two proofs of pinsker s conjecture concerning arbitrarily varying channels m s pinsker 1990 conjectured the following theorem for an arbitrary varying channel avc every rate below the random code capacity is achievable with deterministic list codes of constant list size if the average error criterion is used two proofs of this theorem are given

a joint shannon cipher and privacy amplification approach to attaining exponentially decaying information leakage in this paper we propose a novel layering approach to achieve end to end exponential security without resorting to presumed physical layer conditions the only requirement for such an exponentially secure system is existence of a common key source between legitimate users that is partially known by eve the novel framework includes a random cipher and key stream generating scheme constituting the first layer and universal hash forming the second layer the key generating scheme is based on a novel definition of a randomness extractor that derives a key stream with the required entropy from the common source to be used for cipher all metrics involved in characterizing the quality of secrecy of two layer components are related to renyi entropy and conditional renyi entropy which are all ultimately captured in the adopted information leakage metrics mutual information and eve s distinguishability based on l1 norm distance from uniformity such relationships are exploited to optimize the resulting bounds for secrecy exponents by selecting appropriate operating parameters including required key rate and source entropies as well as the required guessing error rate by eve to attack the first layer

common randomness in information theory and cryptography i secret sharing as the first part of a study of problems involving common randomness at distance locations information theoretic models of secret sharing generating a common random key at two terminals without letting an eavesdropper obtain information about this key are considered the concept of key capacity is defined single letter formulas of key capacity are obtained for several models and bounds to key capacity are derived for other models

towards a matrix theory for unbounded operator matrices sur l espace produit r l 2 r on considere l operateur 7b a a 0 ou d d dx est defini sur d a w 1 r 0 est la mesure de dirac en 0 c l 2 r est un operateur de r dans l 2 r et 7b a a un domaine d 7b a r w 1 r on introduit une fonction caracteristique non commutative donnant une facon efficace pour calculer le spectre de 7b a on obtient des resultats sur la generation de semi groupes par des matrices operateur

criteria for quasi convexity and pseudo convexity relationships and comparisons a first order criterion for pseudo convexity and second order criteria for quasi convexity and pseudo convexity are given for twice differentiable functions on open convex sets the relationships between these second order criteria and other known criteria are also analysed finally the numbers of operations required to verify these criteria are calculated and compared

secret key and private key constructions for simple multiterminal source models we propose an approach for constructing secret and private keys based on the long known slepian wolf code due to wyner for correlated sources connected by a virtual additive noise channel our work is motivated by results of csiszar and narayan which highlight innate connections between secrecy generation by multiple terminals that observe correlated source signals and slepian wolf near lossless data compression explicit procedures for such constructions and their substantiation are provided the performance of low density parity check channel codes in devising a new class of secret keys is examined

brief stability of extremum seeking feedback for general nonlinear dynamic systems while the mainstream methods of adaptive control both linear and nonlinear deal only with regulation to known set points or reference trajectories in many applications the set point should be selected to achieve a maximum of an uncertain reference to output equilibrium map the techniques of the so called extremum control or self optimizing control developed for this problem in the 1950 1960s have long gone out of fashion in the theoretical control literature because of the difficulties that arise in a rigorous analytical treatment in this paper we provide the first proof of stability of an extremum seeking feedback scheme by employing the tools of averaging and singular perturbation analysis our scheme is much more general that the existing extremum control results which represent the plant as a static nonlinear map possibly cascaded with a linear dynamic block we allow the plant to be a general nonlinear dynamic system possibly non affine in control and open loop unstable whose reference to output equilibrium map has a maximum and whose equilibria are locally exponentially stabilizable

uniform random number generation from markov chains non asymptotic and asymptotic analyses in this paper we derive non asymptotic achievability and converse bounds on the random number generation with without side information our bounds are efficiently computable in the sense that the computational complexity does not depend on the block length we also characterize the asymptotic behaviors of the large deviation regime and the moderate deviation regime by using our bounds which implies that our bounds are asymptotically tight in those regimes we also show the second order rates of those problems and derive single letter forms of the variances characterizing the second order rates furthermore we address the relative entropy rate and the modified mutual information rate for these problems

communication with imperfectly shared randomness communication complexity investigates the amount of communication needed for two or more players to determine some joint function of their private inputs for many interesting functions the communication complexity can be much smaller than basic information theoretic measures associated with the players inputs such as the input length the entropy or even the conditional entropy communication complexity of many functions reduces further when the players share randomness classical works studied the communication complexity of functions when the interacting players share randomness perfectly i e they get identical copies of randomness from a common source this paper considers the variant of this question when the players share randomness imperfectly i e when they get noisy copies of the randomness produced by some common source our main result shows that any function that can be computed by a k bit protocol in the perfect sharing model has a 2 k bit protocol in the setting of imperfectly shared randomness and such an exponential growth is necessary our upper bound relies on ideas from locality sensitive hashing while lower bounds rely on hypercontractivity and a new invariance principle tailored for communication protocols

