a provably secure short signature scheme based on discrete logarithms we propose a short signature scheme whose security is closely related to the discrete logarithm assumption in the random oracle model the new scheme offers a better security guarantee than existing discrete logarithm based signature schemes the main advantage of this scheme over the dsa signature scheme is that it has a one fourth reduction in both the signature length and the verification computation the level of security is preserved the new short signatures are needed to low bandwidth communication low storage and low computation environments and particularly applicable to smart cards and wireless devices

continuous dependence for impulsive functional dynamic equations involving variable time scales using a known correspondence between the solutions of impulsive measure functional differential equations and the solutions of impulsive functional dynamic equations on time scales we prove that the limit of solutions of impulsive functional dynamic equations over a convergent sequence of time scales converges to a solution of an impulsive functional dynamic equation over the limiting time scale

the random oracle methodology revisited we take a critical look at the relationship between the security of cryptographic schemes in the random oracle model and the security of the schemes that result from implementing the random oracle by so called cryptographic hash functions the main result of this article is a negative one there exist signature and encryption schemes that are secure in the random oracle model but for which any implementation of the random oracle results in insecure schemes in the process of devising the above schemes we consider possible definitions for the notion of a good implementation of a random oracle pointing out limitations and challenges

transitive signatures new schemes and proofs we present novel realizations of the transitive signature primitive introduced by micali and rivest enlarging the set of assumptions on which this primitive can be based and also providing performance improvements over existing schemes more specifically we propose new schemes based on factoring the hardness of the one more discrete logarithm problem and gap diffie hellman dh groups all these schemes are proven transitively unforgeable under adaptive chosen message attack in the standard not random oracle model we also provide an answer to an open question raised by micali and rivest regarding the security of their rivest shamir adleman rsa based scheme showing that it is transitively unforgeable under adaptive chosen message attack assuming the security of rsa under one more inversion we then present hash based modifications of the rsa factoring and gap diffie hellman based schemes that eliminate the need for node certificates and thereby yield shorter signatures these modifications remain provably secure under the same assumptions as the starting scheme in the random oracle model

optimal resilient threshold gq signatures gq signature scheme is widely used in many cryptographic protocols such as forward secure signature scheme identity based signature scheme etc however there is no threshold version of this important signature scheme in the open literature we proposed the first threshold gq signature scheme the scheme is proved unforgeable and robust against any adaptive adversary by assuming hardness of computing discrete logarithm modulo a safe prime and existence of fully synchronous broadcast channel furthermore with some modifications our scheme achieves optimal resilience such that the adversary can corrupt up to a half of the players as an extension of our work we provided a threshold identity based signature scheme and a threshold forward secure signature scheme which is the threshold version of the most efficient forward secure signature scheme up to now

how to construct random functions a constructive theory of randomness for functions based on computational complexity is developed and a pseudorandom function generator is presented this generator is a deterministic polynomial time algorithm that transforms pairs g r where g is any one way function and r is a random k bit string to polynomial time computable functions r 1 2 k 1 2 k these r s cannot be distinguished from random functions by any probabilistic polynomial time algorithm that asks and receives the value of a function at arguments of its choice the result has applications in cryptography random constructions and complexity theory

certificate based verifiably encrypted signatures from pairings we propose a new verifiably encrypted signature scheme from pairings by choosing a certificate authority ca as an adjudicator in this scheme a certificate or generally a signature acts not only as the binding of the public key and its holder but also as ca s guarantee against partiality in adjudication under the cdh assumption and in the random oracle model we show that the new scheme is euf cma secure in a stronger security model in this security model there are three types of inside adversaries with more power than those in previous verifiably encrypted signature schemes the proposed scheme can solve the authentication problem of public keys and relax excessive reliance on the trustworthiness of the adjudicator so that the adjudicator only needs to be trusted by the signer hence the fair exchange protocols of signatures based on the new scheme is more trustworthy and practical than the previous ones

an identity based strongly unforgeable signature without random oracles from bilinear pairings this paper proposes an identity based id based signature ibs scheme which is strongly unforgeable in the standard model whose security is reduced to the hardness of the computational diffie hellman cdh problem in bilinear groups currently the id based encryption scheme ibe due to waters is known to be the most practically efficient ibe whose security is guaranteed in the standard model depending on the decisional bilinear diffie hellman bdh assumption while as a solution for an id based signature of a total id based public key cryptosystem cooperating with waters ibe we share waters s construction and system parameters to keep a key pair corresponding to each identity unchanged our ibs needs only one group element for signing of messages and two elements for its randomness as supplementary parameters plus the original system parameters accordingly thanks to requiring about half the system parameters against previous id based signatures proved secure without using random oracles under the standard complexity assumptions like cdh or bdh our ibs is the more suitable for storage and communication requirements in particular this covers a stronger security property called strong unforgeability in the standard model in itself without applying any transformation technique

