the algorithm becomes practical.

From the viewpoint of x-coordinate-only arithmetic on elliptic curves, switching between the Edwards model and the Montgomery model is quasi cost-free. We use this observation to speed up Montgomery's algorithm, reducing the complexity of a doubling step from 2M + 2S to 1M + 3S for suitably chosen curve parameters.

Secure group communication is significant for wireless and mobile computing. Overheads can be reduced efficiently when a sender sends multiple messages to multiple recipients using multi-recipient signcryption schemes. In this paper, we proposed the formal definition and security model of multi-recipient signcryption, presented the definition of reproducible signcryption and proposed security theorems for randomness reusing based multi-recipient signcryption schemes. We found that a secure reproducible signcryption scheme can be used to construct an efficient multi-recipient signcryption scheme which has the same security level as the underlying base signcryption scheme. We constructed a multi-recipient scheme which is provable secure in random oracle model assuming that the GDH problem is hard, based on a new BLS-type signcryption scheme. Overheads of the new scheme are only (n+1)/2n times of traditional ways when a sender sends different messages to n distinct recipients. It is more efficient than other known schemes. It creates a possibility for the practice of the public key cryptosystem in ubiquitous computing.

An attack on a recently proposed authentication scheme of Shpilrain and Ushakov is presented. The public information allows the derivation of a system of polynomial equations for the secret key bits. Our attack uses simple elimination techniques to distill linear equations. For the proposed parameter choice, the attack often finds secret keys or alternative secret keys within minutes with moderate resources.

Recently Cash, Kiltz, and Shoup showed a variant of the Cramer-Shoup (CS) public key encryption (PKE) scheme whose chosen-ciphertext (CCA) security relies on the computational Diffie-Hellman (CDH) assumption. The cost for this high security is that the size of ciphertexts is much longer than the CS scheme. In this paper, we show how to achieve CCAsecurity under the CDH assumption without increasing the size of ciphertexts. We further show a more efficient scheme under the hashed Diffie-Hellman (HDH) assumption such that the size of ciphertexts is the same as that of the Kurosawa-Desmedt (KD) scheme. Note that the CDH and HDH assumptions are weaker than the decisional Diffie-Hellman assumption which the CS and KD schemes rely on. Both of our schemes are based on a certain broadcast encryption (BE) scheme while the Cash-Kiltz-Shoup scheme is based on a different paradigm which is called the Twin DH problem. As an independent interest, we also show a generic method of constructing CCA-secure PKE schemes from BE schemes such that the existing CCA-secure constructions can be viewed as special cases.

With the advent of mobile and portable devices such as cell phones and PDAs, wireless content distribution has become a major means of communications and entertainment. In such applications, a central authority needs to deliver encrypted data to a large number of recipients in such a way that only a privileged subset of users can decrypt it. A broadcasting news channel may face this problem, for example, when a large number of people subscribe to a daily exclusive news feature. This is exactly the kind of problem that \textit{broadcast encryption} attempts to efficiently solve. On top of this, especially in the current digital era, junk content or spam is a major turn off in almost every Internet application. If all the users who subscribe to the news feed receive meaningless noise or any unwanted content, then the broadcaster is going to lose them. This results in the additional requirement that subscribers have source authentication with respect to their broadcaster. \textit{Broadcast signcryption}, which enables the broadcaster to simultaneously encrypt and sign the content meant for a specific set of users in a single logical step, provides the most efficient solution to the dual problem of confidentiality and authentication. Efficiency is a major concern, because mobile devices have limited memory and computational power and wireless bandwidth is an extremely costly resource. While several alternatives exist in implementing broadcast signcryption schemes, identity-based (ID-based) schemes are arguably the best suited because of the unique advantage that they provide --- any unique, publicly available parameter of a user can be his public key, which eliminates the need for a complex public key infrastructure. In ASIAN 2004, Mu et al. \cite{MSLR04} propose what they call an ID-based authenticated broadcast encryption scheme, which is also a broadcast signcryption scheme, as the security goals are the same. They claim that their scheme provides message authentication and confidentiality and formally prove that the broadcaster's secret is not compromised, but in this paper, we demonstrate that even without knowing the broadcaster's secret, it is possible for a legal user to impersonate the broadcaster. We demonstrate this by mounting a universal forgeability attack --- any valid user, on receiving and decrypting a valid ciphertext from a broadcaster, can generate a valid ciphertext on any message on behalf of that broadcaster for the same set of legal receivers to which the broadcaster signcrypted the earlier message, without knowing any secrets. Following this, we propose a new ID-based broadcast signcryption (IBBSC) scheme, and formally prove its security under the strongest existing security models for broadcast signcryption (IND-CCA2 and EUF-CMA2).

We address the problem of constructing public-key encryption schemes that meaningfully combine useful {\em computability features} with {\em non-malleability}. In particular, we investigate schemes in which anyone can change an encryption of an unknown message $m$ into an encryption of $T(m)$ (as a {\em feature}), for a specific set of allowed functions $T$, but the scheme is ``non-malleable'' with respect to all other operations. We formulate precise definitions that capture these intuitive requirements and also show relationships among our new definitions and other more standard ones (IND-CCA, gCCA, and RCCA). We further justify our definitions by showing their equivalence to a natural formulation of security in the Universally Composable framework. We also consider extending the definitions to features which combine {\em multiple} ciphertexts, and show that a natural definition is unattainable for a useful class of features. Finally, we describe a new family of encryption schemes that satisfy our definitions for a wide variety of allowed transformations $T$, and which are secure under the standard Decisional Diffie-Hellman (DDH) assumption.

