Rejection Sampling Revisit: How to Choose Parameters in Lattice-Based Signature

Rejection sampling technology is a core tool in the design of lattice-based signatures with ‘Fiat–Shamir with Aborts’ structure, and it is related to signing efficiency and signature, size as well as security. In the rejection sampling theorem proposed by Lyubashevsky, the masking vector of rejection sampling is chosen from discrete Gaussian distribution. However, in practical designs, the masking vector is more likely to be chosen from bounded uniform distribution due to better efficiency and simpler implementation. Besides, as one of the third-round candidate signatures in the NIST postquantum cryptography standardization process, the 3rd round version of CRYSTALS-Dilithium has proposed a new method to decrease the rejection probability in order to achieve better efficiency and smaller signature size by decreasing the number of nonzero coefficients of the challenge polynomial according to the security levels. However, it is seen that small entropies in this new method may lead to higher risk of forgery attack compared with former schemes proposed in its 2nd version. Thus, in this paper, we first analyze the complexity of forgery attack for small entropies and then introduce a new method to decrease the rejection probability without loss of security including the security against forgery attack. This method is achieved by introducing a new rejection sampling theorem with tighter bound by utilizing Rényi divergence where masking vector follows uniform distribution. By observing large gaps between the security claim and actual security bound in CRYSTALS-Dilithium, we propose two series of adapted parameters for CRYSTALS-Dilithium. The first set can improve the efficiency of the signing process in CRYSTALS-Dilithium by factors of 61.7 % and 41.7 % , according to the security levels, and ensure the security against known attacks, including forgery attack. And, the second set can reduce the signature size by a factor of 14.09 % with small improvements in efficiency at the same security level.

On the Power of Some Nonparametric Isotropy Tests

In this paper, properties of nonparametric significance tests verifying the random field isotropy hypothesis are discussed. In particular, the subject of the conducted analysis is the probability of rejecting the null hypothesis when it is true. A potential significant difference of empirical rejection probability from the assumed significance level could distort the results of statistical inference. The tests proposed by Guan, Sherman, Calvin (2004) and Lu, Zimmerman (2005) are considered. A simulation study has been carried out through generating samples from a given theoretical distribution and repeatedly testing the null hypothesis. Isotropic distributions are considered, among others, those based on a multidimensional normal distribution. The main aim of the paper is to compare both considered nonparametric significance tests verifying the random field isotropy hypothesis. For this purpose, the empirical rejection probabilities for both tests have been calculated and compared with the assumed significance level.

Model-Based Comparison of Cloud-Edge Computing Resource Allocation Policies

The rapid and widespread adoption of internet of things-related services advances the development of the cloud-edge framework, including multiple cloud datacenters (CDCs) and edge micro-datacenters (EDCs). This paper aims to apply analytical modeling techniques to assess the effectiveness of cloud-edge computing resource allocation policies from the perspective of improving the performance of cloud-edge service. We focus on two types of physical device (PD)-allocation policies that define how to select a PD from a CDC/EDC for service provision. The first is randomly selecting a PD, denoted as RandAvail. The other is denoted as SEQ, in which an available idle PD is selected to serve client requests only after the waiting queues of all busy PDs are full. We first present the models in the case of an On–Off request arrival process and verify the approximate accuracy of the proposed models through simulations. Then, we apply analytical models for comparing RandAvail and SEQ policies, in terms of request rejection probability and mean response time, under various system parameter settings.

ASYMPTOTIC THEORY FOR KERNEL ESTIMATORS UNDER MODERATE DEVIATIONS FROM A UNIT ROOT, WITH AN APPLICATION TO THE ASYMPTOTIC SIZE OF NONPARAMETRIC TESTS

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered only nearly integrated and stationary autoregressive processes. These results have applications to nonparametric predictive regression models. In particular, we show that the null rejection probability of a nonparametric t test is controlled uniformly in the degree of persistence of the regressor. This provides a rigorous justification for the validity of the usual nonparametric inferential procedures, even in cases where regressors may be highly persistent.

Proximate Predictors of Variation in Egg Rejection Behavior by Hosts of Avian Brood Parasites

The rejection of parasitic eggs by hosts of avian brood parasites is one of the most common and effective defenses against parasitism. Despite its adaptive significance, egg rejection often shows substantial intraspecific variation: some individuals are more likely to remove or abandon parasitic eggs than others. Understanding variation in egg rejection requires that we study factors linked to both the ability to perceive parasitic eggs, as well as factors that may influence the rejection of a foreign egg once it has been recognized. Here we asked what cognitive, physiological, and life-history factors explained variation in the rejection of model eggs by American Robin Turdus migratorius females. We found that the probability of egg rejection was related to the clutch size at the time of parasitism: in support of Weber’s law, females with fewer eggs were more likely to reject the model eggs. In turn, females with greater mass and higher corticosterone levels were less likely to reject eggs, and egg rejection probability was negatively related to incubation progress. Our data thus suggest that proximate predictors of an individual’s egg rejection behavior include components of the nest’s perceptual environment, life-history factors, as well as the physiological state of the animal. However, much of the variation in the responses of robins to the model eggs remained unexplained. Future experiments should aim to understand the causal roles of these and other factors in generating within- and among-individual variation in the rejection of parasitic eggs.

Inference under covariate‐adaptive randomization with multiple treatments

This paper studies inference in randomized controlled trials with covariate‐adaptive randomization when there are multiple treatments. More specifically, we study in this setting inference about the average effect of one or more treatments relative to other treatments or a control. As in Bugni, Canay, and Shaikh (2018), covariate‐adaptive randomization refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve “balance” within each stratum. Importantly, in contrast to Bugni, Canay, and Shaikh (2018), we not only allow for multiple treatments, but further allow for the proportion of units being assigned to each of the treatments to vary across strata. We first study the properties of estimators derived from a “fully saturated” linear regression, that is, a linear regression of the outcome on all interactions between indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity‐consistent estimator of the asymptotic variance are invalid in the sense that they may have limiting rejection probability under the null hypothesis strictly greater than the nominal level; on the other hand, tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact in the sense that they have limiting rejection probability under the null hypothesis equal to the nominal level. For the special case in which the target proportion of units being assigned to each of the treatments does not vary across strata, we additionally consider tests based on estimators derived from a linear regression with “strata fixed effects,” that is, a linear regression of the outcome on indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity‐consistent estimator of the asymptotic variance are conservative in the sense that they have limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level, but tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact, thereby generalizing results in Bugni, Canay, and Shaikh (2018) for the case of a single treatment to multiple treatments. A simulation study and an empirical application illustrate the practical relevance of our theoretical results.

The choice of optimal 3-rd order polynomial packet dropping function for NLRED in the presence of self-similar traffic

Algorithms of queue management in IP routers determine which packet should be deleted when necessary. The article investigates the influence of the self-similarity on the optimal packet rejection probability function in a special case of NLRED queues. This paper describes another approach to the non-linear packet dropping function. We propose to use the solutions based on the polynomials with degree equals to 3. The process of obtaining the optimal dropping packets function has been presented. Our researches were carried out using the Discrete Event Simulator OMNET++. The AQM model was early verified using the discrete-time Markov chain. The obtained results show that the traffic characteristic has the great impact on the network node behavior, but self-similarity of network traffic has no influence on the choosing of the optimal dropping packet function.