cryptanalysis of a diophantine equation oriented public key cryptosystem c h lin et al 1995 proposed a new public key cipher system whose security is based upon the diophantine equations in this note we show that their scheme is insecure under the ciphertext only attack

new schemes for sharing points on an elliptic curve a multiple secret sharing scheme can share a group of secrets in each sharing session this scheme is deemed to be very useful in sharing important secrets however previously no scheme on sharing points on an elliptic curve has been devised in responding to the problem this paper proposes a new t n multi point sharing scheme using self pairing on an elliptic curve the security of the proposed scheme was examined towards the end of the study the researchers concluded that the new scheme was computationally secure if at least n t 1 users in the scheme are honest and if o lgq points at most are shared therefore the threshold digital signature scheme on an elliptic curve can be designed and implemented easily

multiscale image blind denoising arguably several thousands papers are dedicated to image denoising most papers assume a fixed noise model mainly white gaussian or poissonian this assumption is only valid for raw images yet in most images handled by the public and even by scientists the noise model is imperfectly known or unknown end users only dispose the result of a complex image processing chain effectuated by uncontrolled hardware and software and sometimes by chemical means for such images recent progress in noise estimation permits to estimate from a single image a noise model which is simultaneously signal and frequency dependent we propose here a multiscale denoising algorithm adapted to this broad noise model this leads to a blind denoising algorithm which we demonstrate on real jpeg images and on scans of old photographs for which the formation model is unknown the consistency of this algorithm is also verified on simulated distorted images this algorithm is finally compared with the unique state of the art previous blind denoising method

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

cryptanalysis of a knapsack based probabilistic encryption scheme wang et al b wang q wu y hu a knapsack based probabilistic encryption scheme information sciences 177 19 2007 3981 3994 proposed a high density knapsack based probabilistic encryption scheme with non binary coefficients in this paper we present a heuristic attack that can be used to recover the private key parameters from the known public key parameters in particular we show that the restrictions imposed on the system parameters allow the attacker to recover a short list of candidates for the first half of the public key the second half of the public key can then be recovered using an attack based on lattice basis reduction finally by encrypting an arbitrary plaintext using the known public key then decrypting the resulting ciphertext using these estimated candidate solutions the right private key can be uniquely determined

the sharp weighted bound for general calderon zygmund operators for a general calderon zygmund operator t on r n it is shown that ktfkl2 w c t sup q a q w q w 1 a k fkl2 w for all muckenhoupt weights w 2 a2 this optimal estimate was known as the a2 conjecture a recent result of perez treil volberg reduced the problem to a testing condition on indicator functions which is verified in this paper the proof consists of the following elements i a variant of the nazarov treil volberg method of random dyadic systems with just one random system and completely without bad parts ii a resulting representation of a general calderon zygmund operator as an average of dyadic shifts and iii improvements of the lacey petermichl reguera estimates for these dyadic shifts which allow summing up the series in the obtained representation

dyadic harmonic analysis beyond doubling measures we characterize the borel measures on r for which the associated dyadic hilbert transform or its adjoint is of weak type 1 1 and or strong type p p with respect to surprisingly the class of such measures is strictly bigger than the traditional class of dyadically doubling measures and strictly smaller than the whole borel class in higher dimensions we provide a complete characterization of the weak type 1 1 for arbitrary haar shift operators cancellative or not written in terms of two generalized haar systems and these include the dyadic paraproducts our main tool is a new calderon zygmund decomposition valid for arbitrary borel measures which is of independent interest

a knapsack based probabilistic encryption scheme knapsack based cryptosystems had been viewed as the most attractive and the most promising asymmetric cryptographic algorithms for a long time due to their np completeness nature and high speed in encryption decryption unfortunately most of them are broken for the low density feature of the underlying knapsack problems in this paper we investigate a new easy compact knapsack problem and propose a novel knapsack based probabilistic public key cryptosystem in which the cipher text is non linear with the plaintext for properly chosen parameters the underlying knapsack problem enjoys a high density larger than 1 06 in the worst case hence it is secure against the low density subset sum attacks our scheme can also defeat other potential attacks such as the brute force attacks and the simultaneous diophantine approximation attack compared with previous knapsack based cryptosystems our scheme is efficient and practical

a knapsack public key cryptosystem based on elliptic curve discrete logarithm there is no question that knapsack systems still warrant continuous researches as a result of the np completeness nature the faster speed and a desire to have a wide variety of available cryptosystems this paper presents a new knapsack type public key cryptosystem based on a novel application of the elliptic curve logarithm problem the difficulty can be made sufficient to frustrate attacks against the survey major knapsack public key cryptosystems developed in the past more than 20 years and hope fully shed some light on the future of the knapsack cryptosystems the proposed new cryptosystem can be found some theoretic support on confidentiality

the sharp bound for the hilbert transform on weighted lebesgue spaces in terms of the classical ap characteristic we show that the norm of the hilbert transform as an operator in the weighted space l p r for 2 p oo is bounded by a constant multiple of the first power of the classical ap characteristic of this result is sharp we also prove a bilinear imbedding theorem with simple conditions

on a_p a_ infty type estimates for square functions we prove strong type a p a infty estimate for square functions improving on the a p bound due to lerner entropy bounds in the recent innovation of treil volberg are then proved the techniques of proof include parallel stopping cubes pigeon hole arguments and the approach to entropy bounds of lacey spencer

