configurational invariants of hamiltonian systems in this paper we explore the general conditions in order that a two dimensional natural hamiltonian system possess a second invariant which is a polynomial in the momenta and is therefore liouville integrable we examine the possibility that the invariant is preserved by the hamiltonian flow on a given energy hypersurface only weak integrability and derive the additional requirement necessary to have conservation at arbitrary energy strong integrability using null complex coordinates we show that the leading order coefficient of the polynomial is an arbitrary holomorphic function in the case of weak integrability and a polynomial in the coordinates in the strongly integrable one we review the results obtained so far with strong invariants up to degree four and provide some new examples of weakly integrable systems with linear and quadratic invariants

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

superintegrable three body systems on the line we consider classical three body interactions on a euclidean line depending on the reciprocal distance of the particles and admitting four functionally independent quadratic in the momentum first integrals these systems are multiseparable superintegrable and equivalent up to rescalings to a one particle system in the three dimensional euclidean space common features of the dynamics are discussed we show how to determine quantum symmetry operators associated with the first integrals considered here but do not analyze the corresponding quantum dynamics the conformal multiseparability is discussed and examples of conformal first integrals are given the systems considered here in generality include the calogero wolfes and other three body interactions widely studied in mathematical physics

provably secure certificate based signature scheme without pairings in order to simplify certificate management in traditional public key cryptography and solve the key escrow problem in identity based cryptography the notion of certificate based cryptography was introduced recently ming and wang proposed a certificate based signature scheme without pairings they claimed that the scheme was existentially unforgeable against adaptive chosen message and identity attacks in the random oracle in this paper we show that the scheme is insecure against a malicious certifier under existing security model we also propose a new efficient certificate based signature scheme without pairings which is proven secure in the random oracle model compared with the existed certificate based signature schemes without parings our scheme enjoys shorter signature length and less operation cost

continuous leakage resilient certificate based encryption encryption schemes are generally considered to be secure in an ideal environment where the adversary cannot obtain the secret internal state of schemes however in the realistic environment the adversary can gain partial information about decryption private key through various types of side channel attacks in order to capture these attacks it is crucial to design encryption schemes which are resilient to leakage in this article we first formalize a continuous leakage resilient security model of certificate based encryption in the model the adversary continuously obtains partial information about the secret states through the continuous leakage attacks furthermore we construct a continuous leakage resilient certificate based encryption clr cbe scheme which is resilient to continuous leakage and it is secure against adaptive chosen ciphertext attacks under the bilinear diffie hellman inversion bdhi hardness assumption lastly we show the bound on leakage and make comparison between proposed and existing schemes in terms of security properties and efficiency

asymptotic trace formula for the hecke operators given integers m n and k we give an explicit formula with an optimal error term with square root cancelation for the petersson trace formula involving the mth and nth fourier coefficients of an orthonormal basis of s k left n right the weight k newforms with fixed square free level n provided that 4 pi sqrt mn k o left k frac 1 3 right moreover we establish an explicit formula with a power saving error term for the trace of the hecke operator mathcal t n on s k left n right averaged over k in a short interval by bounding the second moment of the trace of mathcal t n over a larger interval we show that the trace of mathcal t n is unusually large in the range 4 pi sqrt n k o left n frac 1 6 right as an application for any fixed prime p coprime to n we show that there exists a sequence k n of weights such that the error term of weyl s law for mathcal t p is unusually large and violates the prediction of arithmetic quantum chaos in particular this generalizes the result of gamburd et al j eur math soc 1 1 51 85 1999 theorem 1 4 with an improved exponent

a unified treatment of quartic invariants at fixed and arbitrary energy two dimensional hamiltonian systems admitting second invariants which are quartic in the momenta are investigated using the jacobi geometrization of the dynamics this approach allows for a unified treatment of invariants at both arbitrary and fixed energy in the differential geometric picture the quartic invariant corresponds to the existence of a fourth rank killing tensor expressing the jacobi metric in terms of a kahler potential the integrability condition for the existence of the killing tensor at fixed energy is a nonlinear equation involving the kahler potential at arbitrary energy further conditions must be imposed which lead to an overdetermined system with isolated solutions we obtain several new integrable and superintegrable systems in addition to all previously known examples

