are electroencephalogram eeg signals pseudo random number generators abstract in this paper we study if an electroencephalogram eeg signal can be treated as a pseudo random number generator prng we approach this problem by calculating the frequency of both healthy and epileptic eeg signals and we find that all eeg signals obey the gaussian distribution with different standard deviations however under some transformation we can treat eeg signals as prngs our transformation takes the sum of the least significant five bits of the eeg sample amplitude and then outputs the parity of this sum to a binary 0 or 1 sequence our binary sequences have passed nearly all nist pseudo random number tests except a few failures this indicates that the eeg signals can indeed become a prng provided that it undergoes a transformation like ours

dynamical analysis of a class of euclidean algorithms we develop a general framework for the analysis of algorithms of a broad euclidean type the average case complexity of an algorithm is seen to be related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithm the methods rely on properties of transfer operators suitably adapted from dynamical systems theory as a consequence we obtain precise average case analyses of algorithms for evaluating the jacobi symbol of computational number theory fame thereby solving conjectures of bach and shallit these methods also provide a unifying framework for the analysis of an entire class of gcd like algorithms together with new results regarding the probable behaviour of their cost functions

complex architecture of primes and natural numbers prime numbers and their distribution in the sequence of natural numbers are of interest for fundamental as well as practical reasons the authors introduce a stochastic model based on a network representation that closely matches some statistical properties of the prime numbers and that can be useful as a tool in the study of the distribution of primes

color image watermark extraction based on support vector machines abstract this work proposes a novel watermarking technique called svm based color image watermarking sciw based on support vector machines svms for the authentication of color images to protect the copyright of a color image a signature a watermark which is represented by a sequence of binary data is embedded in the color image the watermark extraction issue can be treated as a classification problem involving binary classes the sciw method constructs a set of training patterns with the use of binary labels by employing three image features which are the differences between a local image statistic and the luminance value of the center pixel in a sliding window with three distinct shapes this set of training patterns is gathered from a pair of images an original image and its corresponding watermarked image in the spatial domain a quasi optimal hyperplane a binary classifier can be realized by an svm the sciw method utilizes this set of training patterns to train the svm and then applies the trained svm to classify a set of testing patterns following the results produced by the classifier the trained svm the sciw method retrieves the hidden signature without the original image during watermark extraction experimental results have demonstrated that the sciw method is sufficiently robust against several color image manipulations and that it outperforms other proposed methods considered in this work

on using deterministic functions to reduce randomness in probabilistic algorithms abstract we show the existence of nonuniform schemes for the following sampling problem given a sample space with n points an unknown set of size n 2 and s random points it is possible to generate deterministically from them s k points such that the probability of not hitting the unknown set is exponentially smaller in k than 2 s tight bounds are given for the quality of such schemes explicit uniform versions of these schemes could be used for efficiently reducing the error probability of randomized algorithms a survey of known constructions whose quality is very far from the existential result is included

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

accelerated spectral analysis of compact operators an acceleration technique is developed that significantly improves the accuracy of a wide class of well known numerical procedures for approximating the spectra of linear compact operators a given portion of the spectrum is determined to any desired accuracy by implementing an eigenvalue problem of fixed dimension for a matrix polynomial in the eigenparameter of sufficiently high degree the usual approach employs the eigenvalue problem for a matrix polynomial of degree one and sufficiently large dimension the method is applicable to degenerate as well as nondegenerate portions of the spectrum error expressions are obtained and several numerical examples for integral operators are presented

efficient prediction of marsaglia zaman random number generators we show that the random number generator of marsaglia and zaman 1991 produces the successive digits of a rational b adic number the b adic number system generalizes p adic numbers to an arbitrary integer base b using continued fractions we derive an efficient prediction algorithm for this generator