analysis of the efficiency of the chor rivest cryptosystem implementation in a safe parameter range the chor rivest cryptosystem based on a high density knapsack problem on a finite field f q h was broken by vaudenay for q 200 h 24 and h admitting a factor s verifying a certain condition a new set of parameters q and h which prevent this cryptosystem against vaudenay s attack is presented and the computational aspects of its implementation in the magma computational algebra system are analyzed

convex body domination and weighted estimates with matrix weights abstract we introduce the so called convex body valued sparse operators which generalize the notion of sparse operators to the case of spaces of vector valued functions we prove that calderon zygmund operators as well as haar shifts and paraproducts can be dominated by such operators by estimating sparse operators we obtain weighted estimates with matrix weights we get two weight a 2 a estimates that in the one weight case give us the estimate t l 2 w l 2 w c w a 2 1 2 w a c w a 2 3 2 where t is either calderon zygmund operator with modulus of continuity satisfying the dini condition or a haar shift or a paraproduct

multilinear singular integrals on non commutative l p spaces we prove l p bounds for the extensions of standard multilinear calderon zygmund operators to tuples of text umd spaces tied by a natural product structure the product can for instance mean the pointwise product in text umd function lattices or the composition of operators in the schatten von neumann subclass of the algebra of bounded operators on a hilbert space we do not require additional assumptions beyond text umd on each space in contrast to previous results we e g show that the rademacher maximal function property is not necessary the obtained generality allows for novel applications for instance we prove new versions of fractional leibniz rules via our results concerning the boundedness of multilinear singular integrals in non commutative l p spaces our proof techniques combine a novel scheme of induction on the multilinearity index with dyadic probabilistic techniques in the text umd space setting

optimal inversion of the anscombe transformation in low count poisson image denoising the removal of poisson noise is often performed through the following three step procedure first the noise variance is stabilized by applying the anscombe root transformation to the data producing a signal in which the noise can be treated as additive gaussian with unitary variance second the noise is removed using a conventional denoising algorithm for additive white gaussian noise third an inverse transformation is applied to the denoised signal obtaining the estimate of the signal of interest the choice of the proper inverse transformation is crucial in order to minimize the bias error which arises when the nonlinear forward transformation is applied we introduce optimal inverses for the anscombe transformation in particular the exact unbiased inverse a maximum likelihood ml inverse and a more sophisticated minimum mean square error mmse inverse we then present an experimental analysis using a few state of the art denoising algorithms and show that the estimation can be consistently improved by applying the exact unbiased inverse particularly at the low count regime this results in a very efficient filtering solution that is competitive with some of the best existing methods for poisson image denoising

sharp weighted norm inequalities for singular integrals with non smooth kernels in this paper we prove the sharp weighted bound for certain singular integrals which have non smooth kernels and do not belong to the class of standard calderon zygmund operators our assumptions are weaker than those known in literature since in particular we do not assume the cotlar type inequality condition applications include sharp weighted estimates for the riesz transforms associated to the dirichlet laplacians on open connected domains the riesz transforms associated to the schrodinger operators with real potentials on the euclidean spaces the riesz transforms associated to the degenerate schrodinger operators and the riesz transforms associated to the schrodinger operators with inverse square potentials

linear bounds for calderon zygmund operators with even kernel on umd spaces it is well known that several classical results about calderon zygmund singular integral operators can be extended to x valued functions if and only if the banach space x has the umd property the dependence of the norm of an x valued calderon zygmund operator on the umd constant of the space x is conjectured to be linear we prove that this is indeed the case for sufficiently smooth calderon zygmund operators with cancellation associated to an even kernel our method uses the bellman function technique to obtain the right estimates for the norm of dyadic haar shift operators we then apply the representation theorem of t hytonen to extend the result to general calderon zygmund operators

image denoising using mixtures of projected gaussian scale mixtures we propose a new statistical model for image restoration in which neighborhoods of wavelet subbands are modeled by a discrete mixture of linear projected gaussian scale mixtures mpgsm in each projection a lower dimensional approximation of the local neighborhood is obtained thereby modeling the strongest correlations in that neighborhood the model is a generalization of the recently developed mixture of gsm mgsm model that offers a significant improvement both in psnr and visually compared to the current state of the art wavelet techniques however the computation cost is very high which hampers its use for practical purposes we present a fast em algorithm that takes advantage of the projection bases to speed up the algorithm the results show that when projecting on a fixed data independent basis even computational advantages with a limited loss of psnr can be obtained with respect to the bls gsm denoising method while data dependent bases of principle components offer a higher denoising performance both visually and in psnr compared to the current wavelet based state of the art denoising methods

sharp weighted norm inequalities for littlewood paley operators and singular integrals abstract we prove sharp l p w norm inequalities for the intrinsic square function introduced recently by m wilson in terms of the a p characteristic of w for all 1 p this implies the same sharp inequalities for the classical lusin area integral s f the littlewood paley g function and their continuous analogs s and g also as a corollary we obtain sharp weighted inequalities for any convolution calderon zygmund operator for all 1 p 3 2 and 3 p and for its maximal truncations for 3 p

practical poissonian gaussian noise modeling and fitting for single image raw data we present a simple and usable noise model for the raw data of digital imaging sensors this signal dependent noise model which gives the pointwise standard deviation of the noise as a function of the expectation of the pixel raw data output is composed of a poissonian part modeling the photon sensing and gaussian part for the remaining stationary disturbances in the output data we further explicitly take into account the clipping of the data over and under exposure faithfully reproducing the nonlinear response of the sensor we propose an algorithm for the fully automatic estimation of the model parameters given a single noisy image experiments with synthetic images and with real raw data from various sensors prove the practical applicability of the method and the accuracy of the proposed model