This paper extends Joux-Naccache-Thomé's $e$-th root algorithm to the static Diffie-Hellman problem ({\sc sdhp}). The new algorithm can be adapted to diverse finite fields by customizing it with an {\sc nfs}-like core or an {\sc ffs}-like core. In both cases, after a number of {\sc sdhp} oracle queries, the attacker builds-up the ability to solve new {\sc sdhp} instances {\sl unknown before the query phase}. While sub-exponential, the algorithm is still significantly faster than all currently known {\sc dlp} and {\sc sdhp} resolution methods. We explore the applicability of the technique to various cryptosystems. The attacks were implemented in ${\mathbb F}_{2^{1025}}$ and also in ${\mathbb F}_{p}$, for a $516$-bit $p$.

First we revisit three - BGLS, MBGLS and GZZ verifiably encrypted signature schemes[2,3,6].We find that they are all not strong unforgeable.We remark that the notion of existential unforgeable is not sufficient for fair exchange protocols in most circumstances.So we propose three new - NBGLS, MBGLS and NGZZ verifiably encrypted signature schemes which are strong unforgeable. Also we reconsider other two - ZSS and CA verifiably encrypted signature schemes[4,8], we find that they both cannot resist replacing public key attack. So we strongly suggest that strong unforgeable for verifiably encrypted signature maybe a better notion than existential unforgeable and checking adjudicator knowing its private key is a necessary step for secure verifiably encrypted signature scheme.

Generalized signcryption which proposed by Han is a new cryptographic primitive which can work as an encryption scheme, a signature scheme or a signcryption scheme[5]. However,the security proof in their paper is not very formal.our contribution are as following:First we give security notions for this new primitive.Secnond,we give an attack to [4]which is the first vision of [5] and propose an improved generalized signcryption scheme. Third, we give new very formal proofs for this new scheme.

In 2007, $\ell$-Invertible Cycles ($\ell$IC) was proposed by Ding et al. This is one of the most efficient trapdoors for encryption/signature schemes, and of the mixed field type for multivariate quadratic public-key cryptosystems. Such schemes fit on the implementation over low cost smart cards or PDAs. In 2008, Fouque et al. proposed an efficient attack against the $\ell$IC signature scheme by using Gröbner basis algorithms. However, they only explicitly dealt with the odd case, i.e. $\ell$ is odd, but the even case; they only implemented their proposed attack in the odd case. In this paper, we propose an another practical attack against the $\ell$IC encryption/signature scheme. Our proposed attack does not employ Gröbner basis algorithms, and can be applied to the both even and odd cases. We show the efficiency of the attack by using some experimental results. Furthermore, the attack can be also applied to the $\ell$IC- scheme. To the best of our knowledge, we for the first time show some experimental results of a practical attack against the $\ell$IC- scheme for the even case.

Recently, a fast modular multiexponentiation algorithm for computing A^X B^Y (mod N) was proposed. The authors claimed that on average their algorithm only requires to perform 1.306k modular multiplications (MMs), where k is the bit length of the exponents. This claimed performance is significantly better than all other comparable algorithms, where the best known result by other algorithms achieves 1.503k MMs only. In this paper, we give a formal complexity analysis and show the claimed performance is not true. The actual computational complexity of the algorithm should be 1.556k. This means that the best modular multiexponentiation algorithm based on canonical-sighed-digit technique is still not able to overcome the 1.5k barrier.

How to define the security of undeniable signature schemes is a challenging task. This paper presents two security definitions of undeniable signature schemes which are more useful or natural than the existing definition. It then proves their equivalence. We first define the UC-security, where UC means universal composability. We next show that there exists a UC-secure undeniable signature scheme which does not satisfy the standard definition of security that has been believed to be adequate so far. More precisely, it does not satisfy the invisibility defined by \cite{DP96}. We then show a more adequate definition of invisibility which captures a wider class of (naturally secure) undeniable signature schemes. We finally prove that the UC-security against non-adaptive adversaries is equivalent to this definition of invisibility and the strong unforgeability in $\cF_{ZK}$-hybrid model, where $\cF_{ZK}$ is the ideal ZK functionality. Our result of equivalence implies that all the known proven secure undeniable signature schemes (including Chaum's scheme) are UC-secure if the confirmation/disavowal protocols are both UC zero-knowledge.

In this paper we present a new method to construct a polynomial $u(x) \in \mathbb{Z}[x]$ which will make $\mathrm{\Phi}_{k}(u(x))$ reducible. We construct a finite separable extension of $\mathbb{Q}(\zeta_{k})$, denoted as $\mathbb{E}$. By primitive element theorem, there exists a primitive element $\theta \in \mathbb{E}$ such that $\mathbb{E}=\mathbb{Q}(\theta)$. We represent the primitive $k$-th root of unity $\zeta_{k}$ by $\theta$ and get a polynomial $u(x) \in \mathbb{Q}[x]$ from the representation. The resulting $u(x)$ will make $\mathrm{\Phi}_{k}(u(x))$ factorable.

In 1998, Cai and Cusick proposed a lattice-based public-key cryptosystem based on the similar ideas of the Ajtai-Dwork cryptosystem, but with much less data expansion. However, they didn't give any security proof. In our paper, we present an efficient ciphertext-only attack which runs in polynomial time against the cryptosystem to recover the message, so the Cai-Cusick lattice-based public-key cryptosystem is not secure. We also present two chosen-ciphertext attacks to get a similar private key which acts as the real private key.