on the power of membership queries in agnostic learning we study the properties of the agnostic learning framework of haussler 1992 and kearns schapire and sellie 1994 in particular we address the question is there any situation in which membership queries are useful in agnostic learning our results show that the answer is negative for distribution independent agnostic learning and positive for agnostic learning with respect to a specific marginal distribution namely we give a simple proof that any concept class learnable agnostically by a distribution independent algorithm with access to membership queries is also learnable agnostically without membership queries this resolves an open problem posed by kearns et al 1994 for agnostic learning with respect to the uniform distribution over 0 1 n we show a concept class that is learnable with membership queries but computationally hard to learn from random examples alone assuming that one way functions exist

hardness results for neural network approximation problems we consider the problem of efficiently learning in two layer neural networks we investigate the computational complexity of agnostically learning with simple families of neural networks as the hypothesis classes we show that it is np hard to find a linear threshold network of a fixed size that approximately minimizes the proportion of misclassified examples in a training set even if there is a network that correctly classifies all of the training examples in particular for a training set that is correctly classified by some two layer linear threshold network with k hidden units it is np hard to find such a network that makes mistakes on a proportion smaller than c k2 of the examples for some constant c we prove a similar result for the problem of approximately minimizing the quadratic loss of a two layer network with a sigmoid output unit

thermodynamics of random number generation we analyze the thermodynamic costs of the three main approaches to generating random numbers via the recently introduced information processing second law given access to a specified source of randomness a random number generator rng produces samples from a desired target probability distribution this differs from pseudorandom number generators prng that use wholly deterministic algorithms and from true random number generators trng in which the randomness source is a physical system for each class we analyze the thermodynamics of generators based on algorithms implemented as finite state machines as these allow for direct bounds on the required physical resources this establishes bounds on heat dissipation and work consumption during the operation of three main classes of rng algorithms including those of von neumann knuth and yao and roche and hoshi and for prng methods we introduce a general trng and determine its thermodynamic costs exactly for arbitrary target distributions the results highlight the significant differences between the three main approaches to random number generation one is work producing one is work consuming and the other is potentially dissipation neutral notably trngs can both generate random numbers and convert thermal energy to stored work these thermodynamic costs on information creation complement landauer s limit on the irreducible costs of information destruction

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

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

pseudorandom functions and factoring the computational hardness of factoring integers is the most established assumption on which cryptographic primitives are based this work presents an efficient construction of pseudorandom functions whose security is based on the intractability of factoring in particular we are able to construct efficient length preserving pseudorandom functions where each evaluation requires only a small constant number of modular multiplications per output bit this is substantially more efficient than any previous construction of pseudorandom functions based on factoring and matches up to a constant factor the efficiency of the best known factoring based pseudorandom bit generators

accelerated projection and iterated projection methods with applications to nonlinear integral equations a new approach is developed to numerically approximate fixed points for a class of nonlinear operators by projection and iterated projection methods it is shown that isolated solutions can be determined to any desired accuracy for a fixed choice of the projection neither the structure nor the rank of the projection is altered to achieve increased accuracy instead the fixed point is decomposed by the given projection into a finite and an infinite dimensional component successive approximations to the infinite dimensional component are employed to construct a sequence of accelerated finite dimensional systems their solutions define a sequence of higher order approximations to the finite dimensional component and consequently to the fixed point error expressions are obtained and several examples of solving nonlinear integral equations are given

accelerated degenerate kernel methods for linear integral equations abstract a new approach to the theory of kernel approximations is developed for the numerical solution of fredholm integral equations of the second kind the objective is to determine the solution to any desired accuracy using a degenerate kernel operator of fixed rank that is without increasing the number of terms in the approximate kernel consequently high accuracy is achieved without incurring the computational costs associated with solving large algebraic systems the procedure employs projection techniques to construct accelerated degenerate kernel schemes that give rise to a bisequence of higher order approximate solutions error expressions are obtained and a numerical example of solving a weakly singular equation is given

on the linear and nonlinear complexity profile of nonlinear pseudorandom number generators we obtain lower bounds on the linear and nonlinear complexity profile of a general nonlinear pseudorandom number generator of the inversive generator and of a new nonlinear generator called quadratic exponential generator the results are interesting for applications to cryptography and monte carlo methods