solving low density subset sum problems the subset sum problem is to decide whether or not the 0 l integer programming problem s n i l a i x i m i x i 0 or 1 has a solution where the a i and m are given positive integers this problem is np complete and the difficulty of solving it is the basis of public key cryptosystems of knapsack type an algorithm is proposed that searches for a solution when given an instance of the subset sum problem this algorithm always halts in polynomial time but does not always find a solution when one exists it converts the problem to one of finding a particular short vector v in a lattice and then uses a lattice basis reduction algorithm due to a k lenstra h w lenstra jr and l lovasz to attempt to find v the performance of the proposed algorithm is analyzed let the density d of a subset sum problem be defined by d n log 2 max i a i then for almost all problems of density d d n it is proved that the lattice basis reduction algorithm locates v extensive computational tests of the algorithm suggest that it works for densities d d c n where d c n is a cutoff value that is substantially larger than 1 n this method gives a polynomial time attack on knapsack public key cryptosystems that can be expected to break them if they transmit information at rates below d c n as n

weighted martingale multipliers in the non homogeneous setting and outer measure spaces abstract we investigate the unconditional basis property of martingale differences in weighted spaces l 2 w d in the non homogeneous situation that is when the reference measure is not doubling specifically we prove that finiteness of the quantity w a 2 sup i w i w 1 i defined through averages i relative to the reference measure implies that haar subspaces form an unconditional basis in the weighted space l 2 w d moreover we prove that the unconditional basis constant of this system grows at most linearly in w a 2 the problem is reduced to the sharp weighted estimates of the so called haar multipliers even in the classical case of the standard dyadic lattice in r d with lebesgue reference measure our result is new in that our estimates are independent of the dimension n our approach combines the technique of outer measure spaces with the bellman function argument

cryptanalysis of a quadratic compact knapsack public key cryptosystem recently wang and hu have proposed a high density quadratic compact knapsack public key cryptosystem using the chinese remainder theorem to disguise two secret cargo vectors the system is claimed to be secure against certain known attacks however it has not been demonstrated to fulfill any provable security goals in this work we show that this system is not secure exploiting the special structure of system parameters we first show that a candidate list for the secret modulus can be obtained by solving linear equations with small solutions next we show that with this candidate list all other secrets can be recovered in succession with lattice based methods by solving certain modular linear equations with small solutions as a result recovering a private key can be done in about 11 h for the proposed system parameter n 100 we also discuss a method to thwart the proposed attack

estimates for operator norms on weighted spaces and reverse jensen inequalities we examine the dependence on the a p norm of w of the operator norms of singular integrals maximal functions and other operators in l p w we also examine connections between some fairly general reverse jensen inequalities and the a p and rh p weight conditions

proof of an extension of e sawyer s conjecture about weighted mixed weak type estimates we show that if v in a infty and u in a 1 then there is a constant c depending on the a 1 constant of u and the a infty constant of v such that begin aligned left frac t fv v right l 1 infty uv le c vert f vert l 1 uv end aligned where t can be the hardy littlewood maximal function or any calderon zygmund operator this result was conjectured in cruz uribe et al int math res not 30 1849 1871 2005 and constitutes the most singular case of some extensions of several problems proposed by sawyer and muckenhoupt and wheeden we also improve and extends several quantitative estimates

on two way fa with monotonic counters and quadratic diophantine equations we show an interesting connection between two way deterministic finite automata with monotonic counters and quadratic diophantine equations the automaton m operates on inputs of the form a1i1 anin for some fixed n and distinct symbols a1 an where i1 in are nonnegative integers we consider the following reachability problem given a machine m a state q and a presburger relation e over counter values is there i1 in such that m when started in its initial state on the left end of the input a1i1 anin with all counters initially zero reaches some configuration where the state is q and the counter values satisfy e in particular we look at the case when the relation e is an equality relation i e a conjunction of relations of the form ci cj we show that this case and variations of it are equivalent to the solvability of some special classes of systems of quadratic diophantine equations we also study the nondeterministic version of two way finite automata augmented with monotonic counters with respect to the reachability problem finally we introduce a technique which uses decidability and undecidability results to show separation between language classes

numerical solution of certain exponential and non linear diophantine systems of equations by using a discrete particle swarm optimization algorithm this article proposes the numerical solution of some non linear systems of diophantine equations including some exponential cases by its transformation into an optimization problem for the first example the implemented algorithm is able to find all the non negative integer roots in a given region of the domain of the objective function when compared to the analytic solution systems of different sizes are solved as an example for these their answers were found being them of excellent quality in terms of accuracy and precision even though there is no way of being certain that they are the only ones following matiyasevich theorem however and for systems of modest size the computation time increased considerably when the search space was increased

ant colony optimization theory a survey research on a new metaheuristic for optimization is often initially focused on proof of concept applications it is only after experimental work has shown the practical interest of the method that researchers try to deepen their understanding of the method s functioning not only through more and more sophisticated experiments but also by means of an effort to build a theory tackling questions such as how and why the method works is important because finding an answer may help in improving its applicability ant colony optimization which was introduced in the early 1990s as a novel technique for solving hard combinatorial optimization problems finds itself currently at this point of its life cycle with this article we provide a survey on theoretical results on ant colony optimization first we review some convergence results then we discuss relations between ant colony optimization algorithms and other approximate methods for optimization finally we focus on some research efforts directed at gaining a deeper understanding of the behavior of ant colony optimization algorithms throughout the paper we identify some open questions with a certain interest of being solved in the near future