The irreducible factor $r(x)$ of $\mathrm{\Phi}_{k}(u(x))$ and $u(x) $ are often used in constructing pairing-friendly curves. $u(x)$ and $u_{c} \equiv u(x)^{c} \pmod{r(x)}$ are selected to be the Miller loop control polynomial in Ate pairing and $\mathrm{Ate}_{i}$ pairing. In this paper we show that when $4|k$ or the minimal prime which divides $k$ is larger than $2$, some $u(x)$ and $r(x)$ can not be used as curve generation parameters if we want $\mathrm{Ate}_{i}$ pairing to be efficient. We also show that the Miller loop length can not reach the bound $\frac{\mathrm{log_{2}r}}{\varphi(k)}$ when we use the factorization of $\mathrm{\Phi}_{k}(u(x))$ to generate elliptic curves.

In this paper, based on the scheme proposed by Barreto et al in ASIACRYPT 2005, an identity-based signcryption scheme in multiple Private Key Generator (PKG) environment is proposed, which mitigates the problems referred to users' private keys escrow and distribution in single PKG system. For security of the scheme, it is proved to satisfy the properties of message confidentiality and existential signature-unforgeability, assuming the intractability of the q-Strong Diffie-Hellman problem and the q-Bilinear Diffie-Hellman Inversion problem. For efficiency, compared with the state-of-the-art signcryption schemes of the same kind, our proposal needs less pairing computations and is shown to be the most efficient identity-based signcryption schemes for multiple PKGs up to date.

We give a generic construction for universal designated-verifier signature schemes from a large class, C, of signature schemes. The resulting schemes are efficient and have two important properties. Firstly, they are provably DV-unforgeable, non-transferable and also non-delegatable. Secondly, the signer and the designated verifier can independently choose their cryptographic settings. We also propose a generic construction for identity-based signature schemes from any signature scheme in C and prove that the construction is secure against adaptive chosen message and identity attacks. We discuss possible extensions of our constructions to hierarchical identity-based signatures, identity-based universal designated verifier signatures, and identity-based ring signatures from any signature in C.

This was a short note that deals with the design of Rainbow or ``stagewise unbalanced oil-and-vinegar'' multivariate signature schemes. We exhibit new cryptanalysis for current schemes that relates to flawed choices of system parameters in current schemes. These can be ameliorated according to an updated list of security design criteria.

Abelian class group Cl(D) of imaginary quadratic order with odd squarefree discriminant D is used in public key cryptosystems, based on discrete logarithm problem in class group and in cryptosystems, based on isogenies of elliptic curves. Discrete logarithm problem in Cl(D) is hard if #Cl(D) is prime or has large prime divisor. But no algorithms for generating such D are known. We propose probabilistic algorithm that gives discriminant of imaginary quadratic order O_D with subgroup of given prime order l. Algorithm is based on properties of Hilbert class field polynomial H_D for elliptic curve over field of p^l elements. Let trace of Frobenius endomorphism is T, discriminant of Frobenius endomorphism D = T^2-4p^l and j is not in prime field. Then deg(H_D) = #Cl(O_D) and #Cl(D)=0 (mod l). If Diophantine equation D = T^2-4p^l with variables l<O(|D|^(1/4)), prime p and T has solution only for l=1, then class number is prime.

In this paper we view interleaved Gabidulin codes and describe how to correct errors up to a rank equal to the amount of redundancy of the code with high probability. We give a detailed proof for our estimation of the probability of correct decoding. In a second part, we view the application to variants of the GPT cryptosystem. For GGPT this leads to an efficient attack on the remaining secure instances, whereas it allows to derive at least partial information of the plaintext in the case of RRC-GPT.

Proxy Signatures, introduced by Mambo, Usuda and Okamoto, allow a designated person to sign on behalf of an original signer. Braid groups has been playing an important role in the theory of cryptography as these are non commutative groups used in cryptography. Some digital signature schemes have been given but no proxy signature scheme has been introduced over braid groups. In this paper we have proposed proxy signature scheme using conjugacy search problem over braid groups. Our proxy signature scheme is partial delegated protected proxy signature.

We show how the Fiat-Shamir transform can be used to convert three-move identification protocols into two-tier signature schemes (a primitive we define) with a proof of security that makes a standard assumption on the hash function rather than modeling it as a random oracle. The result requires security of the starting protocol against concurrent attacks. We can show that numerous protocols have the required properties and so obtain numerous efficient two-tier schemes. Our first application is an efficient transform of any unforgeable signature scheme into a strongly unforgeable one, which uses as a tool any two-tier scheme. (This extends work of Boneh, Shen and Waters whose transform only applies to a limited class of schemes.) The second application is new one-time signature schemes that, compared to one-way function based ones of the same computational cost, have smaller key and signature sizes.

We use hybrid encryption with Fuzzy Identity-Based Encryption (Fuzzy-IBE) schemes, and present the first and efficient fuzzy identity-based key encapsulation mechanism (Fuzzy-IB-KEM) schemes which are chosen-ciphertext secure (CCA) without random oracle in the selective-ID model. To achieve these goals, we consider Fuzzy-IBE schemes as consisting of separate key and data encapsulation mechanisms (KEM-DEM), and then give the definition of Fuzzy-IB-KEM. Our main idea is to enhance Sahai and Waters' "large universe" construction (Sahai and Waters, 2005), chosen-plaintext secure (CPA) Fuzzy-IBE, by adding some redundant information to the ciphertext to make it CCA-secure.