performance improvement for the ggm construction of pseudorandom functions a pseudorandom function is a function that cannot be efficiently distinguished from a truly random function the first construction of pseudorandom functions was introduced by goldreich goldwasser and micali ggm construction in this paper we propose a variant of the ggm construction and compare its performance with the original construction we show that a 4 ary tree variant construction can achieve the best performance under the assumption that the underlying pseudorandom generators generate pseudorandom bits sequentially

a simple unpredictable pseudo random number generator two closely related pseudo random sequence generators are presented the 1 p generator with input p a prime outputs the quotient digits obtained on dividing 1 by p the x 2 bmod n generato

coin flipping of any constant bias implies one way functions we show that the existence of a coin flipping protocol safe against any nontrivial constant bias e g 499 implies the existence of one way functions this improves upon a result of haitner and omri focs 11 who proved this implication for protocols with bias s 2 1 2 o 1 t 207 unlike the result of haitner and omri our result also holds for weak coin flipping protocols

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

trace representation of some generalized cyclotomic sequences of length pq this paper contributes to trace representation of some generalized cyclotomic sequences of length pq p qprime which are defined by ding and helleseth from the relations between these sequences and the legendre sequence we firstly confirm the defining pairs of these sequences of arbitrary order then we obtain their trace representation from which we give their linear complexity using key s method it can be seen that bai et al s conclusion is a special case of our result when the order is two finally an example is given to illustrate the validity of our result

a comparison of two approaches to pseudorandomness the concept of pseudorandomness plays an important role in cryptography in this note we contrast the notions of complexity theoretic pseudorandom strings from algorithmic information theory and pseudorandom strings from cryptography for example we show that we can easily distinguish a complexity theoretic pseudorandom ensemble from the uniform ensemble both notions of pseudorandom strings are uniformly unpredictable in contrast with pseudorandom strings complexity theoretic pseudorandom strings are not polynomial time unpredictable

on the uniformity of distribution of the rsa pairs let m pl be a product of two distinct primes p and l we show that for almost all exponents e with gcd e m 1 the rsa pairs x x e are uniformly distributed modulo m when x runs through the group of units z m modulo m that is as in the classical rsa scheme the set of k products x i1 ik 1 i 1 i k n where 1 n e z m are selected at random that is as in the recently introduced rsa scheme with precomputation these results are based on some new bounds of exponential sums

a unified set of single step algorithms part 3 the beta m method a generalization of the newmark scheme introduced herein is a generalization of newmark s time marching integration scheme called the m method like the sspj method introduced in parts 1 and 2 of this series the m method provides a gcneral single step scheme applicable to any set of initial value problems the method is specialized by specifying the method order m along with rn integration parameters 0 1 m 1 for a particular choice of m the integration parameters provide a subfamily of methods which control accuracy and stability as well as offering options for explicit or implicit algorithms for the most part attention is focused on the application to structural dynamic equations most well known methods e g newmark wilson houbolt etc are shown to be special cases within the m family hence one computationally efficient and surprisingly simple algorithm unifies old and new methods stability and accuracy analyses are presented for method orders m 2 3 and 4 to determine optimal parameters for implicit and explicit schemes along with numerical verification

accelerated refinement with applications to integral equations an acceleration procedure is developed that significantly improves the convergence rate associated with successive approximations to discrete linear systems the technique produces a sequence of accelerated refinement schemes that converge at progressively higher rates even when applied to large ill conditioned problems optimal iterative procedures that achieve a prescribed error bound in minimal time are constructed error expressions are obtained and several numerical examples of solving discrete models of second kind integral equations are given

on the linear complexity of some new q ary sequences some new q ary sequences with period q 3 e k 1 q p m p an odd prime m e k integers are first constructed and then inspired by antweiler s method their linear complexity is examined the exact value of linear complexity k 6e w is determined when email protected i 1 wp e i furthermore an upper bound of the linear complexity is given for the other values of r our results show that this sequence has larger linear span than gmw sequence with the same parameters finally the results of a maple program are included to illustrate the validity of the results