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

the super separability of the three body inverse square calogero system the geometrical theory of the variable separation for the hamilton jacobi equation is applied to the classical three body inverse square calogero system it is proved that this system is separable in infinitely many inequivalent ways related to five different kinds of separable webs in the euclidean three space and the corresponding systems of independent first integrals in involution are computed

two dimensional metrics admitting precisely one projective vector field we give a complete list of 2 dimensional metrics that admit an essential projective vector field this solves a problem explicitly posed by sophus lie in 1882

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

a class of liouville integrable hamiltonian systems with two degrees of freedom a class of two dimensional liouville integrable hamiltonian systems is studied separability of the corresponding hamilton jacobi equation for these systems is shown to be equivalent to other fundamental properties of hamiltonian systems such as the existence of the lax and bi hamiltonian representations of certain fixed types applications to physical models including the calogero moser model an integrable case of the henon heiles potential and the nonperiodic toda lattice are presented

first integrals and symmetries of time dependent hamiltonian systems in this paper first integrals of one dimensional time dependent hamiltonians h q p t are studied first of all it is shown that the second first integral j q h t t dq hp valid for autonomous hamiltonians h q p can be extended to the case of nonautonomous hamiltonians h q p t provided hp resp t is replaced with ip where i q p t is a first integral of h q p t resp a new time t j q i t t dq ip in a second part we derive a technique leading to a first integral i q p t from a lie symmetry as an example this technique together with the expression of the second first integral j q i t is used to completely integrate a special case of the linear harmonic oscillator with a time dependent frequency as a result lewis first integral is recovered from a lie symmetry in a way that generalizes the recent work of shivamoggi and muilenberg phys lett a 154 1 1991

orthogonal separation of variables for the hamilton jacobi and wave equations in three dimensional minkowski space we give a complete solution of the eisenhart integrability conditions in three dimensional minkowski space obtaining 39 orthogonally separable webs and 58 inequivalent metrics in adapted coordinate systems which permit orthogonal separation of variables for the associated hamilton jacobi and wave equations the corresponding transformations from canonical separable coordinates to canonical pseudo cartesian coordinates are listed for each of the 58 cases and characteristic killing tensors are given for each of the 39 webs

invariants at fixed and arbitrary energy a unified geometric approach invariants at arbitrary and fixed energy strongly and weakly conserved quantities for two dimensional hamiltonian systems are treated in a unified way this is achieved by utilizing the jacobi metric geometrization of the dynamics using killing tensors we obtain an integrability condition for quadratic invariants which involves an arbitrary analytic function s z for invariants at arbitrary energy the function s z is a second degree polynomial with real second derivative the integrability condition then reduces to darboux s condition for quadratic invariants at arbitrary energy the four types of classical quadratic invariants for positive definite two dimensional hamiltonians are shown to correspond to certain conformal transformations we derive the explicit relation between invariants in the physical and jacobi time gauges in this way knowledge about the invariant in the physical time gauge enables one to write down directly the components of the corresponding killing tensor for the jacobi metric we also discuss the possibility of searching for linear and quadratic invariants at fixed energy and its connection with the problem of the third integral in galactic dynamics in our approach linear and quadratic invariants at fixed energy can be found by solving a linear ordinary differential equation of the first or second degree respectively

a new form of the circle method and its application to quadratic forms if the coefficients r n satisfy suitable arithmetic conditions the behaviour of f will be determined by an appropriate rational approximation a q to with small values of q usually producing large values of f when lies in an interval a q a q with q small a major arc one hopes to estimate f asymptotically while if the corresponding q is large for the minor arcs one hopes that f will be small at least on average one can distinguish two different types of application of the circle method the first type following the above pattern uses one of a variety of mean value techniques hua s inequality for example to give an upper bound for the minor arc contribution results on waring s problem are generally proved this way for example the second type of application on which we shall be focusing our attention avoids the minor arcs completely and treats f asymptotically for all here one cannot take advantage of the mean value ideas used in the first type of problem the savings come instead from the availability of good estimates for complete exponential sums kloosterman s work 12 on quaternary quadratic forms and the papers of the author 5 and hooley 8 and 9 on cubic forms are of this latter type we should point out that such applications do not include any problems in which f is the generating function for a polynomial of degree 4 or more there are