weighted weak type 1 1 estimates via rubio de francia extrapolation the classical rubio de francia extrapolation result asserts that if an operator t lp0 u lp0 u is bounded for some p0 1 and every u ap0 then for every 1 1 and every u in this class then for every u a1 1 t is of restricted weak type 1 1 2 for every e 0 t l log l e u lloc1 u moreover for a big class of operators including calderon zygmund maximal operators g functions and the intrinsic square function we obtain a weak type 1 1 estimate with respect to every u a1

nonparametric multiscale blind estimation of intensity frequency dependent noise the camera calibration parameters and the image processing chain which generated a given image are generally not available to the receiver this happens for example with scanned photographs and for most jpeg images these images have undergone various nonlinear contrast changes and also linear and nonlinear filters to deal with remnant noise in such images we introduce a general nonparametric intensity and frequency dependent noise model we demonstrate by simulated and experiments with real images that this model which requires the estimation of more than 1000 parameters performs an efficient noise estimation the proposed noise model is a patch model its estimation can therefore be used as a preliminary step to any patch based denoising method our noise estimation method introduces several new tools for performing this complex estimation one of them is a new sparse patch distance function permitting to find noisy patches with similar underlying geometry a validation of the noise model and of its estimation method is obtained by comparing its results to ground truth noise curves for both raw and jpeg encoded images and by visual inspection of the denoising results of real images a fair comparison with the state of the art is also performed

finitely randomized dyadic systems and bmo on metric measure spaces abstract we study the connection between bmo and dyadic bmo in metric measure spaces using finitely randomized dyadic systems and give a garnett jones type proof for a theorem of uchiyama on a construction of certain bmo functions we obtain a relation between the bmo norm of a suitable expectation over dyadic systems and the dyadic bmo norms of the original functions in different systems the expectation is taken over only finitely randomized dyadic systems to overcome certain measurability questions applying our result we derive uchiyama s theorem from its dyadic counterpart which we also prove

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

commutators in the two weight setting let r be the vector of riesz transforms on mathbb r n and let mu lambda in a p be two weights on mathbb r n 1 p infty the two weight norm inequality for the commutator b r l p mu rightarrow l p lambda is shown to be equivalent to the function b being in a bmo space adapted to mu and lambda this is a common extension of a result of coifman rochberg weiss in the case of both lambda and mu being lebesgue measure and bloom in the case of dimension one

true random number generator based on mouse movement and chaotic hash function a true random number generator trng makes use of a non deterministic source to produce randomness it is considered as more secure than a pseudorandom number generator as the degree of randomness is higher in this letter we propose a novel trng which generates random bits by moving the mouse casually it is convenient universal and low cost for the personal computer pc platform to eliminate the regular patterns of mouse movements caused by the habit of the same user we propose three trngs based on chaotic hash functions experiments are conducted to evaluate the speed diffusion and randomness performance of these trngs the results show that two of them possess satisfactory performance and can be implemented on common pc platform

sharp weighted estimates for classical operators abstract we give a general method based on dyadic calderon zygmund theory to prove sharp one and two weight norm inequalities for some of the classical operators of harmonic analysis the hilbert and riesz transforms the beurling ahlfors operator the maximal singular integrals associated to these operators the dyadic square function and the vector valued maximal operator in the one weight case we prove the sharp dependence on the a p constant by finding the best value for the exponent p such that t f l p w c n t w a p p f l p w for the hilbert transform the riesz transforms and the beurling ahlfors operator the sharp value of p was found by petermichl and volberg 2007 2008 2002 47 48 49 their proofs used approximations by the dyadic haar shift operators bellman function techniques and two weight norm inequalities our proofs again depend on dyadic approximation but avoid bellman functions and two weight norm inequalities we instead use a recent result due to a lerner 2010 34 to estimate the oscillation of dyadic operators by applying this we get a straightforward proof of the sharp dependence on the a p constant for any operator that can be approximated by haar shift operators in particular we provide a unified approach for the hilbert and riesz transforms the beurling ahlfors operator and their corresponding maximal singular integrals dyadic paraproducts and haar multipliers furthermore we completely solve the open problem of sharp dependence for the dyadic square functions and vector valued hardy littlewood maximal function in the two weight case we use the very same techniques to prove sharp results in the scale of a p bump conditions for the singular integrals considered above we show they map l p v into l p u 1 p if the pair u v satisfies sup q u 1 p a q v 1 p b q where a b p and b b p are orlicz functions this condition is sharp furthermore this condition characterizes in the scale of these a p bump conditions the corresponding two weight norm inequality for the hardy littlewood maximal operator m and its dual i e m l p v l p u and m l p u 1 p l p v 1 p muckenhoupt and wheeden conjectured that these two inequalities for m are sufficient for the hilbert transform to be bounded from l p v into l p u thus in the scale of a p bump conditions we prove their conjecture we prove similar sharp two weight results for the dyadic square function and the vector valued maximal operator

boundedness of a class of bi parameter square functions in the upper half space abstract we consider a class of bi parameter kernels and related square functions in the upper half space and give an efficient proof of a boundedness criterion for them the proof uses modern probabilistic averaging methods and is based on controlling double whitney averages over good cubes