arbitrarily small amounts of correlation for arbitrarily varying quantum channels as our main result show that in order to achieve the randomness assisted message and entanglement transmission capacities of a finite arbitrarily varying quantum channel it is not necessary that sender and receiver share asymptotically perfect common randomness rather it is sufficient that they each have access to an unlimited amount of uses of one part of a correlated bipartite source this access might be restricted to an arbitrary small nonzero fraction per channel use without changing the main result we investigate the notion of common randomness it turns out that this is a very costly resource generically it cannot be obtained just by local processing of a bipartite source this result underlines the importance of our main result also the asymptotic equivalence of the maximal and average error criterion for classical message transmission over finite arbitrarily varying quantum channels is proven at last we prove a simplified symmetrizability condition for finite arbitrarily varying quantum channels

multivariable extremum seeking for pde dynamic systems in this article we address the design and analysis of multivariable newton based extremum seeking es for static locally quadratic maps subject to actuation dynamics governed by diffusion partial differential equations pdes multi input systems with distinct diffusion coefficients in each individual input channel are dealt with the phase compensation of the dither signals is handled as a trajectory generation problem and the inclusion of a multivariable diffusion feedback controller with a perturbation based averaging based estimate of the hessian s inverse allow to obtain local exponential convergence results to a small neighborhood of the optimal point the stability analysis is carried out using backstepping transformation and averaging in infinite dimensions capturing the infinite dimensional state due the diffusion pdes in addition the generalization of the results for different classes of parabolic reaction advection diffusion pdes wave equations and or first order hyperbolic transport dominated pdes is also discussed as for ordinary differential equations case the proposed newton approach removes the dependence of the algorithm s convergence rate on the unknown hessian of the nonlinear map to be optimized being user assignable unlike the gradient algorithm a numerical example illustrates the performance of our multivariable es for compensating pde based systems

security analysis of varepsilon almost dual universal 2 hash functions smoothing of min entropy versus smoothing of renyi entropy of order 2 recently varepsilon almost dual universal2 hash functions have been proposed as a new and wider class of hash functions using this class of hash functions several efficient hash functions were proposed this paper evaluates the security performance when we apply this kind of hash functions we evaluate the security in several kinds of setting based on the l 1 distinguishability criterion and the modified mutual information criterion the obtained evaluation is based on smoothing of renyi entropy of order 2 and or min entropy we clarify the difference between these two methods

the method of types information theory the method of types is one of the key technical tools in shannon theory and this tool is valuable also in other fields in this paper some key applications are presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method and a wide selection of further applications are surveyed these range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems while the method of types is suitable primarily for discrete memoryless models its extensions to certain models with memory are also discussed

on the ergodic secret key agreement over spatially correlated multiple antenna channels with public discussion we consider secret key agreement with public discussion over multiple input multiple output mimo rayleigh fast fading channels under correlated environment we assume that transmit legitimate receiver and eavesdropper antennas are correlated the legitimate receiver and the eavesdropper are assumed to have perfect channel knowledge while the transmitter has only knowledge of the correlation matrices first we derive the expression of the secret key capacity under the considered setup we prove that the optimal transmit strategy achieving the secret key capacity consists in transmitting independent gaussian signals along the eingenvectors of the transmit correlation matrix the powers allocated to each channel mode are determined as the solution to a numerical optimization problem a necessary and sufficient condition for beamforming i e transmitting along the strongest channel mode to be capacity achieving is derived moreover we analyze the impact of correlation matrices on the system performance finally we study the system s performance in the two extreme power regimes in the high power regime we provide closed form expressions of the gain loss due to correlation in the low signal to noise ratio snr regime we investigate the energy efficiency of the system by determining the minimum energy required for sharing a secret key bit and the wideband slope while highlighting the impact of correlation matrices

the common randomness capacity of a pair of independent discrete memoryless channels we study the following problem two agents alice and bob are connected to each other by independent discrete memoryless channels they wish to generate common randomness i e agree on a common random variable by communicating interactively over the two channels assuming that alice and bob are allowed access to independent external random sources at rates in bits per step of communication of h sub a and h sub b respectively we show that they can generate common randomness at a rate of max min h sub a h w q i p v min h sub b h v p i q w bits per step by exploiting the noise on the two channels here v is the channel from alice to bob and w is the channel from bob to alice the maximum is over all probability distributions p and q on the input alphabets of v and w respectively we also prove a strong converse which establishes the above rate as the highest attainable in this situation

large deviation analysis for quantum security via smoothing of renyi entropy of order 2 it is known that the security evaluation can be done by smoothing of renyi entropy of order 2 in the classical and quantum settings when we apply universal 2 hash functions using the smoothing of renyi entropy of order 2 we derive security bounds for l 1 distinguishability and modified mutual information criterion under the classical and quantum setting and have derived these exponential decreasing rates these results are extended to the case when we apply e almost dual universal 2 hash functions furthermore we apply this analysis to the secret key generation with error correction

applications of ldpc codes to the wiretap channel with the advent of quantum key distribution qkd systems perfect i e information theoretic security can now be achieved for distribution of a cryptographic key qkd systems and similar protocols use classical error correcting codes for both error correction for the honest parties to correct errors and privacy amplification to make an eavesdropper fully ignorant from a coding perspective a good model that corresponds to such a setting is the wire tap channel introduced by wyner in 1975 in this correspondence we study fundamental limits and coding methods for wire tap channels we provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel we also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes in some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity for the special case of a noiseless main channel and binary erasure channel we consider encoder and decoder design for codes achieving secrecy on the wiretap channel we show that it is possible to construct linear time decodable secrecy codes based on low density parity check ldpc codes that achieve secrecy