We give an algorithm that produces families of Weil numbers for ordinary abelian varieties over finite fields with prescribed embedding degree. The algorithm uses the ideas of Freeman, Stevenhagen, and Streng to generalize the Brezing-Weng construction of pairing-friendly elliptic curves. We discuss how CM methods can be used to construct these varieties, and we use our algorithm to give examples of pairing-friendly ordinary abelian varieties of dimension 2 and 3 that are absolutely simple and have smaller $\rho$-values than any previous such example.

In this paper we propose two public key BE schemes that have efficient complexity measures. The first scheme, called the PBE-PI scheme, has $O(r)$ header size, $O(1)$ public keys and $O(\log N)$ private keys per user, where $r$ is the number of revoked users. This is the first public key BE scheme that has both public and private keys under $O(\log N)$ while the header size is $O(r)$. These complexity measures match those of efficient secret key BE schemes. \par Our second scheme, called the PBE-SD-PI scheme, has $O(r)$ header size, $O(1)$ public key and $O(\log N)$ private keys per user also. However, its decryption time is remarkably $O(1)$. This is the first public key BE scheme that has $O(1)$ decryption time while other complexity measures are kept low. Overall, this is the most efficient public key BE scheme up to now. \par Our basic schemes are one-way secure against {\em full collusion of revoked users} in the random oracle model under the BDH assumption. We modify our schemes to have indistinguishably security against adaptive chosen ciphertext attacks.

Certificateless cryptography achieves the best of the two worlds: it inherits from identity-based techniques a solution to the certificate management problem in public-key encryption, whilst removing the secret key escrow functionality inherent to the identity-based setting. Signcryption schemes achieve confidentiality and authentication simultaneously by combining public-key encryption and digital signatures, offering better overall performance and security. In this paper, we introduce the notion of certificateless signcryption and present an efficient construction which guarantees security under insider attacks, and therefore provides forward secrecy and non-repudiation. The scheme is shown to be secure using random oracles under a variant of the bilinear Diffie-Hellman assumption.

$k$-times anonymous authentication ($k$-TAA) schemes allow members of a group to be authenticated anonymously by application providers for a bounded number of times. Dynamic $k$-TAA allows application providers to independently grant or revoke users from their own access group so as to provide better control over their clients. In terms of time and space complexity, existing dynamic $k$-TAA schemes are of complexities O($k$), where $k$ is the allowed number of authentication. In this paper, we construct a dynamic $k$-TAA scheme with space and time complexities of $O(log(k))$. We also outline how to construct dynamic $k$-TAA scheme with a constant proving effort. Public key size of this variant, however, is $O(k)$. We then describe a trade-off between efficiency and setup freeness of AP, in which AP does not need to hold any secret while maintaining control over their clients. To build our system, we modify the short group signature scheme into a signature scheme and provide efficient protocols that allow one to prove in zero-knowledge the knowledge of a signature and to obtain a signature on a committed block of messages. We prove that the signature scheme is secure in the standard model under the $q$-SDH assumption. Finally, we show that our dynamic $k$-TAA scheme, constructed from bilinear pairing, is secure in the random oracle model.

The purpose of this paper is a description of a model of Kummer surfaces in characteristic 2, together with the associated formulas for the pseudo-group law. Since the classical model has bad reduction, a renormalization of the parameters is required, that can be justified using the theory of algebraic theta functions. The formulas that are obtained are very efficient and may be useful in cryptographic applications. We also show that applying the same strategy to elliptic curves gives Montgomery-like formulas in odd characteristic that are of some interest, and we recover already known formulas by Stam in characteristic 2.

The main purpose of this paper is to suggest that public key encryption can be secure against the "encryption emulation" attack (on the sender's encryption) by computationally unbounded adversary, with one reservation: a legitimate receiver decrypts correctly with probability that can be made arbitrarily close to 1, but not equal to 1.

In this paper, we introduce the Fractional Window-w Multibase Non-Adjacent Form (Frac-wmbNAF) method to perform the scalar multiplication. This method generalizes the recently developed Window-w mbNAF (wmbNAF) method by allowing an unrestricted number of precomputed points. We then make a comprehensive analysis of the most recent and relevant methods existent in the literature for the ECC scalar multiplication, including the presented generalization and its original non-window version known as Multibase Non-Adjacent Form (mbNAF). Moreover, we present new improvements in the point operation formulae. Specifically, we reduce further the cost of composite operations such as doubling-addition, tripling, quintupling and septupling of a point, which are relevant for the speed up of methods using multiple bases. Following, we also analyze the precomputation stage in scalar multiplications and present efficient schemes for the different studied scenarios. Our analysis includes the standard elliptic curves using Jacobian coordinates, and also Edwards curves, which are gaining growing attention due to their high performance. We demonstrate with extensive tests that mbNAF is currently the most efficient method without precomputations not only for the standard curves but also for the faster Edwards form. Similarly, Frac-wmbNAF is shown to attain the highest performance among window-based methods for all the studied curve forms.

Recently, democratic group signatures(DGSs) particularly catch our attention due to their great flexibilities, \emph{i.e}., \emph{no group manager}, \emph{anonymity}, and \emph{individual traceability}. In existing DGS schemes, individual traceability says that any member in the group can reveal the actual signer's identity from a given signature. In this paper, we formally describe the definition of DGS, revisit its security notions by strengthening the requirement for the property of traceability, and present a concrete DGS construction with $(t, n)$-\emph{threshold traceability} which combines the concepts of group signatures and of threshold cryptography. The idea behind the $(t, n)$-threshold traceability is to distribute between $n$ group members the capability of tracing the actual signer such that any subset of not less than $t$ members can jointly reconstruct a secret and reveal the identity of the signer while preserving security even in the presence of an active adversary which can corrupt up to $t-1$ group members.