the tb theorem on non homogeneous spaces 0 introduction main objects and results 3 0 1 main results 4 0 2 an application of t1 heorem electric intensity capacity 7 0 3 how to interpret calderon zygmund operator t 9 0 3 1 bilinear form is defined on lipschitz functions 10 0 3 2 bilinear form is defined for smooth functions 11 0 3 3 apriori boundedness 12 0 4 plan of the paper 15

a new public key cipher system based upon the diophantine equations a new public key two key cipher scheme is proposed in this paper in our scheme keys can be easily generated in addition both encryption and decryption procedures are simple to encrypt a message the sender needs to conduct a vector product of the message being sent and the enciphering key on the other hand the receiver can easily decrypt it by conducting several multiplication operations and modulus operations for security analysis we also examine some possible attacks on the presented scheme

estimation of gaussian poissonian gaussian and processed visual noise and its level function we propose a method for estimating the image and video noises of different types white gaussian signal independent mixed poissonian gaussian signal dependent or processed non white our method also estimates the noise level function nlf of these types we do so by classifying image patches based on their intensity and variance in order to find homogeneous regions that best represent the noise we assume that the noise variance is a piecewise linear function of intensity in each intensity class to find noise representative regions noisy signal free patches are first nominated in each intensity class next clusters of connected patches are weighted where the weights are calculated based on the degree of similarity to the noise model the highest ranked cluster defines the peak noise variance and other selected clusters are used to approximate the nlf the more information we incorporate such as temporal data and camera settings the more reliable the estimation becomes to account for the processed noise i e remaining after in camera processing we consider the ratio of low to high frequency energies we address noise variations along video signals using a temporal stabilization of the estimated noise objective and subjective simulations demonstrate that the proposed method outperforms other noise estimation techniques both in accuracy and speed

sparse domination and the strong maximal function abstract we study the problem of dominating the dyadic strong maximal function by 1 1 type sparse forms based on rectangles with sides parallel to the axes and show that such domination is impossible our proof relies on an explicit construction of a pair of maximally separated point sets with respect to an appropriately defined notion of distance

a fast parallel algorithm for blind estimation of noise variance a blind noise variance algorithm that recovers the variance of noise in two steps is proposed the sample variances are computed for square cells tessellating the noise image several tessellations are applied with the size of the cells increasing fourfold for consecutive tessellations the four smallest sample variance values are retained for each tessellation and combined through an outlier analysis into one estimate the different tessellations thus yield a variance estimate sequence the value of the noise variance is determined from this variance estimate sequence the blind noise variance algorithm is applied to 500 noisy 256 256 images in 98 of the cases the relative estimation error was less than 0 2 with an average error of 0 06 application of the algorithm to differently sized images is also discussed

quantitative boundedness of littlewood paley functions on weighted lebesgue spaces in the schrodinger setting abstract let l v be the schrodinger operator on r n with n 3 where v is a non negative potential which belongs to certain reverse holder class r h q r n with q n 2 in this article the authors obtain the quantitative weighted boundedness of littlewood paley functions g l s l and g l associated to l on weighted lebesgue spaces l p w where w belongs to the class of muckenhoupt a p weights adapted to l

on pointwise and weighted estimates for commutators of calderon zygmund operators abstract in recent years it has been well understood that a calderon zygmund operator t is pointwise controlled by a finite number of dyadic operators of a very simple structure called the sparse operators we obtain a similar pointwise estimate for the commutator b t with a locally integrable function b this result is applied into two directions if b b m o we improve several weighted weak type bounds for b t if b belongs to the weighted bmo we obtain a quantitative form of the two weighted bound for b t due to bloom holmes lacey wick

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

secure public key encryption scheme without random oracles since the first practical and secure public key encryption scheme without random oracles proposed by cramer and shoup in 1998 cramer shoup s scheme and its variants remained the only practical and secure public key encryption scheme without random oracles until 2004 in 2004 canetti et al proposed a generic transformation from a selective identity based encryption scheme to a public key encryption by adding a one time strongly signature scheme since then some transformation techniques from a selective identity based encryption scheme to a public key encryption have been proposed to enhance the computational efficiency for example boneh katz s construction and boyen mei waters scheme these transformations have either traded off the publicly verifiable properties or tightness of security reduction in 2007 zhang proposed another generic transformation by adding chameleon hash functions in this paper we introduce another technique from the boneh boyen s selective identity based encryption scheme to a public key encryption which is publicly verifiable and is slightly more efficient than zhang s transformation the proposed public key encryption scheme is based on the decisional bilinear diffie hellman assumption and the target collision resistant hash functions

improved cryptanalysis of a knapsack based probabilistic encryption scheme wang et al b wang q wu y hu information sciences 177 2007 proposed a knapsack based probabilistic encryption scheme with non binary coefficients which enjoys a high density larger than 1 06 in the worst case in this work we successfully attack this scheme by showing that a public key and a restriction on system parameters allow the attacker to recover a secret key in a cubic time complexity using modular equations this approach is much more efficient than the previous attack by youssef a m youssef information sciences 179 2009 in which lattice basis reductions are used recovering secret keys can be done within 4h and 4days when n 100 and 200 respectively a simple modification that helps resist known attacks is also discussed

