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

correction to the sullivan conjecture on maps from classifying space on page 49 i assert that given an unstable coalgebra c over the mod p steenrod algebra a c e ca the module of primitives pc is the suspension of an unstable a module e pc e u this is true for p 2 but certainly false for p 2 consider for instance the a coalgebra h bzp which plays such a large role in this paper this error makes nonsense of the spectral sequence 2 5 ext m 1rp cp ext s e ma c which is central to the proof of the sullivan conjecture however we may proceed as follows consider instead of the category u the category v of a modules satisfying the modified unstable condition xpt ofor lxi 2pt

certificateless threshold ring signature we propose a t out of n certificateless threshold ring signature cl trs scheme and prove its security under a new and stronger set of security models the models capture a new adversarial capability called user partial key replacement attack which has been considered practical and realistic but has never been formalized before the new scheme requires only a constant number of bilinear pairing operations for signature verification it also has a compact signature size which is linear to the number of non signers i e n t rather than that of actual signers we also propose a 1 out of n cl trs i e a certificateless ring signature scheme which has the most efficient verification among all the certificateless ring signature schemes currently known

local entropy averages and projections of fractal measures we show that for families of measures on euclidean space which satisfy an ergodic theoretic form of self similarity under the operation of re scaling the dimension of linear images of the measure behaves in a semi continuous way we apply this to prove the following conjecture of furstenberg let m n be integers which are not powers of the same integer and let x y be closed subsets of the unit interval which are invariant respectively under times m mod 1 and times n mod 1 then for any non zero t dim x ty min 1 dim x dim y a similar result holds for invariant measures and gives a simple proof of the rudolph johnson theorem our methods also apply to many other classes of conformal fractals and measures as another application we extend and unify results of peres shmerkin and nazarov and of moreira concerning projections of products self similar measures and gibbs measures on regular cantor sets we show that under natural irreducibility assumptions on the maps in the ifs the image measure has the maximal possible dimension under any linear projection other than the coordinate projections we also present applications to bernoulli convolutions and to the images of fractal measures under differentiable maps

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

convergence under q of p invariant measures on the circle abstract consider the semigroup of maps tn n n where tn x nx mod 1 suppose p and q are multiplicatively independent integers in that they are not both powers of the same integer further suppose that is a borel probability measure invariant ergodic and of positive entropy for tp we show that the sequence of measures tiq converges weak to lebesgue measure on a subsequence of values i of uniform full density

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

iribe intrusion resilient identity based encryption abstract in order to limit the damage of key exposure for identity based encryption we propose a new paradigm called intrusion resilient identity based encryption iribe in this paper compared with key insulated identity based encryption and forward secure identity based encryption iribe can achieve a stronger level of security in our proposed scheme the ciphertexts in any other time periods are secure even after arbitrarily many compromises of the base and the user as long as compromises do not happen simultaneously furthermore the intruder cannot decrypt the ciphertexts pertaining to previous time periods even if it compromises the base and the user simultaneously therefore our iribe scheme can greatly enhance the security of identity based encryption we also formalize the definition and the security notions of this paradigm the proposed scheme is proven secure in the standard model

invariant measures and arithmetic quantum unique ergodicity we classify measures on the locally homogeneous space i sl 2 r l which are invariant and have positive entropy under the diagonal subgroup of sl 2 r and recurrent under l this classification can be used to show arithmetic quantum unique ergodicity for compact arithmetic surfaces and a similar but slightly weaker result for the finite volume case other applications are also presented in the appendix joint with d rudolph we present a maximal ergodic theorem related to a theorem of hurewicz which is used in theproof of the main result

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

a new ring signature scheme with signer admission property in this paper we introduce an extended ring signature scheme in which the actual signer has the ability to admit to having signed a document at his will generally speaking this scheme can be considered as an extension and improvement of the ring signature suggested by rivest et al in 2001 the proposed scheme is called signer admission ring signature which combines the idea of the designated confirmer signatures proposed by chaum in 1994 and the designated verifier proofs proposed by jakobsson et al in 1996 this paper presents a scenario explaining why the signer admission property is valuable in real life applications an actual signer may possibly want to expose himself if in doing so he will acquire an enormous benefit here we propose a generic construction of the signer admission ring signature as well as a demonstration modified from rivest et al s scheme to achieve signer admission