In this paper we provide explicit formul\ae\ to compute bilinear pairings in compressed form. We indicate families of curves where the proposed compressed computation method can be applied and where particularly generalized versions of the Eta and Ate pairings due to Zhao \emph{et al.} are especially efficient. Our approach introduces more flexibility when trading off computation speed and memory requirement. Furthermore, compressed computation of reduced pairings can be done without any finite field inversions. We also give a performance evaluation and compare the new method with conventional pairing algorithms.

In this paper we present a new method for scalar multiplication that uses a generic multibase representation to reduce the number of required operations. Further, a multibase NAF-like algorithm that efficiently converts numbers to such representation without impacting memory or speed performance is developed and showed to be sublinear in terms of the number of nonzero terms. Additional representation reductions are discussed with the introduction of window-based variants that use an extended set of precomputations. To realize the proposed multibase scalar multiplication with or without precomputations in the setting of Elliptic Curve Cryptosystems (ECC) over prime fields, we also present a methodology to derive fast composite operations such as tripling or quintupling of a point that require less memory than previous point formulae. Point operations are then protected against simple side-channel attacks using a highly efficient atomic structure. Extensive testing is carried out to show that our multibase scalar multiplication is the fastest method to date in the setting of ECC and exhibits a small footprint, which makes it ideal for implementation on constrained devices.

Recently, Au et al. pointed out a seemingly neglected security concern for certificateless public key encryption (CL-PKE) scheme, where a malicious key generation center (KGC) can compromise the confidentiality of the messages by embedding extra trapdoors in the system parameter. Although some schemes are secure against such an attack, they require random oracles to prove the security. In this paper, we first show that two existing CL-PKE schemes without random oracles are not secure against malicious KGC, we then propose the first CL-PKE scheme secure against malicious KGC attack, with proof in the standard model.

We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly hard) instance of the knapsack problem. We provide both complexity results (size of the key, time needed to encypher/decypher...) and experimental results. Security results are given for the second cryptosystem ( the fastest one and the one with the shortest key). Probabilistic polynomial reductions show that finding the private key is as difficult as factorizing a product of two primes. We also consider heuristic attacks. First, the density of the cryptosystem can be chosen arbitrarily close to one, discarding low density attacks. Finally, we consider explicit heuristic attacks based on the LLL algorithm and we prove that with respect to these attacks, the public key is as secure as a random key.

Direct Anonymous Attestation (DAA) is a cryptographic mechanism that enables remote authentication of a user while preserving privacy under the user's control. The DAA scheme developed by Brickell, Camenisch, and Chen has been adopted by the Trust Computing Group (TCG) for remote anonymous attestation of Trusted Platform Module (TPM), a small hardware device with limited storage space and communication capability. In this paper, we provide two contributions to DAA. We first introduce simplified security notions of DAA including the formal definitions of user controlled anonymity and traceability. We then propose a new DAA scheme from elliptic curve cryptography and bilinear maps. The lengths of private keys and signatures in our scheme are much shorter than the lengths in the original DAA scheme, with a similar level of security and computational complexity. Our scheme builds upon the Camenisch-Lysyanskaya signature scheme and is efficient and provably secure in the random oracle model under the LRSW (stands for Lysyanskaya, Rivest, Sahai and Wolf) assumption and the decisional Bilinear Diffie-Hellman assumption.

Elliptic curve cryptography (ECC), independently introduced by Koblitz and Miller in the 80's, has attracted increasing attention in recent years due to its shorter key length requirement in comparison with other public-key cryptosystems such as RSA. Shorter key length means reduced power consumption and computing effort, and less storage requirement, factors that are fundamental in ubiquitous portable devices such as PDAs, cellphones, smartcards, and many others. To that end, a lot of research has been carried out to speed-up and improve ECC implementations, mainly focusing on the most important and time-consuming ECC operation: scalar multiplication. In this thesis, we focus in optimizing such ECC operation at the point and scalar arithmetic levels, specifically targeting standard curves over prime fields. At the point arithmetic level, we introduce two innovative methodologies to accelerate ECC formulae: the use of new composite operations, which are built on top of basic point doubling and addition operations; and the substitution of field multiplications by squarings and other cheaper operations. These techniques are efficiently exploited, individually or jointly, in several contexts: to accelerate computation of scalar multiplications, and the computation of pre-computed points for window-based scalar multiplications (up to 30% improvement in comparison with previous best method); to speed-up computations of simple side-channel attack (SSCA)-protected implementations using innovative atomic structures (up to 22% improvement in comparison with scalar multiplication using original atomic structures); and to develop parallel formulae for SIMD-based applications, which are able to execute three and four operations simultaneously (up to 72% of improvement in comparison with a sequential scalar multiplication). At the scalar arithmetic level, we develop new sublinear (in terms of Hamming weight) multibase scalar multiplications based on NAF-like conversion algorithms that are shown to be faster than any previous scalar multiplication method. For instance, proposed multibase scalar multiplications reduce computing times in 10.9% and 25.3% in comparison with traditional NAF for unprotected and SSCA-protected scenarios, respectively. Moreover, our conversion algorithms overcome the problem of converting any integer to multibase representation, solving an open problem that was defined as hard. Thus, our algorithms make the use of multiple bases practical for applications as ECC scalar multiplication for first time.