multivariable newton based extremum seeking we present a newton based extremum seeking algorithm for the multivariable case the design extends the recent newton based extremum seeking algorithms for the scalar case and introduces a dynamic estimator of the inverse of the hessian matrix that removes the difficulty with the possible singularity of a possible direct estimate of the hessian matrix the estimator of the inverse of the hessian has the form of a differential riccati equation we prove local stability of the new algorithm for general nonlinear dynamic systems using averaging and singular perturbations in comparison with the standard gradient based multivariable extremum seeking the proposed algorithm removes the dependence of the convergence rate on the unknown hessian matrix and makes the convergence rate of both the parameter estimates and of the estimates of the hessian inverse user assignable in particular the new algorithm allows all the parameters to converge with the same speed yielding straight trajectories to the extremum even with maps that have highly elongated level sets in contrast to curved steepest descent trajectories of the gradient algorithm simulation results show the advantage of the proposed approach over gradient based extremum seeking by assigning equal desired convergence rates to all the parameters using newton s approach

feedback based collaborative secrecy encoding over binary symmetric channels in this paper we propose a feedback scheme for transmitting secret messages between two legitimate parties over an eavesdropped communication link relative to wyner s traditional encoding scheme our feedback based encoding often yields larger rate equivocation regions and achievable secrecy rates more importantly by exploiting the channel randomness inherent in the feedback channels our scheme achieves a strictly positive secrecy rate even when the eavesdropper s channel is less noisy than the legitimate receiver s channel all channels are modeled as binary and symmetric we demonstrate the versatility of our feedback based encoding method by using it in three different configurations the stand alone configuration the mixed configuration when it combines with wyner s scheme and the reversed configuration depending on the channel conditions significant improvements over wyner s secrecy capacity can be observed in all configurations

compensating actuator and sensor dynamics governed by diffusion pdes for possibly unstable ode systems with actuator delay predictor based infinite dimensional feedback can compensate for actuator delay of arbitrary length and achieve stabilization we extend this concept to another class of pde ode cascades where the infinite dimensional part of the plant is of diffusive rather than convective type we derive predictor like feedback laws and observers with explicit gain kernels the gain kernels involve second order matrix exponentials of the system matrix of the ode plant which is the result of the second order in space character of the actuator sensor dynamics the construction of the kernel functions is performed using the continuum version of the backstepping method robustness to small perturbations in the diffusion coefficient is proved

information theoretic key agreement of multiple terminals part i we study the problem of information theoretically secure secret key agreement under the well known source model and channel model in both of these models multiple terminals wish to create a shared secret key that is secure from a passive eavesdropper the terminals have access to a noiseless public communication channel and an additional resource that depends on the model in the source model the resource is an external source that repeatedly beams correlated randomness to the terminals whereas in the channel model the resource is a secure but noisy discrete memoryless broadcast channel we derive new lower and upper bounds on the secret key capacity under both the source model and the channel model the technique used for deriving our bound for the source model is to find certain properties of functions of joint probability distributions which applied to the joint distribution of the source will imply that they dominate the secret key capacity and then prove the bound by a verification argument a similar technique is used for the channel model finally we also define a problem of communication for omniscience by a neutral observer and establish the equivalence between this new problem and the problem of secret key agreement this generalizes an earlier result of csiszar and narayan

rate distortion theory for secrecy systems secrecy in communication systems is measured herein by the distortion that an adversary incurs the transmitter and receiver share secret key which they use to encrypt communication and ensure distortion at an adversary a model is considered in which an adversary not only intercepts the communication from the transmitter to the receiver but also potentially has side information in particular the adversary may have causal or noncausal access to a signal that is correlated with the source sequence or the receiver s reconstruction sequence the main contribution is the characterization of the optimal tradeoff among communication rate secret key rate distortion at the adversary and distortion at the legitimate receiver it is demonstrated that causal side information at the adversary plays a pivotal role in this tradeoff it is also shown that measures of secrecy based on normalized equivocation are a special case of the framework

secret key generation with limited interaction a basic two terminal secret key generation model is considered where the interactive communication rate between the terminals may be limited and in particular may not be enough to achieve the maximum key rate we first prove a multi letter characterization of the key communication rate region where the number of auxiliary random variables depends on the number of rounds of the communication and then provide an equivalent but simpler characterization in terms of concave envelopes in the case of unlimited number of rounds two extreme cases are given special attention first in the regime of very low communication rates the key bits per interaction bit kbib is expressed with a new symmetric strong data processing constant which has a concave envelope characterization analogous to that of the conventional strong data processing constant the symmetric strong data processing constant can be upper bounded by the supremum of the maximal correlation coefficient over a set of distributions which allows us to determine the kbib for binary symmetric sources and conclude in particular that the interactive scheme is not more efficient than the one way scheme at least in the low communication rate regime second a new characterization of the minimum interaction rate needed for achieving the maximum key rate mimk is given and we resolve a conjecture by tyagi regarding the mimk for possibly nonsymmetric binary sources we also propose a new conjecture for binary symmetric sources that the interactive scheme is not more efficient than the one way scheme at any communication rate