a_p weights and quantitative estimates in the schrodinger setting suppose l delta v is a schrodinger operator on mathbb r n with a potential v belonging to certain reverse holder class rh sigma with sigma ge n 2 the aim of this paper is to study the a p weights associated to l denoted by a p l which is a larger class than the classical muckenhoupt a p weights we first prove the quantitative a p l bound for the maximal function and the maximal heat semigroup associated to l then we further provide the quantitative a p q l bound for the fractional integral operator associated to l we point out that all these quantitative bounds are known before in terms of the classical a p q constant however since a p q subset a p q l the a p q l constants are smaller than a p q constant hence our results here provide a better quantitative constant for maximal functions and fractional integral operators associated to l next we prove two weight inequalities for the fractional integral operator these have been unknown up to this point finally we also have a study on the exp log link between a p l and bmo l the bmo space associated with l and show that for w in a p l log w is in bmo l and that the reverse is not true in general

quantitative estimates and extrapolation for multilinear weight classes in this paper we prove a quantitative multilinear limited range extrapolation theorem which allows us to extrapolate from weighted estimates that include the cases where some of the exponents are infinite this extends the recent extrapolation result of li martell and ombrosi we also obtain vector valued estimates including ell infty spaces and in particular we are able to reprove all the vector valued bounds for the bilinear hilbert transform obtained through the helicoidal method of benea and muscalu moreover our result is quantitative and in particular allows us to extend quantitative estimates obtained from sparse domination in the banach space setting to the quasi banach space setting our proof does not rely on any off diagonal extrapolation results and we develop a multilinear version of the rubio de francia algorithm adapted to the multisublinear hardy littlewood maximal operator as a corollary we obtain multilinear extrapolation results for some upper and lower endpoints estimates in weak type and mathrm bmo spaces

a sparse approach to mixed weak type inequalities in this paper we provide some quantitative mixed weak type estimates assuming conditions that imply that uv in a infty for calderon zygmund operators rough singular integrals and commutators the main novelty of this paper lies in the fact that we rely upon sparse domination results pushing an approach to endpoint estimates that was introduced in domingo salazar et al bull lond math soc 48 1 63 73 2016 and extended in lerner et al adv math 319 153 181 2017 and li et al j geom anal 2018

non injective knapsack public key cryptosystems abstract two public key 0 1 knapsack cryptosystems are proposed that have so high a density and use so weak a modular multiplication as a trapdoor that known attacks can be avoided decryption is fairly slow and may produce more than one decipherment but all alternative decipherments can be found disambiguating protocols are needed to determine the correct decipherment it is suggested to use also redundancy for this purpose in the first system the initial knapsack is constructed from the powers of two which are multiplied by a constant and reduced with respect to a modulus to a specific range thus producing the easy knapsack then weak modular multiplication is used as a trapdoor transformation with respect to another modulus which is typically smaller than some or all of the elements of the easy knapsack the second knapsack is constructed iteratively from modularly injective or nearly injective components decryption of small components is based on look up tables the specific form of the proposal uses also one large non injective component which is generated and decrypted in a way that resembles superincrease

positive operators and maximal operators in a filtered measure space abstract in a filtered measure space a characterization of weights for which the trace inequality of a positive operator holds is given by the use of discrete wolff s potential a refinement of the carleson embedding theorem is also introduced sawyer type characterization of weights for which a two weight norm inequality for a generalized doob s maximal operator holds is established by an application of our carleson embedding theorem moreover hytonen perez type one weight norm estimate for doob s maximal operator is obtained by the use of our two weight characterization

cryptanalysis of a quadratic knapsack cryptosystem wang and hu b wang and y hu quadratic compact knapsack public key cryptosystem comput math appl 59 1 2010 194 206 proposed a knapsack type public key cryptosystem by introducing an easy quadratic compact knapsack problem and then using the chinese remainder theorem to disguise the easy knapsack instant in this paper we present a heuristic stereotyped message attack that allows the cryptanalyst to recover the plaintext message when partial information about the original message is known in particular as shown by our experiments for the proposed system parameter n 100 which corresponds to a block length of 400 bits exposing 60 of the plaintext allows the cryptanalyst to recover the remaining 160 bits of the message with a success probability of about 90 in about 2 hours

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

weighted littlewood paley inequalities for heat flows in rcd spaces abstract we establish inequalities on vertical littlewood paley square functions for heat flows in the weighted l 2 space over metric measure spaces satisfying the rcd 0 n condition with n 1 and the maximum volume growth assumption in the noncompact setting the later assumption can be removed by showing that the volume of the ball growths at least linearly the estimates are sharp on the growth of the 2 heat weight and the 2 muckenhoupt weight considered the p muckenhoupt weight and the p heat weight are also compared for all p 1

a different approach to endpoint weak type estimates for calderon zygmund operators abstract we present a new proof of the classical weak type 1 1 estimate for calderon zygmund operators this proof is inspired by ideas of nazarov treil and volberg that address the non doubling setting an application to a weighted weak type inequality is also given

sharp logarithmic estimates for positive dyadic shifts the paper contains the study of sharp logarithmic estimates for positive dyadic shifts a a given on probability spaces x x equipped with a tree like structure for any k 0 k 0 we determine the smallest constant l l k l l k such that e a f d k r f d l k e where t t 1 log t 1 t t t 1 log t 1 t e is an arbitrary measurable subset of x and f is an integrable function on x the proof exploits bellman function method we extract the above estimate from the existence of an appropriate special function enjoying certain size and concavity type conditions as a corollary a dual exponential bound is obtained

weak and strong type weighted estimates for multilinear calderon zygmund operators abstract in this paper we study the weighted estimates for multilinear calderon zygmund operators from l p 1 w 1 l p m w m to l p v w where 1 p p 1 p m with 1 p 1 1 p m 1 p and w w 1 w m is a multiple a p weight we give weak and strong type weighted estimates of mixed a p a type moreover the strong type weighted estimate is sharp whenever max i p i p m p 1