In this paper we introduce the concept of an \emph{optimal pairing}, which by definition can be computed using only $\log_2 r/ \varphi(k)$ basic Miller iterations, with $r$ the order of the groups involved and $k$ the embedding degree. We describe an algorithm to construct optimal ate pairings on all parametrized families of pairing friendly elliptic curves. Finally, we conjecture that any non-degenerate pairing on an elliptic curve without efficiently computable endomorphisms different from powers of Frobenius requires at least $\log_2 r/ \varphi(k)$ basic Miller iterations.

A blind signature is a cryptographic premitive in which a user can obtain a signature from the signer without revealing any information about message signature pair.Blind signatures are used in electronic payment systems, electronic voting machines etc.The anonymity can be misused by criminals by money laundering or by dubious money.To prevent these crimes, the idea of fair blind signature scheme was given by stadler et al.In fair blind signature scheme, there is a trusted third party judge who can provide a linking protocol to signer to link his view to the message signature pair.In this paper we are proposing some identity based fair blind signatures.

We present a public-key encryption scheme which is provably secure against adaptive chosen ciphertext attack. The scheme is constructed using Cramer-Shoup paradigm. The security of the scheme is based on the Decisional Bilinear Diffie-Hellman problem

Generalized signcryption is a new cryptographic primitive in which a signcryption scheme can work as an encryption scheme as well as a signature scheme. This paper presents an identity based generalized signcryption scheme based on bilinear pairing and discusses its security for message confidentiality non repudiation and ciphertext authentication.

It is widely believed to take exponential time to find a solution of a system of random multivariate polynomials because of the NP-completeness of such a task. On the other hand, in most of multivariate public key cryptosystems proposed so far, the computational complexity of cryptanalysis is apt to be polynomial time due to the trapdoor structure. In this paper, we develop the concept, piece in hand matrix (PH matrix, for short), which aims to bring the computational complexity of cryptanalysis of multivariate public key cryptosystems close to exponential time by adding random polynomial terms to original cryptosystems. This is a general concept which can be applicable to any reasonable type of multivariate public key cryptosystems for the purpose of enhancing their security. There are two types of the PH matrices: a linear matrix whose elements are constants and a nonlinear matrix whose elements are polynomial functions of the plain text or random numbers. In the present paper, we focus our thought on the nonlinear PH matrix method and develop the framework of it. The nonlinear PH matrix method is obtained by generalizing the linear PH matrix method, and the nonlinearity may bring an additional randomization to the original linear PH matrix method. Thus, the nonlinear PH matrix method may enhance the security of the original multivariate public key cryptosystem more than the linear PH matrix method. We show, in an experimental manner, that this actually holds in the enhancement of the security of the Matsumoto-Imai cryptosystem and RSE(2)PKC against the Gröbner basis attack.

In this contribution we investigate practical issues with implementing the NFS algorithm to solve the DLP arising in XTR-based cryptosystems. We can transform original XTR-DLP to a DLP instance in $\mathbb{F}_{p^6},$ where $p$ is a medium sized prime. Unfortunately, for practical ranges of $p,$ the optimal degree of NFS polynomial is less than the required degree 6. This leads to a problem to find enough smooth equations during the sieve stage of the NFS algorithm. We discuss several techniques that can increase the NFS output, i.e. the number of equations produced during the sieve, without increasing the smoothness bound.

We present and analyze two algorithms for computing the Hilbert class polynomial H_D(X). The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing H_D(X), and we show that all methods have comparable run times.

We present an algorithm that, on input of a CM-field $K$, an integer $k \ge 1$, and a prime $r \equiv 1 \bmod k$, constructs a $q$-Weil number $\pi \in \O_K$ corresponding to an ordinary, simple abelian variety $A$ over the field $\F$ of $q$ elements that has an $\F$-rational point of order $r$ and embedding degree $k$ with respect to $r$. We then discuss how CM-methods over $K$ can be used to explicitly construct $A$.

We present here a thorough discussion of the problem of fast arithmetic on elliptic curves over prime order &#64257;nite &#64257;elds. Since elliptic curves were independently pro- posed as a setting for cryptography by Koblitz [53] and Miller [67], the group of points on an elliptic curve has been widely used for discrete logarithm based cryptosystems. In this thesis, we survey, analyse and compare the fastest known serial and parallel algorithms for elliptic curve scalar multiplication, the primary operation in discrete logarithm based cryptosystems. We also introduce some new algorithms for the basic group operation and several new parallel scalar multiplication algorithms. We present a mathematical basis for comparing the various algorithms and make recommendations for the fastest algorithms to use in di&#64256;erent circumstances.

The computation speed of pairing based cryptosystems is slow compared with the other public key cryptosystems even though several efficient computation algorithms have been proposed. Thus more efficient computation of the Tate pairing is an important research goal. GF(3m) multiplication in GF(36m) in the pairing algorithm is the greatest consumer of time. Past research concentrated on reducing the number of GF(3m) multiplications, for instance the Karatsuba method. In this article, we propose a new method to reduce the number of online precomputations( precomputations) in GF(3m) multiplications for the eta T pairing. The proposed algorithm reduces 18 online precomputations in GF(36m) in the eta T pairing to 4 online precomputations by reusing the intermediate products obtained in precomputation.We implement the proposed algorithm and compare the time taken by the proposed algorithm with that of the previous work. Our algorithm offers a 40% performance increase for GF(3m) multiplications in GF(36m) on an AMD 64-bit processor. Additionally, a completely new finding is obtained. The results show that the reducing the number of the multiplications in GF(36m) does not necessarily lead to a speed-up of the eta T pairing calculation.