a lossy source coding interpretation of wyner s common information wyner s common information was originally defined for a pair of dependent discrete random variables its significance is largely reflected in and also confined to several existing interpretations in various source coding problems this paper attempts to expand its practical significance by providing a new operational interpretation in the context of the gray wyner network it is established that wyner s common information has a new lossy source coding interpretation specifically it is established that under suitable conditions wyner s common information equals to the smallest common message rate when the total rate is arbitrarily close to the rate distortion function with joint decoding for the gray wyner network a surprising observation is that such equality holds independent of the values of distortion constraints as long as the distortions are within some distortion region the new lossy source coding interpretation provides the first meaningful justification for defining wyner s common information for continuous random variables and the result can also be extended to that of multiple variables examples are given for characterizing the rate distortion region for the gray wyner lossy source coding problem and for identifying conditions under which wyner s common information equals that of the smallest common rate as a by product the explicit expression for the common information between a pair of gaussian random variables is obtained

a novel secret image sharing scheme in color images using small shadow images over the past several years secret image sharing techniques have become another branch of the effort to prevent secret images from being eavesdropped on in addition to traditional cryptography because smaller shadows can speed up the transmission of a secret color image in this paper we combine chang and wu s gradual search algorithm for a single bitmap btc gsbtc and shamir s k n threshold concept to propose a novel secret color image sharing scheme that generates smaller shadows experimental results confirm that the proposed scheme successfully reduces shadow size and that each shadow behaves as a random like image that prevents leakage of information about the secret color image furthermore the correlation between two vertically or horizontally adjacent pixels in each shadow is significantly less than those in a color secret image and the presented scheme also achieves on average an npcr 0 414 and auci 32 78 thus with our scheme one pixel difference could cause a significant difference in the corresponding shadows therefore the security of the presented scheme is also confirmed

change of multivariate mutual information from local to global we study the change of multivariate mutual information among a set of random variables when some common randomness is added to or removed from a subset of the random variables this is formulated more precisely as two new multiterminal secret key agreement problems that respectively ask how one can increase the secrecy capacity efficiently by adding common randomness to a small subset of users and how one can simplify the source model by removing redundant common randomness that does not contribute to the secrecy capacity characterizations and strongly polynomial time computations are derived for the rates of change maximum usable increment and redundancy these results can be applied to study the communication complexity for secret key agreement

the common randomness capacity of a network of discrete memoryless channels we generalize our previous results on generating common randomness at two terminals to a situation where any finite number of agents interconnected by an arbitrary network of independent point to point discrete memoryless channels wish to generate common randomness by interactive communication over the network our main result is an exact characterization of the common randomness capacity of such a network i e the maximum number of bits of randomness that all the agents can agree on per step of communication as a by product we also obtain a purely combinatorial result viz a characterization of the incidence vectors of the spanning arborescences rooted at a specified vertex in a digraph and having exactly one edge exiting the root as precisely the extreme points of a certain unbounded convex polyhedron described by a system of linear inequalities

common randomness in information theory and cryptography ii cr capacity for pt i see ibid vol 39 p 1121 1993 the common randomness cr capacity of a two terminal model is defined as the maximum rate of common randomness that the terminals can generate using resources specified by the given model we determine cr capacity for several models including those whose statistics depend on unknown parameters the cr capacity is shown to be achievable robustly by common randomness of nearly uniform distribution no matter what the unknown parameters are our cr capacity results are relevant for the problem of identification capacity and also yield a new result on the regular transmission capacity of arbitrarily varying channels with feedback

distillation of secret key and entanglement from quantum states we study and solve the problem of distilling a secret key from quantum states representing correlation between two parties alice and bob and an eavesdropper eve via oneway public discussion we

extremum seeking for static maps with delays in this paper we address the design and analysis of multi variable extremum seeking for static maps subject to arbitrarily long time delays both gradient and newton based methods are considered multi input systems with different time delays in each individual input channel as well as output delays are dealt with the phase compensation of the dither signals and the inclusion of predictor feedback with a perturbation based averaging based estimate of the hessian allow to obtain local exponential convergence results to a small neighborhood of the optimal point even in the presence of delays the stability analysis is carried out using backstepping transformation and averaging in infinite dimensions capturing the infinite dimensional state due the time delay in particular a new backstepping like transformation is introduced to design the predictor for the gradient based extremum seeking scheme with multiple and distinct input delays the proposed newton based extremum seeking approach removes the dependence of the convergence rate on the unknown hessian of the nonlinear map to be optimized being user assignable as in the literature free of delays a source seeking example illustrates the performance of the proposed delay compensated extremum seeking schemes

perfect omniscience perfect secrecy and steiner tree packing we consider perfect secret key generation for a pairwise independent network model in which every pair of terminals share a random binary string with the strings shared by distinct terminal pairs being mutually independent the terminals are then allowed to communicate interactively over a public noiseless channel of unlimited capacity all the terminals as well as an eavesdropper observe this communication the objective is to generate a perfect secret key shared by a given set of terminals at the largest rate possible and concealed from the eavesdropper first we show how the notion of perfect omniscience plays a central role in characterizing perfect secret key capacity second a multigraph representation of the underlying secrecy model leads us to an efficient algorithm for perfect secret key generation based on maximal steiner tree packing this algorithm attains capacity when all the terminals seek to share a key and in general attains at least half the capacity third when a single helper terminal assists the remaining user terminals in generating a perfect secret key we give necessary and sufficient conditions for the optimality of the algorithm also a weak helper is shown to be sufficient for optimality