coefficient of maass forms and the siegel zero with an appendix by dorian goldfeld jeffrey hoffstein and daniel lieman

indivisibility of class numbers of imaginary quadratic fields and orders of tate shafarevich groups of elliptic curves with complex multiplication since gauss ideal class groups of imaginary quadratic fields have been the focus of many investigations and recently there have been many investigations regarding tateshafarevich groups of elliptic curves in both cases the literature is quite extensive but little is known throughout d will denote a fundamental discriminant of a quadratic field let cl d denote the class group of q d and let h d denote its order i e the usual class number of primitive positive binary quadratic forms with discriminant d one of the main problems deals with the structure of cl d and so one naturally studies the divisibility of h d by primes here we consider imaginary quadratic fields gauss genus theory precisely determines the parity of h d but the divisibility of h d by odd primes is much less well understood in view of these difficulties cohen and lenstra c l gave heuristics describing the expected behavior of cl d and in particular they predicted that the probability that h d is

solution of second order supersymmetrical intertwining relations in minkowski plane supersymmetrical susy intertwining relations are generalized to the case of quantum hamiltonians in minkowski space for intertwining operators supercharges of second order in derivatives the intertwined hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta in terms of components the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest constant ansatzes for the metric matrix in second order part of the supercharges the corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of metric matrices and their properties are discussed

r separation of variables for the time dependent hamilton jacobi and schrodinger equations the theory of r separation of variables is developed for the time dependent hamilton jacobi and schrodinger equations on a riemannian manifold v n where time dependent vector and scalar potentials are permitted as an application it is shown how to obtain all r separable coordinates for the n sphere and euclidean n space

geometrical classification of killing tensors on bidimensional flat manifolds valence two killing tensors in the euclidean and minkowski planes are classified under the action of the group which preserves the type of the corresponding killing web the classification is based on an analysis of the system of determining partial differential equations for the group invariants and is entirely algebraic the approach allows one to classify both characteristic and noncharacteristic killing tensors

optimal strong approximation for quadratic forms for a nondegenerate integral quadratic form f x1 xd in d 5 variables we prove an optimal strong approximation theorem let be a fixed compact subset of the affine quadric f x1 xd 1 over the real numbers take a small ball b of radius 0 0 finally assume that an integral vector 1 d mod m is given then we show that there exists an integral solution x x1 xd of f x n such that xi imodm and xn b provided that all the local conditions are satisfied we also show that 4 is the best possible exponent moreover for a nondegenerate integral quadratic form in four variables we prove the same result if n is odd and n r 1m 6 based on our numerical experiments on the diameter of lps ramanujan graphs and the expected square root cancellation in a particular sum that appears in remark 6 8 we conjecture that the theorem holds for any quadratic form in four variables with the optimal exponent 4

new examples of integrable conservative systems on s 2 and the case of goryachev chaplygin in this paper we propose new examples of conservative systems on s 2 possessing cubic integrals in momenta we obtain a classification of a large class of such systems we show that this class contains new families of integrable systems as well as the classical case of goryachev chaplygin

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

1 1 dimensional separation of variables in this paper we explore general conditions which guarantee that the geodesic flow on a two dimensional manifold with indefinite signature is locally separable this is equivalent to showing that a two dimensional natural hamiltonian system on the hyperbolic plane possesses a second integral of motion which is a quadratic polynomial in the momenta associated with a secind rank killing tensor we examine the possibility that the integral is preserved by the hamiltonian flow on a given energy hypersurface only weak integrability and derive the additional requirement necessary to have conservation at arbitrary values of the hamiltonian strong integrability using null coordinates we show that the leading order coefficients of the invariant are arbitrary functions of one variable in the case of weak integrability these functions are quadratic polynomials in the coordinates in the case of strong integrability we show that for 1 1 dimensional systems there are three possible types of conformal killing