In this work we deal with one-round key-agreement protocols, called Merkle's Puzzles, in the random oracle model, where the players Alice and Bob are allowed to query a random permutation oracle $n$ times. We prove that Eve can always break the protocol by querying the oracle $O(n^2)$ times. The long-time unproven optimality of the quadratic bound in the fully general, multi-round scenario has been proven recently by Barak and Mahmoody-Ghidary. The results in this paper have been found independently of their work.

We present a new methodology to derive faster composite operations of the form dP+Q, where d is a small integer >= 2, for generic ECC scalar multiplications over prime fields. In particular, we present an efficient Doubling-Addition (DA) operation that can be exploited to accelerate most scalar multiplication methods, including multiscalar variants. We also present a new precomputation scheme useful for window-based scalar multiplications that is shown to achieve the lowest cost among all known methods using only one inversion. In comparison to the remaining approaches that use none or several inversions, our scheme offers higher performance for most common I/M ratios. By combining the benefits of our precomputation scheme and the new DA operation, we can save up to 6.2% in the scalar multiplication using fractional wNAF.

Here we propose an identity based signcryption scheme in the multi-PKG environment where sender and receiver receive public key from different PKG. We also define security models for our scheme and give security proofs in random oracle model.

In this paper, a new identity-based proxy signcryption scheme is presented. The proposed scheme allows partial delegation of signing rights. Consequently, a signature created by the proxy signer is distinguishable from that created by the principal signer. This level of security is a common requirement in many applications to prevent malicious proxy agents from impersonating the principal signer. Moreover, the scheme is based on bilinear pairings over elliptic curves and thus smaller key sizes are required compared to schemes not utilizing elliptic curves. A revocation protocol of dishonest agents is given together with a renewal procedure for the proxies of honest agents. Finally, an application scenario for the proposed scheme is presented.

In this paper, we propose a new method for constructing a bilinear pairing over (hyper)elliptic curves, which we call the R-ate pairing. This pairing is a generalization of the Ate and Ate_i pairing, and also improves efficiency of the pairing computation. Using the R-ate pairing, the loop length in Miller's algorithm can be as small as ${\rm log}(r^{1 / \phi(k)})$ for some pairing-friendly elliptic curves which have not reached this lower bound. Therefore we obtain from 29 % to 69 % savings in overall costs compared to the Ate_i pairing. On supersingular hyperelliptic curves of genus 2, we show that this approach makes the loop length in Miller's algorithm shorter than that of the Ate pairing.

Anonymity of consumers is an essential functionality that should be supported in e-cash systems, locations based services, electronic voting systems as well as digital rights management system. Privacy protection is an important aspect for wider acceptance of consumers of DRM systems. The concept of a blind signature is one possible cryptographic solution, yet it has not received much attention in the identity-based setting. In the identity-based setting, the public key of a user is derived from his identity, thus simplifying certificates management process compared to traditional public key cryptosystems. In this paper, a new blind identity-based signature scheme with message recovery based on bilinear pairings on elliptic curves is presented. The use of bilinear pairings over elliptic curves enables utilizing smaller key sizes, while achieving the same level of security compared to other schemes not utilizing elliptic curves. The scheme achieves computational savings compared to other schemes in literature. The correctness of the proposed scheme is validated and the proof of the blindness property is provided. Performance and other security related issues are also addressed.

A blind signature scheme is a cryptographic protocol for obtaining a signature from a signer such that the signer's view of the protocol cannot be linked to the resulting message signature pair. In this paper we have proposed two blind signature schemes using Braid groups. The security of given schemes depends upon conjugacy search problem in Braid groups.

In this paper I study the MOR cryptosystem using the special linear group over finite fields. At our current state of knowledge, I show that the MOR cryptosystem is more secure than the ElGamal cryptosystem over finite fields.

If factoring is hard, this paper shows that straight line programs cannot efficiently solve the low public exponent RSA problem. More precisely, no efficient algorithm can take an RSA public key as input and then output a straight line program that efficiently solves the low public exponent RSA problem for the given public key --- unless factoring is easy.

We introduce a new cryptographic primitive which is the signature analogue of fuzzy identity based encryption(IBE). We call it fuzzy identity based signature(IBS). It possesses similar error-tolerance property as fuzzy IBE that allows a user with the private key for identity $\omega$ to decrypt a ciphertext encrypted for identity $\omega'$ if and only if $\omega$ and $\omega'$ are within a certain distance judged by some metric. A fuzzy IBS is useful whenever we need to allow the user to issue signature on behalf of the group that has certain attributes. Fuzzy IBS can also be applied to biometric identity based signature. To our best knowledge, this primitive was never considered in the identity based signature before. We give the definition and security model of the new primitive and present the first practical implementation based on Sahai-Waters construction\cite{6} and the two level hierarchical signature of Boyen and Waters\cite{9}. We prove that our scheme is existentially unforgeable against adaptively chosen message attack without random oracles.

We study the provable security of identity-based (ID-based) key agreement protocols. Although several published protocols have been proven secure in the random oracle model, only a weak adversarial model is considered -- the adversary is not allowed to ask Session-Key Reveal queries that will allow the adversary to learn previously established session keys. Recent research efforts devoted to providing a stronger level of security require strong assumptions, such as assuming that the simulator has access to a non-existential computational or decisional oracle. In this work, we propose an ID-based key agreement protocol and prove its security in the widely accepted indistinguishability-based model of Canetti and Krawczyk. In our proof, the simulator does not require access to any non-existential computational or decisional oracle. We then extend our basic protocol to support ad-hoc anonymous key agreement with bilateral privacy. To the best of our knowledge, this is the first protocol of its kind as previously published protocols are for fixed group and provide only unilateral privacy (i.e., only one of the protocol participants enjoy anonymity).