a digital signature scheme secure against adaptive chosen message attacks we present a digital signature scheme based on the computational difficulty of integer factorization the scheme possesses the novel property of being robust against an adaptive chosen message attack an adversary who receives signatures for messages of his choice where each message may be chosen in a way that depends on the signatures of previously chosen messages cannot later forge the signature of even a single additional message this may be somewhat surprising since in the folklore the properties of having forgery being equivalent to factoring and being invulnerable to an adaptive chosen message attack were considered to be contradictory more generally we show how to construct a signature scheme with such properties based on the existence of a claw free pair of permutations a potentially weaker assumption than the intractibility of integer factorization the new scheme is potentially practical signing and verifying signatures are reasonably fast and signatures are compact

universal designated verifier transitive signatures for graph based big data in this paper we propose a new type of digital signatures which is specifically designed for graph based big data system the properties of the proposed signatures are twofold on one side it possesses the features of transitive signatures one can sign a graph in such a way that given two signatures on adjacent edges i j and j k anyone with public information can compute a signature on edge i k the efficiency advancement o 1 communication overhead in transitive signatures is especially important in big data paradigm on the other side it is universal designated verifiable it allows any signature holder to prove to a designated verifier that a message has been signed by the signer but the verifier cannot convince even sharing all secret information any other third party of this fact the new notion is called universal designated verifier transitive signatures udvts for short as an integration of transitive signatures and universal designated verifier signatures udvts can efficiently address privacy issues associated with dissemination of transitive signatures of graph based big data we further prove that our proposed design is secure in the random oracle model

practical fully distributed signatures provably secure in the standard model a distributed signature scheme allows participants in a qualified set to jointly generate a signature which cannot be forged even when any unqualified set of participants collude together in this paper we propose an efficient scheme that supports any monotone access structures and show its unforgeability and robustness under the computational diffie hellman cdh assumption in the standard model for 192 bit security its secret key shares and signature fragments are as short as 511 bits and 1022 bits which are shorter than existing schemes assuming random oracle we then propose two extensions the first one allows new participants to dynamically join the system without any help from the dealer the second one supports a type of multipartite access structures where the participant set is divided into multiple disjoint groups and each group is bounded so that a distributed signature cannot be generated unless a pre defined number of participants from multiple groups work together finally we present a fully distributed signature scheme such that the centralized trusted dealer can be removed from the system and the secret keys shares can be jointly computed by the involved participants we propose a cdh based distributed signature scheme in the standard model we provide two extensions of the basic distributed signature scheme we propose a distributed key generation protocol over bilinear group we provide a cdh based fully distributed signature scheme in the standard model

on continuous dependence of solutions of dynamic equations the main goal of the paper is to present a new approach to the problem of continuous dependence of solutions of differential or dynamic problems on their domains this is of particular interests when we use dynamic difference in particular equations as discretization of a given one we cover a standard construction based of difference approximations for the continuous one but we are not restricted only to this case for a given differential equation we take a sequence of time scales and we study the convergence of time scales to the domain of the considered problem we choose a kind of convergence of such approximated solutions to the exact solution this is a step for creating numerical analysis on time scales and we propose to replace in such a situation the difference equations by dynamic ones in the proposed approach we are not restricted to the case of classical numerical algorithms moreover this allows us to find an exact solution for considered problems as a limit of a sequence of solutions for appropriate time scales instead of solving it analytically or calculating approximated solutions for the original problems

characteristic generators and dualization for tail biting trellises this paper focuses on dualizing tail biting trellises particularly kv trellises these trellises are based on characteristic generators as introduced by koetter vardy 2003 and may be regarded as a natural generalization of minimal conventional trellises even though they are not necessarily minimal two dualization techniques will be investigated the local dualization introduced by forney 2001 for general normal graphs and a linear algebra based dualization tailored to the specific class of tail biting bahl cocke jelinek raviv bcjr trellises introduced by nori shankar 2006 it turns out that in general the bcjr dual is a subtrellis of the local dual while for kv trellises these two coincide furthermore making use of both the bcjr construction and the local dualization it will be shown that for each complete set of characteristic generators of a code there exists a complete set of characteristic generators of the dual code such that their resulting kv trellises are dual to each other if paired suitably this proves a stronger version of a conjecture formulated by koetter vardy