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

remarks on the connection between the additive separation of the hamilton jacobi equation and the multiplicative separation of the schrodinger equation i the completeness and robertson conditions the fundamental elements of the variable separation theory are revisited including the eisenhart and robertson theorems kalnins miller theory and the intrinsic characterization of the separation of the hamilton jacobi equation in a unitary and geometrical perspective the general notion of complete integrability of first order normal systems of pdes leads in a natural way to completeness conditions for separated solutions of the schrodinger equation and to the robertson condition two general types of multiplicative separation for the schrodinger equation are defined and analyzed they are called free and reduced separation respectively in the free separation the coordinates are necessarily orthogonal while the reduced separation may occur in nonorthogonal coordinates but only in the presence of symmetries killing vectors

invariants for dissipative nonlinear systems by using rescaling a rescaling transformation of space and time is introduced in the study of nonlinear dissipative systems that are described by a second order differential equation with a friction term proportional to the velocity t v the transformation is of the form x t where x c t t d dt a2 t this rescaling is used to find each potential for which there exists an exact invariant quadratic in the velocity and to find the invariant the invariants are found explicitly for a power law potential t xm 1 m 1 and an arbitrary coefficient of friction t we show in an example how the rescaling transformation can be chosen to give an asymptotic solution of the equation in cases where the exact invariant does not exist for certain parameters the asymptotic solution is a self similar solution that is an attractor for all initial conditions the technique of applying a rescaling transformation has been useful in other problems and may have additional practical applications

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

semiclassical theory of spectral rigidity the spectral rigidity l of a set of quantal energy levels is the mean square deviation of the spectral staircase from the straight line that best fits it over a range of l mean level spacings in the semiclassical limit 0 formulae are obtained giving l as a sum over classical periodic orbits when l l max where l max n 1 for a system of n freedoms l is shown to display the following universal behaviour as a result of properties of very long classical orbits if the system is classically integrable all periodic orbits filling tori l 1 5 l as in an uncorrelated poisson eigenvalue sequence if the system is classically chaotic all periodic orbits isolated and unstable and has no symmetry l in l 2 2 d if 1 l l max as in the gaussian unitary ensemble of random matrix theory if the system is chaotic and has time reversal symmetry l in l 2 e if 1 l l max as in the gaussian orthogonal ensemble when l l max l saturates non universally at a value determined by short classical orbits of order n 1 for integrable systems and in 1 for chaotic systems these results are obtained by using the periodic orbit expansion for the spectral density together with classical sum rules for the intensities of long orbits and a semiclassical sum rule restricting the manner in which their contributions interfere for two examples l is studied in detail the rectangular billiard integrable and the riemann zeta function assuming its zeros to be the eigenvalues of an unknown quantum system whose unknown classical limit is chaotic

nonorthogonal r separable coordinates for four dimensional complex riemannian spaces we classify all r separable coordinate systems for the equations 4 j4i j 1g 1 2 j g1 2gi j i 0 and j4i j 1gi j iw jw 0 with special emphasis on nonorthogonal coordinates and give a group theoretic interpretation of the results for flat space we show that the two equations separate in exactly the same coordinate systems and present a detailed list of the possibilities we demonstrate that every r separable system for the laplace equation 4 0 on a conformally flat space corresponds to a separable system for the helmholtz equations 4 on one of the manifolds e4 s1 s3 s2 s2 and s4

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

mass equidistribution for hecke eigenforms in this work we study the mass equidistribution for holomorphic hecke eigenforms and establish by employing incomplete poincare series and the petersson formula sharp equidistribution results when the average is performed over intervals much shorter than before a key feature is the analysis of the off diagonal terms that result from this shortening of intervals 2003 wiley periodicals inc

invariant classification of the rotationally symmetric r separable webs for the laplace equation in euclidean space an invariant characterization of the rotationally symmetric r separable webs for the laplace equation in euclidean space is given in terms of invariants and covariants of a real binary quartic canonically associated with the characteristic conformal killing tensor which defines the webs

variable separation theory for the null hamilton jacobi equation the theory of the separation of variables for the null hamilton jacobi equation h 0 is systematically revisited and based on levi civita separability conditions with lagrangian multipliers the separation of the null equation is shown to be equivalent to the ordinary separation of the image of the original hamiltonian under a generalized jacobi maupertuis transformation the general results are applied to the special but fundamental case of the orthogonal separation of a natural hamiltonian with a fixed value of the energy the separation is then related to conditions which extend those of stackel and kalnins and miller for the null geodesic case and it is characterized by the existence of conformal killing two tensors of special kind