the capacity of the arbitrarily varying channel revisited positivity constraints a well known result of r ahlswede 1970 asserts that the deterministic code capacity of an arbitrarily varying channel avc under the average error probability criterion either equals its random code capacity or else is zero a necessary and sufficient condition is identified for deciding between these alternative namely the capacity is zero if and only if the avc is symmetrizable the capacity of the avc is determined with constraints on the transmitted codewords as well as on the channel state sequences and it is demonstrated that it may be positive but less than the corresponding random code capacity a special case of the results resolves a weakened version of a fundamental problem of coding theory

brief adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties we pose and solve an extremum seeking control problem for a class of nonlinear systems with unknown parameters extremum seeking controllers are developed to drive system states to the desired set points that extremize the value of an objective function the proposed adaptive extremum seeking controller is inverse optimal in the sense that it minimizes a meaningful cost function that incorporates penalty on both the performance error and control action simulation studies are provided to verify the effectiveness of the proposed approach

entropy analysis and new constructions of biometric key generation systems in this paper a new soft two level approach for the generation of multiple and revocable biometric keys adapted to the analog nature of biometric signals is proposed it consists of a novel randomized soft code offset construction for the euclidean metric at the first level and a code redundancy construction for the hamming metric possibly based on a reed solomon code at the second level the shannon entropy analysis shows that the new construction achieves optimal security with respect to biometric template protection whereas the previously proposed constructions for the euclidean metric are shown to be insecure in the multiple key setting in addition a general code offset construction for the hamming metric is analyzed in terms of the shannon entropy instead of the usual min entropy this allows a nice characterization of the codes that provide biometric template protection in the multiple key scenario as well as a further differentiation among these codes with respect to the achievable security level

secret key agreement over non coherent block fading channels with public discussion motivated by recent interest in physical layer secret key generation over wireless fading channels we study the non coherent secret key generation capacity of a block fading wireless channel with channel reciprocity and bi directional two way communication we assume a non coherent main channel i e the realization of channel gains on the main channel is not known to any terminal the eavesdropper is assumed to have both perfect channel state information of its own channel and orthogonal observations from the forward and backward channels as our main result we establish new upper and lower bounds on the secret key generation capacity with public discussion which are structurally similar the upper bound can be expressed as a sum of three terms one of the terms arises due to channel reciprocity while the other two terms correspond to communication on the forward and backward channels respectively in the limit of long coherence period the contribution from channel reciprocity vanishes to zero whereas the other terms prevail the lower bound is based on a separation based scheme in each coherence block we use the first symbol for training while the remainder of the coherence block is devoted to source emulation i e to generate correlated sources between the terminals the lower bound expression also consists of three terms and admits an interpretation similar to the upper bound expression for rayleigh fading channels in the high signal to noise ratio snr regime the gap between the upper and lower bounds is shown to vanish inversely with the coherence period numerical results indicate significant performance gains over training only schemes even for moderate values of snr and small coherence periods

on non local stability properties of extremum seeking control in this paper we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted this non local stability result is proved by showing semi global practical stability of the closed loop system with respect to the design parameters we show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking simulation examples illustrate our results

the commitment capacity of the gaussian channel is infinite we prove that the commitment capacity of the power constrained gaussian channel i e the optimal rate at which this channel can be used for implementing commitment schemes is infinite

tight exponential analysis of universally composable privacy amplification and its applications motivated by the desirability of universal composability we analyze in terms of l1 distinguishability the task of secret key generation from a joint random variable under this secrecy criterion using the renyi entropy of order 1 s for s 0 1 we derive a new upper bound of eve s distinguishability under the application of the universal2 hash functions it is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions the result is applied to the wiretap channel model and to secret key generation distillation by public discussion

secret key generation for correlated gaussian sources secret key generation by multiple terminals is considered based on their observations of jointly distributed gaussian signals followed by public communication among themselves exploiting an inherent connection between secrecy generation and lossy data compression two main contributions are made the first is a characterization of strong secret key capacity and entails a converse proof technique that is valid for real valued and not necessarily gaussian as well as finite valued signals the capacity formula acquires a simple form when the terminals observe symmetrically correlated jointly gaussian signals for the latter setup with two terminals considering schemes that involve quantization at one terminal the best rate of an achievable secret key is characterized as a function of quantization rate secret key capacity is attained as the quantization rate tends to infinity structured codes are shown to attain the optimum tradeoff between secret key rate and quantization rate constituting our second main contribution

the conditional common information in classical and quantum secret key distillation in this paper we consider two extensions of the gacs korner common information to three variables the conditional common information cci and the coarse grained conditional common information ccci both quantities are shown to be useful technical tools in the study of classical and quantum resource transformations in particular the ccci is shown to have an operational interpretation as the optimal rate of secret key extraction from an eavesdropped classical source p xyz when alice x and bob y are unable to communicate but share common randomness with the eavesdropper eve z moving to the quantum setting we consider two different ways of generating a tripartite quantum state from classical correlations p xyz 1 coherent encodings sum xyz sqrt p xyz xyz rangle and 2 incoherent encodings sum xyz p xyz xyz rangle langle xyz we study how well can alice and bob extract secret key from these quantum sources using quantum operations compared with the extraction of key from the underlying classical sources p xyz using classical operations while the power of quantum mechanics increases alice and bob s ability to generate shared randomness it also equips eve with a greater arsenal of eavesdropping attacks therefore it is not obvious who gains the greatest advantage for distilling secret key when replacing a classical source with a quantum one we first demonstrate that the classical key rate of p xyz is equivalent to the quantum key rate for an incoherent quantum encoding of the distribution for coherent encodings we next show that the classical and quantum rates are generally incomparable and in fact their difference can be arbitrarily large in either direction finally we introduce a zoo of entangled tripartite states all characterized by the conditional common information of their encoded probability distributions remarkably for these states almost all entanglement measures such as alice and bob s entanglement cost squashed entanglement and relative entropy of entanglement can be sharply bounded or even exactly expressed in terms of the conditional common information in the latter case we thus present a rare instance in which the various entropic entanglement measures of a quantum state can be explicitly calculated