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

formal security proofs with minimal fuss we show how implicit computational complexity can be used in order to increase confidence in game based security proofs in cryptography for this purpose we extend cslr a probabilistic lambda calculus with a type system that guarantees the existence of a probabilistic polynomial time bound on computations this allows us to define cryptographic constructions feasible adversaries security notions computational assumptions game transformations and game based security proofs in a unified framework we also show that the standard practice of cryptographers ignoring that polynomial time turing machines cannot generate all uniform distributions is actually sound we illustrate our calculus on cryptographic constructions for public key encryption and pseudorandom bit generation

on the linear complexity profile of the power generator we obtain a lower bound on the linear complexity profile of the power generator of pseudo random numbers modulo a blum integer a different method is also proposed to estimate the linear complexity profile of the blum blum shub 1986 generator in particular these results imply that lattice reduction attacks on such generators are not feasible

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

periodic orbits of the ensemble of sinai arnold cat maps and pseudorandom number generation we propose methods for constructing high quality pseudorandom number generators rngs based on an ensemble of hyperbolic automorphisms of the unit two dimensional torus sinai arnold map or cat map while keeping a part of the information hidden the single cat map provides the random properties expected from a good rng and is hence an appropriate building block for an rng although unnecessary correlations are always present in practice we show that introducing hidden variables and introducing rotation in the rng output accompanied with the proper initialization dramatically suppress these correlations we analyze the mechanisms of the single cat map correlations analytically and show how to diminish them we generalize the percival vivaldi theory in the case of the ensemble of maps find the period of the proposed rng analytically and also analyze its properties we present efficient practical realizations for the rngs and check our predictions numerically we also test our rngs using the known stringent batteries of statistical tests and find that the statistical properties of our best generators are not worse than those of other best modern generators

properties of the x sup 2 mod n pseudorandom number generator in 1986 l blum r i blum and m shub introduced the x sup 2 mod n generator of pseudorandom bit strings and showed given certain plausible but unproved hypotheses that it has the desirable cryptographic property of unpredictability they also studied the period length of the sequences produced by this generator and proposed a way to guarantee that these sequences will have maximum possible period in this correspondence we prove that it is very likely that for many values of n the sequences produced by the x sup 2 mod n generator are usually not balanced that is having equal frequency of 0 s and 1 s we further prove that the proposed method for guaranteeing long periods is also very likely to guarantee relatively large imbalances between the frequencies of 0 s and 1 s however we also prove that the average imbalance for these sequences is no worse than what would be expected in a truly random bit string of the same length thus our results provide further support for the use of the x sup 2 mod n generator in cryptographic applications

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

number theoretic constructions of efficient pseudo random functions we describe efficient constructions for various cryptographic primitives in private key as well as public key cryptography our main results are two new constructions of pseudo random functions we prove the pseudo randomness of one construction under the assumption that factoring blum integers is hard while the other construction is pseudo random if the decisional version of the diffie hellman assumption holds computing the value of our functions at any given point involves two subset products this is much more efficient than previous proposals furthermore these functions have the advantage of being in tc0 the class of functions computable by constant depth circuits consisting of a polynomial number of threshold gates this fact has several interesting applications the simple algebraic structure of the functions implies additional features such as a zero knowledge proof for statements of the form y e fs x and y n fs x given a commitment to a key s of a pseudo random function fs

relative to a random oracle a bf p a ne bf np a ne text co bf np a with probability 1 let a be a language chosen randomly by tossing a fair coin for each string x to determine whether x belongs to a with probability 1 each of the relativized classes textbf logspace a bf p a bf np a bf pp a and textbf pspace a is properly contained in the next also bf np a ne text co bf np a with probability 1 by contrast with probability 1 the class bf p a coincides with the class bf bpp a of languages recognized by probabilistic oracle machines with error probability uniformly bounded below tfrac 1 2 bf np a is shown with probability 1 to contain a bf p a immune set i e a set having no infinite subset in bf p a the relationship of bf p a immunity to p sparseness and bf np a completeness is briefly discussed bf p a immune sets in bf np a can be sparse or moderately dense but not co sparse relativization with respect to a random length preserving permutation pi instead of a rand