one dimensional schrodinger operators with δ interactions on cantor type sets we introduce a novel approach for defining a interaction on a subset of the real line of lebesgue measure zero which is based on sturm liouville differential expression with measure coefficients this enables us to establish basic spectral properties e g self adjointness lower semiboundedness and spectral asymptotics of hamiltonians with interactions concentrated on sets of complicated structures

a polynomial time algorithm for breaking the basic merkle hellman cryptosystem the merkle hellman cryptosystem is one of the two major public key cryptosystems proposed so far it is shown that the basic variant of this cryptosystem in which the elements of the public key are modular multiples of a superincreasing sequence is breakable in polynomial time

generic security amplifying methods of ordinary digital signatures digital signatures are one of the most fundamental primitives in cryptography in this paper three new paradigms are proposed to obtain signatures that are secure against existential forgery under adaptively chosen message attacks fully secure in short from any weakly secure signature these transformations are generic simple and provably secure in the standard model in the first paradigm based on a weakly secure signature scheme the construction of a fully secure signature scheme requires one time signature additionally however the other two are built only on weakly secure signatures to the best of our knowledge it is observed for the first time in this paper that two weakly secure signature schemes are sufficient to construct a fully secure signature scheme based on the new proposed paradigms several efficient instantiations without random oracles are also presented we also show that these fully secure signature schemes have many special interesting properties in application

cramer damgard signatures revisited efficient flat tree signatures based on factoring at crypto 96 cramer and damgard proposed an efficient tree based signature scheme that is provably secure against adaptive chosen message attacks under the assumption that inverting rsa is computationally infeasible in this paper we show how to modify their basic construction in order to achieve a scheme that is provably secure under the assumption that factoring large composites of a certain form is hard our scheme is as efficient as the original cramer damgard solution while relying on a seemingly weaker intractability assumption

identity based identification from algebraic coding theory cryptographic identification schemes allow a remote user to prove his her identity to a verifier who holds some public information of the user such as the user public key or identity most of the existing cryptographic identification schemes are based on number theoretic hard problems such as discrete log and factorization this paper focuses on the design and analysis of identity based identification ibi schemes based on algebraic coding theory we first revisit an existing code based ibi scheme which is derived by combining the courtois finiasz sendrier signature scheme and the stern zero knowledge identification scheme previous results have shown that this ibi scheme is secure under passive attacks in this paper we prove that the scheme in fact can resist active attacks however whether the scheme can be proven secure under concurrent attacks the most powerful attacks against identification schemes remains open in addition we show that it is difficult to apply the conventional or proof approach to this particular ibi scheme in order to obtain concurrent security we then construct a special or proof variant of this scheme and prove that the resulting ibi scheme is secure under concurrent attacks

sharing dss by the chinese remainder theorem in this paper we propose a new threshold scheme for the digital signature standard dss using asmuth bloom secret sharing based on the chinese remainder theorem crt to achieve the desired result we first show how to realize certain other threshold primitives using asmuth bloom secret sharing such as joint random secret sharing joint exponential random secret sharing and joint exponential inverse random secret sharing we prove the security of our scheme against a static adversary to the best of our knowledge this is the first provably secure threshold dss scheme based on crt

concurrent zero knowledge concurrent executions of a zero knowledge protocol by a single prover with one or more verifiers may leak information and may not be zero knowledge in toto in this article we study the problem of maintaining zero knowledge we introduce the notion of an timing constraint for any two processors p1 and p2 if p1 measures elapsed time on its local clock and p2 measures elapsed time on its local clock and p2 starts after p1 does then p2 will finish after p1 does we show that if the adversary is constrained by an assumption then there exist four round almost concurrent zero knowledge interactive proofs and perfect concurrent zero knowledge arguments for every language in np we also address the more specific problem of deniable authentication for which we propose several particularly efficient solutions deniable authentication is of independent interest even in the sequential case our concurrent solutions yield sequential solutions without recourse to timing that is in the standard model

on the algebraic structure of linear tail biting trellises tail biting trellises are important graphical representations of codes which can be simpler to decode than conventional trellises while conventional trellises are well understood the general theory of tail biting trellises is still under development in this paper we first develop a new algebraic framework for a systematic analysis of linear trellises which enables us to address open foundational questions in particular we present a useful and powerful characterization of linear trellis isomorphy we also obtain a new proof of the linear factorization theorem of koetter vardy and point out unnoticed problems for the group case next we apply our framework to 1 describe all the factorizations of linear trellises 2 determine and classify all the minimal linear trellises for a given linear code and 3 prove that nonmergeable one to one linear trellises are determined by the edge label sequences of certain closed paths we also provide new insight into mergeability and state how results on reduced linear trellises can be extended to nonreduced ones our classification results are relevant to iterative linear programming decoding as we show that minimal linear trellises can yield different pseudocodewords even if they have the same graph structure