a large deviations approach to secure lossy compression a shannon cipher system for memoryless sources in which distortion is allowed at the legitimate decoder is considered the source is compressed using a secured rate distortion code which satisfies a constraint on the compression rate as well as a constraint on the exponential rate of the excess distortion probability at the legitimate decoder secrecy is measured by the exponential rate of the exiguous distortion probability at the eavesdropper rather than by the traditional measure of equivocation the perfect secrecy exponent is defined as the maximal exiguous distortion exponent achievable when the key rate is unlimited the reproduction based estimate exponent is defined as the maximal exiguous distortion exponent achievable for a genie aided eavesdropper which knows the secret key under limited key rate it is proved that the maximal achievable exiguous distortion exponent is equal to the minimum between the key rate plus the reproduction based estimate exponent and the perfect secrecy exponent the result is generalized to a fairly general class of variable key rate and coding rate codes

strong secrecy from channel resolvability we analyze physical layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability instead of considering capacity based constructions which associate to each message a subcode that operates just below the capacity of the eavesdropper s channel we consider channel resolvability based constructions which associate to each message a subcode that operates just above the resolvability of the eavesdropper s channel building upon the work of csiszar and hayashi we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels specifically we show that at least for symmetric wiretap channels random capacity based constructions fail to achieve the strong secrecy capacity while channel resolvability based constructions achieve it we then leverage channel resolvability to establish the secrecy capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics finally we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information csi mixed channels and compound channels with receiver csi as well as the secret key capacity of source models for secret key agreement by tying secrecy to channel resolvability we obtain achievable rates for strong secrecy metrics with simple proofs

equivocations exponents and second order coding rates under various renyi information measures we evaluate the asymptotics of equivocations their exponents as well as their second order coding rates under various renyi information measures specifically we consider the effect of applying a hash function on a source and we quantify the level of non uniformity and dependence of the compressed source from another correlated source when the number of copies of the sources is large unlike previous works that use shannon information measures to quantify randomness information or uniformity we define our security measures in terms of a more general class of information measures the renyi information measures and their gallager type counterparts a special case of these renyi information measure is the class of shannon information measures we prove tight asymptotic results for the security measures and their exponential rates of decay we also prove bounds on the second order asymptotics and show that these bounds match when the magnitudes of the second order coding rates are large we do so by establishing new classes non asymptotic bounds on the equivocation and evaluating these bounds using various probabilistic limit theorems asymptotically

correlated sources help transmission over an arbitrarily varying channel it is well known that the deterministic code capacity for the average error probability criterion of an arbitrarily varying channel avc either equals its random code capacity or zero here it is shown that if two components of a correlated source are additionally available to the sender and receiver respectively the capacity always equals its random code capacity

rateless codes for avc models the arbitrarily varying channel avc is a channel model whose state is selected maliciously by an adversary fixed blocklength coding assumes a worst case bound on the adversary s capabilities which leads to pessimistic results this paper defines a variable length perspective on this problem for which achievable rates are shown that depend on the realized actions of the adversary specifically rateless codes are constructed which require a limited amount of common randomness these codes are constructed for two kinds of avc models in the first the channel state cannot depend on the channel input and in the second it can as a by product the randomized coding capacity of the avc with state depending on the transmitted codeword is found and shown to be achievable with a small amount of common randomness the results for this model are proved using a randomized strategy based on list decoding

on extracting common random bits from correlated sources suppose alice and bob receive strings of unbiased independent but noisy bits from some random source they wish to use their respective strings to extract a common sequence of random bits with high probability but without communicating how many such bits can they extract the trivial strategy of outputting the first k bits yields an agreement probability of 1 e k 2 1 44ke where e is the amount of noise we show that no strategy can achieve agreement probability better than 2 ke 1 e on the other hand we show that when k 10 2 1 e e there exists a strategy which achieves an agreement probability of 0 003 ke 1 2 2 ke 1 e

identification via channels the authors main finding is that any object among doubly exponentially many objects can be identified in blocklength n with arbitrarily small error probability via a discrete memoryless channel dmc if randomization can be used for the encoding procedure a novel doubly exponential coding theorem is presented which determines the optimal r that is the identification capacity of the dmc as a function of its transmission probability matrix this identification capacity is a well known quantity namely shannon s transmission capacity for the dmc

randomness and dependencies extraction via polarization with applications to slepian wolf coding and secrecy the polarization phenomenon for a single source is extended to a framework with multiple correlated sources it is shown in addition to extracting the randomness of the source the polar transforms take the original arbitrary dependencies to extremal dependencies polar coding schemes for the slepian wolf sw coding problem and for secret key generations are then proposed based on this phenomenon in particular secret keys achieving the secrecy capacity and compression schemes achieving the sw capacity region are obtained with a complexity of o n log n