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

substitution permutation networks pseudorandom functions and natural proofs this article takes a new step towards closing the gap between pseudorandom functions prf and their popular bounded input length counterparts this gap is both quantitative because these counterparts are more efficient than prf in various ways and methodological because these counterparts usually fit in the substitution permutation network paradigm spn which has not been used to construct prf we give several candidate prf fi that are inspired by the spn paradigm most of our candidates are more efficient than previous ones our main candidates are as follows f1 0 1 n 0 1 n is an spn whose s box is a random function on b bits given as part of the seed we prove that f1 resists attacks that run in time 2eb f2 0 1 n 0 1 n is an spn where the s box is patched field inversion a common choice in practical constructions we show that f2 is computable with boolean circuits of size n logo 1 n and that it has exponential security 2 n against linear and differential cryptanalysis f3 0 1 n 0 1 is a nonstandard variant on the spn paradigm where states grow in length we show that f3 is computable with tc0 circuits of size n1 p e for any e 0 and that it is almost 3 wise independent f4 0 1 n 0 1 uses an extreme setting of the spn parameters one round one s box no diffusion matrix the s box is again patched field inversion we show that f4 is computable by circuits of size n logo 1 n and that it fools all parity tests on 20 9n outputs assuming the security of our candidates our work narrows the gap between the natural proofs barrier and existing lower bounds in three models circuits tc0 circuits and turing machines

dynamic transient analysis by a mixed iterative method summary mixed methods solved by an iterative process have been shown to provide an inexpensive procedure for improving the results of standard displacement analysis this paper shows the possibilities present in their application to dynamic problems where again accuracy improvement is achieved at small additional expense the advantages of the formulation presented are particularly noteworthy in explicit forms where the difficulties of hour glass modes associated with minimal integration rules ae avoided without cost increase

an efficient binary sequence generator with cryptographic applications as the internet has become more and more important the need for secure systems has increased accordingly our proposal is an efficient sequence generator that can be used in these secure systems it is based on the powers of a block upper triangular matrix and besides achieving great statistical results and efficiency it is very flexible and can be easily adapted to different applications the matricial techniques employed can also be used in other kinds of cryptographic primitives

how to turn loaded dice into fair coins we present a new technique for simulating fair coin flips using a biased stationary source of randomness sequences of random numbers are of pervasive importance in cryptography and vital to many other computing applications many sources of randomness such as radioactive or quantum mechanical sources possess the property of stationarity in other words they produce independent outputs over fixed probability distributions the output of such sources may be viewed as the result of rolling a biased or loaded die while a biased die may be a good source of entropy many applications require input in the form of unbiased bits rather than biased ones for this reason von neumann 1951 presented a now well known and extensively investigated technique for using a biased coin to simulate a fair coin we describe a new generalization of von neumann s algorithm distinguished by its high level of practicality and amenability to analysis in contrast to previous efforts we are able to prove our algorithm optimally efficient in the sense that it simulates the maximum possible number of fair coin flips for a given number of die rolls in fact we are able to prove that in an asymptotic sense our algorithm extracts the full entropy of its input moreover we demonstrate experimentally that our algorithm achieves a high level of computational and output efficiency in a practical setting

how to generate cryptographically strong sequences of pseudo random bits we give a set of conditions that allow one to generate 50 50 unpredictable bits based on those conditions we present a general algorithmic scheme for constructing polynomial time deterministic algorithms that stretch a short secret random input into a long sequence of unpredictable pseudo random bits we give an implementation of our scheme and exhibit a pseudo random bit generator for which any efficient strategy for predicting the next output bit with better than 50 50 chance is easily transformable to an equally efficient algorithm for solving the discrete logarithm problem in particular if the discrete logarithm problem cannot be solved in probabilistic polynomial time no probabilistic polynomial time algorithm can guess the next output bit better than by flipping a coin if head guess 0 if tail guess 1