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 ring signatures from rsa shamir proposed in 1984 the first identity based signature scheme whose security relies on the rsa problem a similar scheme was proposed by guillou and quisquater in 1988 formal security of these schemes was not argued and or proved until many years later d pointcheval j stern security arguments for digital signatures and blind signatures journal of cryptology 13 3 2000 361 396 y dodis j katz s xu m yung strong key insulated signature schemes in proceedings of pkc 03 in lncs vol 2567 springer verlag 2002 pp 130 144 m bellare c namprempre g neven security proofs for identity based identification and signature schemes in proceedings of eurocrypt 04 in lncs vol 3027 springer verlag 2004 pp 268 286 taking the guillou quisquater scheme as the starting point we design and analyze in this work ring signature schemes and distributed ring signature schemes for identity based scenarios whose security is based on the hardness of the rsa problem these are the first identity based ring signature schemes which do not employ bilinear pairings furthermore the resulting schemes satisfy an interesting property the real author s of a ring signature can later open the anonymity and prove that he is actually the person who signed the message

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

dimension growth for iterated sumsets we study dimensions of sumsets and iterated sumsets and provide natural conditions which guarantee that a set f subseteq mathbb r satisfies overline dim mathrm b f f overline dim mathrm b f or even dim mathrm h n f rightarrow 1 our results apply to for example all uniformly perfect sets which include ahlfors david regular sets our proofs rely on hochman s inverse theorem for entropy and the assouad and lower dimensions play a critical role we give several applications of our results including an erd s volkmann type theorem for semigroups and new lower bounds for the box dimensions of distance sets for sets with small dimension

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

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

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

concurrent signature without random oracles a concurrent signature provides an efficient way to exchange digital signatures between parties in a fair manner since its introduction in eurocrypt 2004 removing the random oracle heuristic in the security analysis of a concurrent signature scheme has become an open problem and the security of all the existing provably secure schemes could have only been done in the random oracle model while it has been known that the security in the random oracle model may not be guaranteed when the underlying random oracles are replaced by real life hash functions in this paper we solve this open problem by proposing a new concurrent signature scheme which allows us to prove its security without random oracles the security model we consider in this paper also slightly differs from previous works signatures before revealing the keystone are strongly ambiguous or anonymous in the sense that everyone is able to produce signatures that are indistinguishable from those generated honestly by the parties involved in the exchange while signatures after revealing the keystone remain unforgeable without sacrificing the fairness property in the multi user setting and without random oracles we prove the security of our scheme based on the intractability of computational diffie hellman cdh problem and collision resistance of hash functions

efficient chosen ciphertext secure certificateless threshold key encapsulation mechanism abstract as a practical extension of our previous work on certificateless threshold cryptosystem this paper proposes the first direct certificateless threshold key encapsulation mechanism that inherits the same trust level of the original scheme and removes the length limitation of a traditional public key encryption security against threshold chosen ciphertext attacks are proved in a random oracle model under a new assumption it tolerates the type i adversary that can replace public keys and the type ii adversary that has access to the system s master key the implied encapsulation scheme is very efficient when compared to the most efficient schemes in a traditional public key cryptosystem and it is slightly more efficient in terms of key length and encapsulation speed when compared to the identity based cryptosystems that have the same ciphertext overhead finally we describe several potential modifications of our scheme

certificateless undeniable signature scheme in this paper we present the first certificateless undeniable signature scheme the scheme does not suffer from the key escrow problem which is inherent in identity based cryptosystems also it can avoid the onerous management of certificates particularly by using some cryptographic and mathematical techniques we guarantee that the scheme s two component protocols satisfy the properties of zero knowledge proofs to address the security issues we extend security notions of undeniable signatures to the complex certificateless setting and consider two different types of adversaries based on these formally defined security notions we prove that in the random oracle model the certificateless undeniable signature scheme is secure in the sense of existential unforgeability under the bilinear diffie hellman assumption and is secure in the sense of invisibility under the decisional bilinear diffie hellman assumption