list decoding for the arbitrarily varying channel under state constraints list decoding for arbitrarily varying channels avcs under state constraints is investigated it is shown that rates within of the randomized coding capacity of avcs with input dependent state can be achieved under maximal error with list decoding using lists of size o 1 under the average error criterion an achievable rate and converse bound are given for lists of size l these bounds are based on two different notions of symmetrizability and do not coincide in general an example is given which shows that for list size l the capacity may be positive but strictly smaller than the randomized coding capacity in contrast to the situation without constraints

a framework for extremum seeking control of systems with parameter uncertainties traditionally the design of extremum seeking algorithm treats the system as essentially a black box which for many applications means disregarding known information about the model structure in contrast to this approach there have been recent examples where a known plant structure with uncertain parameters has been used in the online optimization of plant operation however the results for these approaches have been restricted to specific classes of plants and optimization algorithms this paper seeks to provide general results and a framework for the design of extremum seekers applied to systems with parameter uncertainties general conditions for an optimization method and a parameter estimator are presented so that their combination guarantees convergence of the extremum seeker for both static and dynamic plants tuning guidelines for the closed loop scheme are also presented the generality and flexibility of the proposed framework is demonstrated through a number of parameter estimators and optimization algorithms that can be combined to obtain extremum seeking examples of anti lock braking and model reference adaptive control are used to illustrate the effectiveness of the proposed framework

stochastic averaging in discrete time and its applications to extremum seeking we investigate stochastic averaging theory for locally lipschitz discrete time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete time stochastic extremum seeking algorithms firstly by defining two average systems one is continuous time the other is discrete time we develop discrete time stochastic averaging theorem for locally lipschitz nonlinear systems with stochastic perturbation our results only need some simple and applicable conditions which are easy to verify and remove a significant restriction present in existing results global lipschitzness of the nonlinear vector field secondly we provide a discrete time stochastic extremum seeking algorithm for a static map in which measurement noise is considered and an ergodic discrete time stochastic process is used as the excitation signal finally for discrete time nonlinear dynamical systems in which the output equilibrium map has an extremum we present a discrete time stochastic extremum seeking scheme and with a singular perturbation reduction we prove the stability of the reduced system compared with classical stochastic approximation methods while the convergence that we prove is in a weaker sense the conditions of the algorithm are easy to verify and no requirements e g boundedness are imposed on the algorithm itself

secret key agreement over unauthenticated public channels part ii the simulatability condition for pt i see ibid vol 49 no 4 p 822 31 2003 in the first part we showed that when two parties willing to generate a secret key but connected only by a completely insecure communication channel have access to independent repetitions of some random experiment then the possibility of secret key agreement depends on a certain property called simulatability of the probability distribution modeling the parties initial knowledge more generally the simulatability condition is important in the context of identification and authentication among parties sharing some correlated but not necessarily identical partially secret keys unfortunately this condition is a priori not very useful since it is not clear how to decide efficiently whether it is satisfied or not for a given distribution p sub xyz we introduce a new formalism based on a mechanical model for representing the involved quantities that allows for dealing with discrete joint distributions of random variables and their manipulations by noisy channels we show that this representation leads to a simple and efficient characterization of the possibility of secret key agreement secure against active adversaries

exact random coding secrecy exponents for the wiretap channel we analyze the exact exponential decay rate of the expected amount of information leaked to the wiretapper in wyner s wiretap channel setting using wiretap channel codes constructed from both i i d and constant composition random codes our analysis for those sampled from i i d random coding ensemble shows that the previously known achievable secrecy exponent using this ensemble is indeed the exact exponent for an average code in the ensemble furthermore our analysis on wiretap channel codes constructed from the ensemble of constant composition random codes leads to an exponent which in addition to being the exact exponent for an average code is larger than the achievable secrecy exponent that has been established so far in the literature for this ensemble which in turn was known to be smaller than that achievable by wiretap channel codes sampled from i i d random coding ensemble we show examples where the exact secrecy exponent for the wiretap channel codes constructed from random constant composition codes is larger than that of those constructed from i i d random codes and examples where the exact secrecy exponent for the wiretap channel codes constructed from i i d random codes is larger than that of those constructed from constant composition random codes we hence conclude that unlike the error correction problem there is no general ordering between the two random coding ensembles in terms of their secrecy exponent

communication in key distribution schemes a g b key distribution scheme allows conferences of g users to generate secret keys such that disjoint coalitions of b users cannot gain any information on the generated key in the information theoretic sense we study the relationships between communication and space efficiency of key distribution schemes we prove that communication does not help in the context of unrestricted schemes on the other hand we show that for restricted schemes which are secure only when used by a limited number of conferences communication can substantially improve the space efficiency we also present lower bounds on the space efficiency of restricted schemes