period of the power generator and small values of carmichael s function consider the pseudorandom number generator u n u e n 1 mod m 0 u n m 1 n 1 2 where we are given the modulus m the initial value u 0 and the exponent e one case of particular interest is when the modulus m is of the form pl where p i are different primes of the same magnitude it is known from work of the first and third authors that for moduli m pl if the period of the sequence u n exceeds m 3 4 e then the sequence is uniformly distributed we show rigorously that for almost all choices of p l it is the case that for almost all choices of e the period of the power generator exceeds pl 1 e and so in this case the power generator is uniformly distributed we also give some other cryptographic applications namely to ruling out the cycling attack on the rsa cryptosystem and to so called time release crypto the principal tool is an estimate related to the carmichael function m the size of the largest cyclic subgroup of the multiplicative group of residues modulo m in particular we show that for any log log n 3 we have m n exp for all integers m with l m n apart from at most n exp 0 69 log 1 3 exceptions

on the implementation of huge random objects we initiate a general study of the feasibility of implementing huge random objects and demonstrate its applicability to a number of areas in which random objects occur naturally we highlight two types of measures of the quality of the implementation with respect to the desired specification the first type corresponds to various standard notions of indistinguishability applied to function ensembles whereas the second type is a novel notion that we call truthfulness intuitively a truthful implementation of a random object of type t must always be an object of type t and not merely be indistinguishable from a random object of type t our formalism allows for the consideration of random objects that satisfy some fixed property or have some fixed structure as well as the consideration of objects supporting complex queries for example we consider the truthful implementation of random hamiltonian graphs as well as supporting complex queries regarding such graphs e g providing the next vertex along a fixed hamiltonian path in such a graph

fail stop signatures fail stop signatures can briefly be characterized as digital signatures that allow the signer to prove that a given forged signature is indeed a forgery after such a proof has been published the system can be stopped this type of security is strictly stronger than that achievable with ordinary digital signatures as introduced by diffie and hellman in 1976 and formally defined by goldwasser micali and rivest in 1988 which was widely regarded as the strongest possible definition this paper formally defines fail stop signatures and shows their relation to ordinary digital signatures a general construction and actual schemes derived from it follow they are efficient enough to be used in practice next we prove lower bounds on the efficiency of any fail stop signature scheme in particular we show that the number of secret random bits needed by the signer the only parameter where the complexity of all our constructions deviates from ordinary digital signatures by more than a small constant factor cannot be reduced significantly

arithmetic cryptography we study the possibility of computing cryptographic primitives in a fully black box arithmetic model over a finite field f in this model the input to a cryptographic primitive e g encryption scheme is given as a sequence of field elements the honest parties are implemented by arithmetic circuits that make only a black box use of the underlying field and the adversary has a full non black box access to the field this model captures many standard information theoretic constructions we prove several positive and negative results in this model for various cryptographic tasks on the positive side we show that under coding related intractability assumptions computational primitives like commitment schemes public key encryption oblivious transfer and general secure two party computation can be implemented in this model on the negative side we prove that garbled circuits additively homomorphic encryption and secure computation with low online complexity cannot be achieved in this model our results reveal a qualitative difference between the standard boolean model and the arithmetic model and explain in retrospect some of the limitations of previous constructions

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

iterative method for constrained and mixed approximation an inexpensive improvement of f e m performance a general iterative procedure for solving mixed lagrangian finite element equations is introduced the method allows a dramatic improvement in accuracy of simple irreducible formulations to be achieved in a few resolutions applications to incompressible flow stress analysis and metal forming problems are given the procedures can be easily implemented into standard programs

accelerated spectral refinement with applications to integral operators accelerated refinement procedures are developed for the resolution of nearly degenerate simple spectra associated with large discrete linear systems error expressions are obtained the spectral analysis of integral operators is discussed and a numerical example of resolving an ill conditioned spectrum is presented