entropy of convolutions on the circle given ergodic p invariant measures f ig on the 1 torus w e give a sharp condition on their entropies guaranteeing that the entropy of the convolution 1 n converges to logp we also prove a variant of this result for joinings of full entropy on in conjunction with a method of host this yields the following denote aeq x qx mod 1 then for every p invariant ergodic with positive entropy 1 n p ni1 n 0 aecn converges weak to lebesgue measure as n i 1 under a certain mild combinatorial condition onfckg for instance the condition is satisfled if p 10 and ck 2 k 6 k or ck 2 2 k this extends a result of johnson and rudolph who considered the sequence ck q k when p and q are multiplicatively independent we also obtain the following corollary concerning hausdorfi dimension of sum sets for any sequence fsig of p invariant closed subsets of i f p dimh si j log dimh si j 1 then dimh s1 sn i 1

degenerate fibres in the stone cech compactification of the universal bundle of a finite group applied to a continuous surjection e b of completely regular hausdorff spaces e and b the stone cech compactification functor yields a surjection e b for an n fold covering map we show that the fibres of while never containing more than n points may degenerate to sets of cardinality properly dividing n in the special case of the universal bundle eg bg of a p group g we show more precisely that every possible type of g orbit occurs among the fibres of to prove this we use a weak form of the so called generalized sullivan conjecture

two extensions of the ring signature scheme of rivest shamir taumann two extensions of rst rivest shamir and taumann ring signature are proposed which keep the form of rst ring signature unchanged one extension is to implement the verifiability property with which the real signer is able to prove that she actually signed the ring signature if she publishes her secret value in contrast to the available verifiable ring signatures this scheme is very simple secure and efficient in this scheme only the glue value of rst ring signature is replaced by the output of a hash function which takes as input a secret value and some signature parameters and the real signer is able to prove himself any times the other extension is to construct an anonymous subliminal channel in rst ring signature so that the subliminal sender the real signer is able to keep herself subliminal anonymous to the subliminal receiver the subliminal anonymity is implemented for the first time in this paper in addition if the sender wants to revoke the subliminal anonymity she is able to use the first extension

a digital signature with multiple subliminal channels and its applications in this paper we present two schemes for embedding multiple subliminal messages into one time signature schemes otsss proposed by lamport 1971 1981 35 36 our schemes have the advantage that the subliminal receivers cannot forge a valid signature since they do not share the signer s secret key our schemes can also provide more than one independent subliminal message and the numbers of subliminal messages and receivers are larger than that of the subliminal messages in previous schemes

forward secure identity based signature security notions and construction the security of traditional identity based signatures wholly depends on the security of secret keys exposure of secret keys requires reissuing all previously assigned signatures this limitation becomes more obvious today as key exposure is more common with increasing use of mobile and unprotected devices under this background mitigating the damage of key exposure in identity based signatures is an important problem to deal with this problem we propose to integrate forward security into identity based signatures in this paper we firstly formalize the definition and security notions for forward secure identity based signature scheme and then construct an efficient scheme all parameters in our scheme have at most log squared complexity in terms of the total number of time periods the scheme is provably secure without random oracles

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

a propos de conjectures de serre et sullivan we first give a new proof of a conjecture of j p serre on the homotopy of finite complexes which was recently proved by c mcgibbon and j neisendorfer the emphasis is on a property of the mod 2 homology of certain spaces their quasi boundedness as right modules over the steenrod algebra this property is preserved when one goes from a simply connected space to its loop space and also when one takes a covering of anh space then we show that this notion of quasi boundedness simplifies h miller s proof of d sullivan s conjecture on the contractibility of the space of pointed maps from the classifying space of the groupe 2 into a finite complex