key generation algorithms for pairwise independent networks based on graphical models we consider two secret key generation problems under a pairwise independent network model and propose low complexity key generation schemes in a framework that connects our problems to network flow problems in graphs our schemes have two components 1 local key generation and 2 global key propagation in the local key generation we use point to point source coding with side information to establish pairwise keys from which we construct a graph with the capacity of each edge being the key rate of the corresponding point to point local key in the global key propagation depending on the particular problem secret keys are delivered to users in the network using various network flow algorithms in particular in the first problem in which one is required to generate a group key for a group of users in the network we propose a network coding based global key propagation approach this approach has a low complexity and has a better performance than the existing approach in the second problem in which one is required to generate multiple keys simultaneously for different pairs of users we propose a multicommodity flow based global key propagation approach we show that the proposed approach is optimal for the case of generating two keys for the general case of generating more than two keys we show that the sum rate of the proposed scheme is larger than an upper bound characterized in this paper divided by a constant

coding theorems for a 2 2 threshold scheme with detectability of impersonation attacks coding theorems on a 2 2 threshold scheme with an opponent are discussed in an asymptotic setup where the opponent tries to impersonate one of the two participants a situation is considered where n secrets s n from a memoryless source is blockwisely encoded to two shares and the two shares are decoded to s n with permitting negligible decoding error we introduce correlation level of the two shares and characterize the minimum attainable rates of the shares and a uniform random number for realizing a 2 2 threshold scheme that is secure against the impersonation attack by the opponent it is shown that if the correlation level between the two shares equals to ell geq 0 the minimum attainable rates coincide with h s ell where h s denotes the entropy of the source and the maximum attainable exponent of the success probability of the impersonation attack equals to ell it is also shown that a simple scheme using an ordinary 2 2 threshold scheme attains all the bounds as well

how many queries will resolve common randomness a set of m terminals observing correlated signals communicate interactively to generate common randomness for a given subset of them knowing only the communication how many direct queries of the value of the common randomness will resolve it a general upper bound valid for arbitrary signal alphabets is developed for the number of such queries by using a query strategy that applies to all common randomness and associated communication when the underlying signals are independent and identically distributed repetitions of m correlated random variables the number of queries can be exponential in signal length for this case the mentioned upper bound is tight and leads to a single letter formula for the largest query exponent which coincides with the secret key capacity of a corresponding multiterminal source model in fact the upper bound constitutes a strong converse for the optimum query exponent and implies also a new strong converse for secret key capacity a key tool estimating the size of a large probability set in terms of renyi entropy is interpreted separately too as a lossless block coding result for general sources as a particularization it yields the classic result for a discrete memoryless source

control and state estimation of the one phase stefan problem via backstepping design this paper develops a control and estimation design for the one phase stefan problem the stefan problem represents a liquid solid phase transition as time evolution of a temperature profile in a liquid solid material and its moving interface this physical process is mathematically formulated as a diffusion partial differential equation pde evolving on a time varying spatial domain described by an ordinary differential equation ode the state dependency of the moving interface makes the coupled pde ode system a nonlinear and challenging problem we propose a full state feedback control law an observer design and the associated output feedback control law of both neumann and dirichlet boundary actuations via the backstepping method also the state feedback control law is provided when a robin boundary input is considered the designed observer allows the estimation of the temperature profile based on the available measurements of liquid phase length and the heat flux at the interface the associated output feedback controller ensures the global exponential stability of the estimation errors the mathcal h 1 norm of the distributed temperature and the moving interface at the desired setpoint under some explicitly given restrictions on the setpoint and observer gain

maximizing map sensitivity and higher derivatives via extremum seeking we present a generalization to the scalar newton based extremum seeking algorithm which through perturbation induced measurements of an unknown steady state input to output map maximizes the map s higher derivatives as with other extremum seeking es problems the scheme relies on derivative estimators and learning dynamics operating in different time scales we provide analysis for the typical deterministic sinusoidal perturbation of the optimal parameter estimate also we alternatively include a stochastic method where the map is perturbed via the sinusoid of brownian motion about the boundary of a circle by properly demodulating the map output corresponding to the manner in which it is perturbed the es algorithm maximizes the n rm th derivative only through measurements of the map the newton based es approach removes the dependence of the convergence rate on the unknown hessian of the higher derivative an effort to improve performance over standard gradient based es our design stems from the existing multivariable newton based es algorithm where a differential riccati equation estimates the inverse hessian of the function to be maximized algebraically computing a direct estimate of the inverse hessian is susceptible to singularity whereas employing the riccati filter removes that potential we prove local stability of the algorithm for general nonlinear equilibrium profiles of dynamic maps and compare the newton based method against the gradient based method we also extend this abstraction to multiplayer noncooperative games but limit our attention to a two player game for notational simplicity and length considerations

secret sharing with public reconstruction all known constructions of information theoretic t out of n secret sharing schemes require secure private communication channels among the parties for the reconstruction of the secret we investigate the cost of performing the reconstruction over public communication channels a naive implementation of this task distributes 2n 2 one times pads to each party this results in shares whose size is 2n 1 times the secret size we present three implementations of such schemes that are substantially more efficient a scheme enabling multiple reconstructions of the secret by different subsets of parties with factor o n t increase in the shares size a one time scheme enabling a single reconstruction of the secret with o log n t increase in the shares size a one time scheme enabling a single reconstruction by a set of size exactly t with factor o 1 increase in the shares size we prove that the first implementation is optimal up to constant factors by showing a tight spl omega n t lower bound for the increase in the shares size

common randomness and distributed control a counterexample when agents collaborate to perform a control task it is of interest to characterize the set of joint probability distributions they can achieve on their joint action space when they are passively provided with external common randomness we give a simple counterexample to a natural conjecture about this class of joint distributions