robust threshold dss signatures we present threshold dss digital signature standard signatures where the power to sign is shared by n players such that for a given parameter t

certificateless undeniable signatures from bilinear maps certificateless public key cryptosystem avoids the inherent key escrow problem in identity based public key cryptosystem and does not need expensive certificates in the public key infrastructure this cryptographic primitive has received a significant attention since it was introduced and lots of certificateless schemes have been proposed in the past years in this paper we propose an certificateless undeniable signature scheme based on bilinear maps to formally analyze the security of the proposed scheme we extend security notions of undeniable signatures in the traditional public key infrastructure to the certificateless setting under the formally defined security models we prove that our proposed scheme satisfies all the security properties under certain standard assumptions in the random oracle model compared with existed certificateless undeniable signatures the sign algorithm of our scheme is more efficient the weakness is that the unforgeability of our scheme is proved in a weak model

statistically hiding commitments and statistical zero knowledge arguments from any one way function we give a construction of statistically hiding commitment schemes those in which the hiding property holds against even computationally unbounded adversaries under the minimal complexity assumption that one way functions exist consequently one way functions suffice to give statistical zero knowledge arguments for any np statement whereby even a computationally unbounded adversarial verifier learns nothing other than the fact that the assertion being proven is true and no polynomial time adversarial prover can convince the verifier of a false statement these results resolve an open question posed by naor et al j cryptology 11 1998 pp 87 108

from identification to signatures via the fiat shamir transform necessary and sufficient conditions for security and forward security the fiat shamir paradigm for transforming identification schemes into signature schemes has been popular since its introduction because it yields efficient signature schemes and has been receiving renewed interest of late as the main tool in deriving forward secure signature schemes in this paper minimal meaning necessary and sufficient conditions on the identification scheme to ensure security of the signature scheme in the random oracle model are determined both in the usual and in the forward secure cases specifically it is shown that the signature scheme is secure respectively forward secure against chosen message attacks in the random oracle model if and only if the underlying identification scheme is secure respectively forward secure against impersonation under passive i e eavesdropping only attacks and has its commitments drawn at random from a large space an extension is proven incorporating a random seed into the fiat shamir transform so that the commitment space assumption may be removed

a relation between the characteristic generators of a linear code and its dual it was conjectured by koetter and vardy that if the k characteristic generators of a linear code c are linearly independent then the corresponding n k characteristic generators of the dual code c sup spl perp are also linearly independent in this correspondence we prove that the conjecture is true for self dual codes and cyclic codes

optimal error correction for computationally bounded noise for adversarial but computationally bounded models of error we construct appealingly simple and efficient cryptographic encoding and unique decoding schemes whose error correction capability is much greater than classically possible in particular 1 for binary alphabets we construct positive rate coding schemes that are uniquely decodable under a 1 2 error rate for any constant 0 2 for large alphabets we construct coding schemes that are uniquely decodable under a 1 r error rate for any information rate r 0 our results for large alphabets are actually optimal since the computationally bounded but adversarial channel can simulate the behavior of the q ary symmetric channel where q denotes the size of the alphabet the capacity of which is known to be upper bounded by 1 r our results hold under minimal assumptions on the communication infrastructure namely 1 we allow the channel to be more powerful than the receiver and 2 we only assume that some information about the sender a public key is known in particular we do not require any shared secret key or joint local state between sender and receivers

new t n threshold directed signature scheme with provable security directed signature scheme allows only a designated verifier to check the validity of the signature issued to him and at the time of trouble or if necessary any third party can verify the signature with the help of the signer or the designated verifier as well due to its merits directed signature scheme is widely used in situations where the receiver s privacy should be protected threshold directed signature is an extension of the standard directed signature in which several signers may be required to cooperatively sign messages for sharing the responsibility and authority to the best of our knowledge threshold directed signature has not been well studied till now therefore in this paper we would like to formalize the threshold directed signature and its security model then present a new t n threshold directed signature scheme from bilinear pairings and use the techniques from provable security to analyze its security