This paper presents a new paradigm to realize cryptographic primitives such as authenticated key exchange and key encapsulation without random oracles under three assumptions: the decisional Diffie-Hellman (DDH) assumption, target collision resistant (TCR) hash functions and a class of pseudo-random functions (PRFs), $\pi$PRFs, PRFs with pairwise-independent random sources. We propose a (PKI-based) two-pass authenticated key exchange (AKE) protocol that is comparably as efficient as the existing most efficient protocols like MQV and that is secure without random oracles (under these assumptions). Our protocol is shown to be secure in the (currently) strongest security definition, the extended Canetti-Krawczyk (eCK) security definition introduced by LaMacchia, Lauter and Mityagin. We also show that a variant of the Kurosawa-Desmedt key encapsulation mechanism (KEM) using a $\pi$PRF is CCA-secure under the three assumptions. This scheme is secure in a stronger security notion, the chosen public-key and ciphertext attack (CPCA) security, with using a generalized TCR (GTCR) hash function in place of a TCR hash function. The proposed schemes in this paper are validity-check-free and the implication is that combining them with validity-check-free symmetric encryption (DEM) will yield validity-check-free (e.g., MAC-free) CCA-secure hybrid encryption.

This paper surveys the literature on certificateless encryption schemes. In particular, we examine the (large number of) security models that have been proposed to prove the security of certificateless encryption schemes and propose a new nomenclature for these models. This allows us to "rank" the notions of security for a certificateless encryption scheme against an outside attacker and a passive key generation centre, and we suggest which of these notions should be regarded as the "correct" model for a secure certificateless encryption scheme. We also examine the security models that aim to provide security against an actively malicious key generation centre and against an outside attacker who attempts to deceive a legitimate sender into using an incorrect public key (with the intention to deny the the legitimate receiver that ability to decrypt the ciphertext). We note that the existing malicious key generation centre model fails to capture realistic attacks that a malicious key generation centre might make and propose a new model. Lastly, we survey the existing certificateless encryption schemes and compare their security proofs. We show that few schemes provide the correct notion of security without appealing to the random oracle model. The few schemes that do provide sufficient security guarantees are comparatively inefficient. Hence, we conclude that more research is needed before certificateless encryption schemes can be thought to be a practical technology.

We describe a new method for constructing Brezing-Weng-like pairing-friendly elliptic curves. The new construction uses the minimal polynomials of elements in a cyclotomic field. Using this new construction we present new ``record breaking'' families of pairing-friendly curves with embedding degrees of $k \in \{16,18,36,40\}$, and some interesting new constructions for the cases $k \in \{8,32\}$

We introduce a new simplified notion of plaintext awareness, which we term PA2I, and show that this is equivalent to the standard definition of PA2 plaintext awareness for encryption schemes that satisfy certain weak security and randomness requirements. We also show that PA2 plaintext awareness is equivalent to PA2+ plaintext awareness under similar security and randomness requirements. This proves a conjecture of Dent that, for suitably random public-key encryption schemes, PA2 plaintext awareness implies PA1+ plaintext awareness.

Let $P$ be a point on an elliptic curve over a finite field of large characteristic. Exactly how many points $2P,3P,5P,7P,9P,\ldots,mP$ should be precomputed in a sliding-window computation of $nP$? Should some or all of the points be converted to affine form, and at which moments during the precomputation should these conversions take place? Exactly how many field multiplications are required for the resulting computation of $nP$? The answers depend on the size of $n$, the $\inversions/\mults$ ratio, the choice of curve shape, the choice of coordinate system, and the choice of addition formulas. This paper presents answers that, compared to previous analyses, are more carefully optimized and cover a much wider range of situations.

This technical report describes a novel certificateless signature scheme suitable for aggregation that requires no pairing computations for signing and only 3 pairing computations for signature verification. We provide proofs for the security of single and aggregate signatures.

One day, you suddenly find that a private key corresponding to your Identity is up for sale at e-Bay. Since you do not suspect a key compromise, perhaps it must be the PKG who is acting dishonestly and trying to make money by selling your key. How do you find out for sure and even prove it in a court of law? This paper introduces the concept of Accountable Authority Identity based Encryption (A-IBE). A-IBE is a new approach to mitigate the (inherent) key escrow problem in identity based encryption schemes. Our main goal is to restrict the ways in which the PKG can misbehave. In our system, if the PKG ever maliciously generates and distributes a decryption key for an Identity, it runs the risk of being caught and prosecuted. In contrast to other mitigation approaches, our approach does not require multiple key generation authorities.

In this paper a new efficient public key cryptosystem usable for both encryption and digital signatures is presented. Due to its simple structure this public key cipher can be implemented easily in every software or hardware device, making the cryptosystem available for circumstances where the implementation of an alternative like RSA, El Gamal / Diffie - Hellmann, etc. is too complicated. Furthermore the construction on the closest and shortest vector problem using a new homomorph "almost" linear one-way function gives not only strong evidence of the ciphers security, but may be also the base for a new class of "errorprone" cryptographic primitives based on lattice problems. Therefore this cipher and its construction is a good alternative to cryptosystems based on the integer factoriziation problem or the discrete logarithm and might be a base for secure "errorprone" application like biometrics or image watermarking.

This paper presents the first constructions for certificateless encryption (CLE) schemes that are provably secure against strong adversaries in the standard model. It includes both a generic construction for a strongly secure CLE scheme from any passively secure scheme as well as a concrete construction based on the Waters identity-based encryption scheme.