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

quadratic compact knapsack public key cryptosystem knapsack type cryptosystems were among the first public key cryptographic schemes to be invented their np completeness nature and the high speed in encryption decryption made them very attractive however these cryptosystems were shown to be vulnerable to the low density subset sum attacks or some key recovery attacks in this paper additive knapsack type public key cryptography is reconsidered we propose a knapsack type public key cryptosystem by introducing an easy quadratic compact knapsack problem the system uses the chinese remainder theorem to disguise the easy knapsack sequence the encryption function of the system is nonlinear about the message vector under the relinearization attack model the system enjoys a high density we show that the knapsack cryptosystem is secure against the low density subset sum attacks by observing that the underlying compact knapsack problem has exponentially many solutions it is shown that the proposed cryptosystem is also secure against some brute force attacks and some known key recovery attacks including the simultaneous diophantine approximation attack and the orthogonal lattice attack

sharp a2 inequality for haar shift operators as a corollary to the main result of the paper we give a new proof of the inequality rm t f l 2 w lesssim w a 2 f l 2 w where t is either the hilbert transform amer j math 129 5 1355 1375 2007 a riesz transform proc amer math soc 136 4 1237 1249 2008 or the beurling operator duke math j 112 2 281 305 2002 the weight w is non negative and the linear growth in the a2 characteristic on the right is sharp prior proofs relied strongly on haar shift operators cr acad sci paris ser i math 330 6 455 460 2000 and bellman function techniques the new proof uses haar shifts and then uses an elegant two weight t 1 theorem of nazarov treil volberg math res lett 15 3 583 597 2008 to immediately identify relevant carleson measure estimates which are in turn verified using an appropriate corona decomposition of the weight w

beltrami operators in the plane we determine optimal lp properties for the solutions of the general nonlinear elliptic system in the plane of the form fz h z fz h l c where h is a measurable function satisfying h z w1 h z w2 k w1 w2 and k is a constant k 1 we will also establish the precise invertibility and spectral properties in lp c for the operators i t i t and t where t is the beurling transform these operators are basic in the theory of quasiconformal mappings and in linear and nonlinear elliptic partial differential equations in two dimensions in particular we prove invertibility in lp c whenever 1 p 1 1 we also prove related results with applications to the regularity of weakly quasiconformal mappings

unconditionally secure cryptosystems based on quantum cryptography most modern cryptographic studies design cryptosystems and algorithms using mathematical concepts in designing and analyzing cryptosystems and protocols mathematical concepts are critical in supporting the claim that the intended cryptosystem is secure most early cryptographic algorithms are based either on factorization or on discrete logarithm problem such systems generally adopt rather simple mathematics and therefore need extensive secondary index computation this study discusses quantum cryptosystems protection of system security and optimization of system efficiency quantum cryptography detects intrusion and wiretap in quantum mechanics a wiretap is neither external nor passive rather it modifies its entity based on the internal component of the system the status of the quantum system changes once a wiretap is detected hence only the designer of the system can discover the quantum status of the system an eavesdropper can neither determine the quantum state nor duplicate the system the quantum cryptosystem can achieve unconditional security and thus guarantees secure communication

jpeg compression history estimation for color images we routinely encounter digital color images that were previously compressed using the joint photographic experts group jpeg standard en route to the image s current representation the previous jpeg compression s various settings termed its jpeg compression history ch are often discarded after the jpeg decompression step given a jpeg decompressed color image this paper aims to estimate its lost jpeg ch we observe that the previous jpeg compression s quantization step introduces a lattice structure in the discrete cosine transform dct domain this paper proposes two approaches that exploit this structure to solve the jpeg compression history estimation chest problem first we design a statistical dictionary based chest algorithm that tests the various chs in a dictionary and selects the maximum a posteriori estimate second for cases where the dct coefficients closely conform to a 3 d parallelepiped lattice we design a blind lattice based chest algorithm the blind algorithm exploits the fact that the jpeg ch is encoded in the nearly orthogonal bases for the 3 d lattice and employs novel lattice algorithms and recent results on nearly orthogonal lattice bases to estimate the ch both algorithms provide robust jpeg chest performance in practice simulations demonstrate that jpeg chest can be useful in jpeg recompression the estimated ch allows us to recompress a jpeg decompressed image with minimal distortion large signal to noise ratio and simultaneously achieve a small file size

tauberian conditions muckenhoupt weights and differentiation properties of weighted bases let b be a homothecy invariant collection of convex sets in r given a measure the associated weighted geometric maximal operator mb is defined by mb f x sup x b b 1

automatic estimation and removal of noise from a single image image denoising algorithms often assume an additive white gaussian noise awgn process that is independent of the actual rgb values such approaches cannot effectively remove color noise produced by today s ccd digital camera in this paper we propose a unified framework for two tasks automatic estimation and removal of color noise from a single image using piecewise smooth image models we introduce the noise level function nlf which is a continuous function describing the noise level as a function of image brightness we then estimate an upper bound of the real nlf by fitting a lower envelope to the standard deviations of per segment image variances for denoising the chrominance of color noise is significantly removed by projecting pixel values onto a line fit to the rgb values in each segment then a gaussian conditional random field gcrf is constructed to obtain the underlying clean image from the noisy input extensive experiments are conducted to test the proposed algorithm which is shown to outperform state of the art denoising algorithms