efficient generic on line off line threshold signatures without key exposure the hash sign switch paradigm was firstly proposed by shamir and tauman with the aim to design an efficient on line off line signature scheme nonetheless all existing on line off line signature schemes based on this paradigm suffer from the key exposure problem of chameleon hashing to avoid this problem the signer should pre compute and store a plenty of different chameleon hash values and the corresponding signatures on the hash values in the off line phase and send the collision and the signature for a certain hash value in the on line phase hence the computation and storage cost for the off line phase and the communication cost for the on line phase in shamir tauman s signature scheme are still a little more overload in this paper we first introduce a special double trapdoor hash family based on the discrete logarithm assumption and then incorporate it to construct a more efficient generic on line off line signature scheme without key exposure furthermore we also present the first key exposure free generic on line off line threshold signature scheme without a trusted dealer additionally we prove that the proposed schemes have achieved the desired security requirements

certificateless threshold signature scheme from bilinear maps a t n threshold signature scheme allows t or more group members to generate signatures on behalf of a group with n members in contrast to the traditional public key cryptography based on public key infrastructure pki and identity based public key cryptography id pkc certificateless public key cryptography cl pkc offers useful properties as it does not require any certificates to ensure the authenticity of public keys and the key escrow problem is eliminated in this paper we investigate the notion of threshold signature schemes in cl pkc we start by pointing out the drawbacks in the two existing certificateless threshold signature schemes subsequently we present an elaborate description of a generic certificateless t n threshold signature scheme with a new security model the adversaries captured in the new model are more powerful than those considered in the existing schemes furthermore we establish the simulatability for certificateless threshold signature schemes and prove the relationship between the security of certificateless threshold signature schemes and that of the underlying non threshold certificateless signature schemes as an instantiation we present a concrete certificateless threshold signature scheme based on bilinear maps using the techniques of verifiable secret sharing and distributed key generation the proposed scheme is shown to be existentially unforgeable against adaptively chosen message attacks assuming the hardness of computational diffie hellman cdh problem

signcryption from randomness recoverable public key encryption we propose a new generic construction for signcryption and show that it is secure under the security models which are comparable to the security against adaptive chosen ciphertext attacks for public key encryption and the existential unforgeability against chosen message attacks for signature in particular the security models also capture the notion of insider security the generic construction relies on the existence of a special class of efficient public key encryption schemes which allow the encryption randomness to be recovered during decryption we also propose two efficient instantiations for the generic construction and show that one of them has less message expansion and yields smaller ciphertext when compared with all the existing signcryption schemes

practical verifiably encrypted signatures without random oracles abstract this paper presents a verifiably encrypted signature scheme that is provably secure without random oracles in a stronger security model where two inside adversaries malicious adjudicator and malicious verifier have more powers than ever the new scheme is more practical and trustworthy than the previous verifiably encrypted signature schemes in the real world since it tallies more with the actual circumstances of the internet

uniform complexity and digital signatures abstract a concept of uniform complexity is defined and a class of functions is shown to have uniform complexity a special case of these results is used to develop a new digital signature method which makes forging signatures as hard as factoring a large number and which allows half of the messages to be signed directly the signature production involves only one exponentiation modulo a large number and the signature checking the comparison of a fourth and second power modulo a large number therefore this new method is faster than known methods with the same degree of safety

linear tail biting trellises characteristic generators and the bcjr construction this paper investigates the constructions of tail biting trellises for linear block codes as introduced by koetter and vardy 2003 and nori and shankar 2006 for a given code the sets of characteristic generators are defined slightly more generally than by koetter and vardy in particular they are not uniquely determined by the code the effect of the choice of characteristic generators on the resulting product trellises called kv trellises is discussed in detail it is shown that each kv trellis is a span based bcjr trellis and that the latter are always nonmergeable finally a duality conjecture posed by koetter and vardy is addressed by making use of a dualization technique of bcjr trellises the conjecture is proven for minimal trellises

a simple transitive signature scheme for directed trees transitive signatures allow a signer to authenticate edges in a graph in such a way that anyone given the public key and two signatures on adjacent edges i j and j k can compute a third signature on edge i k a number of schemes have been proposed for undirected graphs but the case of directed graphs remains an open problem at ct rsa 2007 yi presented a scheme for directed trees based on rsa and a standard signature scheme we present a new conceptually simple and generic construction from standard signatures only apart from not relying on any rsa related security assumptions our scheme outperforms that of yi in both computation time and worst case signature length our results indicate that the setting envisaged by yi is much simpler than the general one of directed transitive signatures which remains an open problem

on the connection between the hilger and radon nikodym derivatives abstract we show that the hilger derivative on time scales is a special case of the radon nikodym derivative with respect to the natural measure associated with every time scale moreover we show that the concept of delta absolute continuity agrees with the one from measure theory in this context