on the distribution of quadratic residues and non residues modulo composite integers and applications to cryptography abstract we develop exact formulas for the distribution of quadratic residues and non residues in sets of the form a x a x mod n x x where n is a prime or the product of two primes and x is a subset of integers with given jacobi symbols modulo prime factors of n we then present applications of these formulas to cocks identity based encryption scheme and statistical indistinguishability

on the distribution of the power generation we present a new method to study the power generator of pseudorandom numbers modulo a blum integer m this includes as special cases the rsa generator and the blum blum shub generator we prove the uniform distribution of these provided that the period t m 3 4 with fixed 0 and under the same condition the uniform distribution of a positive proportion of the leftmost and rightmost bits this sharpens and generalizes previous results which dealt with the rsa generator provided the period t m 23 24 we apply our results to deduce that the period of the binary sequence of the rightmost bit has exponential length

guaranteeing the diversity of number generators a major problem in using iterative number generators of the form xi f xi 1 is that they can enter unexpectedly short cycles this is hard to analyze when the generator is designed hard to detect in real time when the generator is used and can have devastating cryptanalytic implications in this paper we define a measure of security called sequence diversity which generalizes the notion of cycle length for noniterative generators we then introduce the class of counter assisted generators and show how to turn any iterative generator even a bad one designed or seeded by an adversary into a counter assisted generator with a provably high diversity without reducing the quality of generators which are already cryptographically strong 2001 elsevier science

pseudorandom generators hard for k dnf resolution and polynomial calculus resolution a pseudorandom generator gn f0 1g n f0 1g m is hard for a propositional proof system p if roughly speaking p cannot eciently

a pseudorandom generator from any one way function pseudorandom generators are fundamental to many theoretical and applied aspects of computing we show how to construct a pseudorandom generator from any one way function since it is easy to construct a one way function from a pseudorandom generator this result shows that there is a pseudorandom generator if and only if there is a one way function

rsa and rabin functions certain parts are as hard as the whole the rsa and rabin encryption functions e n cdot are respectively defined by raising x in z n to the power e where e is relatively prime to varphi n and squaring modulo n i e e n x x e bmod n e n x x 2 bmod n respectively we prove that for both functions the following problems are computationally equivalent each is probabilistic polynomial time reducible to the other 1 given e n x find x 2 given e n x guess the least significant bit of x with success probability tfrac 1 2 1 operatorname poly n where n is the length of the modulus n this equivalence implies that an adversary given the rsa rabin ciphertext cannot have a non negligible advantage over a random coin flip in guessing the least significant bit of the plaintext unless he can invert rsa factor n the proof techniques also yield the simultaneous security of the log n least significant bits our results improve the efficiency of pseudorandom number generation and

how to sign given any trapdoor permutation a digital signature scheme is presented which is based on the existence of any trapdoor permutation the scheme is secure in the strongest possible natural sense namely it is secure against existential forgery under adaptive chosen message attack

the patch test a condition for assessing fem convergence this paper discusses various forms of the irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency further it is shown that the test can be applied for verification of stability requirements thus providing also a sufficient condition of convergence the patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms

on the notion of infinite pseudorandom sequences abstract three definitions of infinite pseudorandom sequences with respect to polynomial time and space complexity are introduced and compared with each other it is shown that the first two definitions based on martin lof s notion of sequential tests and levin and schnorr s notion of monotonic operator complexity are equivalent with respect to polynomial space complexity while both are strictly stronger than the third definition which is derived from von mises s notion of collectives

accelerated projection methods abstract a new approach to the theory of projection methos is developed in which the objective is determine a projected solution to any desired accuracy for a fixed choice of the projection neither the structure nor the range of the projection is altered to achieve increased accuracy instead an operator equation is derived for the projected solution successive approximations of this equation give rise to a sequence of accelerated projection methods whose solutions converge to the projected solution error expressions are obtained and several numerical examples of solving linear integral equations of the second kind are given

a new approach in non linear mechanics the large time increment method a new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non linearities and is tested on some examples in elastoplasticity the method considerably reduces the number of transfers between local and global levels hence the numerical cost of calculation is also diminished