weighted estimates for the bergman projection on the hartogs triangle abstract we apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the bergman projection in weighted bergman spaces our main theorem focuses on the bergman projection on the hartogs triangle the estimates of the operator norm are in terms of a bekolle bonami type constant as an application of the results obtained we give for example an upper bound for the l p norm of the bergman projection on the generalized hartogs triangle h m n in c 2

image noise level estimation by principal component analysis the problem of blind noise level estimation arises in many image processing applications such as denoising compression and segmentation in this paper we propose a new noise level estimation method on the basis of principal component analysis of image blocks we show that the noise variance can be estimated as the smallest eigenvalue of the image block covariance matrix compared with 13 existing methods the proposed approach shows a good compromise between speed and accuracy it is at least 15 times faster than methods with similar accuracy and it is at least two times more accurate than other methods our method does not assume the existence of homogeneous areas in the input image and hence can successfully process images containing only textures

low rank decomposition based restoration of compressed images via adaptive noise estimation images coded at low bit rates in real world applications usually suffer from significant compression noise which significantly degrades the visual quality traditional denoising methods are not suitable for the content dependent compression noise which usually assume that noise is independent and with identical distribution in this paper we propose a unified framework of content adaptive estimation and reduction for compression noise via low rank decomposition of similar image patches we first formulate the framework of compression noise reduction based upon low rank decomposition compression noises are removed by soft thresholding the singular values in singular value decomposition of every group of similar image patches for each group of similar patches the thresholds are adaptively determined according to compression noise levels and singular values we analyze the relationship of image statistical characteristics in spatial and transform domains and estimate compression noise level for every group of similar patches from statistics in both domains jointly with quantization steps finally quantization constraint is applied to estimated images to avoid over smoothing extensive experimental results show that the proposed method not only improves the quality of compressed images obviously for post processing but are also helpful for computer vision tasks as a pre processing method

multilinear operator valued calderon zygmund theory abstract we develop a general theory of multilinear singular integrals with operator valued kernels acting on tuples of umd banach spaces this in particular involves investigating multilinear variants of the r boundedness condition naturally arising in operator valued theory we proceed by establishing a suitable representation of multilinear operator valued singular integrals in terms of operator valued dyadic shifts and paraproducts and studying the boundedness of these model operators via dyadic probabilistic banach space valued analysis in the bilinear case we obtain a t 1 type theorem without any additional assumptions on the banach spaces other than the necessary umd higher degrees of multilinearity are tackled via a new formulation of the rademacher maximal function rmf condition in addition to the natural umd lattice cases our rmf condition covers suitable tuples of non commutative l p spaces we employ our operator valued theory to obtain new multilinear multi parameter operator valued theorems in the natural setting of umd spaces with property

finding numerical solutions of diophantine equations using ant colony optimization the paper attempts to find numerical solutions of diophantine equations a challenging problem as there are no general methods to find solutions of such equations it uses the metaphor of foraging habits of real ants the ant colony optimization based procedure starts with randomly assigned locations to a fixed number of artificial ants depending upon the quality of these positions ants deposit pheromone at the nodes a successor node is selected from the topological neighbourhood of each of the nodes based on this stochastic pheromone deposit if an ant bumps into an already encountered node the pheromone is updated correspondingly a suitably defined pheromone evaporation strategy guarantees that premature convergence does not take place the experimental results which compares with those of other machine intelligence techniques validate the effectiveness of the proposed method

representation of bi parameter singular integrals by dyadic operators abstract we prove a dyadic representation theorem for bi parameter singular integrals that is we represent certain bi parameter operators as averages of rapidly decaying sums of what we call bi parameter shifts a new version of the product space t 1 theorem is established as a consequence

some obstacles in characterising the boundedness of bi parameter singular integrals the famous t1 theorem for classical calderon zygmund operators is a characterisation for their boundedness in l 2 in the bi parameter case on the other hand the current t1 theorem is merely a collection of sufficient conditions this difference in mind we study a particular dyadic bi parameter singular integral operator namely the full mixed bi parameter paraproductp which is precisely the operator responsible for the outstanding problems in the bi parameter theory we make several remarks about p the common theme of which is to demonstrate the delicacy of the problem of finding a completely satisfactory product t1 theorem for example p need not be unconditionally bounded if it is conditionally bounded a major difference compared to the corresponding one parameter model operators moreover currently the theory even lacks a characterisation for the potentially easier unconditional boundedness the product bmo condition is sufficient but far from necessary we show by example that unconditional boundedness does not even imply the weaker rectangular bmo condition

complexity of sentences over number rings let i be an algebraic integer ring the decision problem of the solvability of diophantine equations with parameters in i is proved to be co np complete however the decision problem of the solvability of diophantine equations with parameters in all algebraic integer rings is in p let varphi x y be a quantifier free arithmetical formula in conjunctive normal form or disjunctive normal form the decision problem of the sentences of the form exists x forall y varphi x y true in i is np complete then the decision problem of the sentences of the form forall x exists y varphi x y true in i is co np complete whereas the decision problem of the sentences of the form forall x exists y varphi x y true in all algebraic integer rings is in p some other related decision problems are also proven to be in p