In this paper,the regression function comparison for paired data is studied.The proposed test statistic is based on the weighted integral of characteristic function marked by the difference of responses.There are seve...In this paper,the regression function comparison for paired data is studied.The proposed test statistic is based on the weighted integral of characteristic function marked by the difference of responses.There are several merits of the proposed statistic.For instance,it takes a simple V-statistic form.No bandwidth is needed.No moment conditions are required for covariates.It can be applied to covariates of any fixed dimension.The asymptotic results are also developed.It is proven that n times the proposed test statistic converges to a finite limit under the null hypothesis and the test is consistent against any fixed alternatives.Local alternative hypotheses which converge to the null hypothesis at the rate of n-1/2 are also detected.A suitable Bootstrap algorithm is also proposed for the implementation of the proposed test statistic.Simulation studies are carried out to illustrate the merits of the proposed method.A real data example is also used to illustrate the proposed testing procedures.展开更多
Function secret sharing(FSS)is a secret sharing technique for functions in a specific function class,mainly including distributed point function(DPF)and distributed comparison function(DCF).As an important basis for f...Function secret sharing(FSS)is a secret sharing technique for functions in a specific function class,mainly including distributed point function(DPF)and distributed comparison function(DCF).As an important basis for function secret sharing,DPF and DCF are the foundation for the extension of this technique to other more general and complex function classes.However,the function classes corresponding to the current DPF and DCF schemes are almost all unary function classes,and there is no efficient construction for multivariate function classes.The applications of FSS can be extended with the development of a multivariate scheme,e.g.,a multi-keyword private information retrieval scheme can be constructed.To solve this problem,this paper presents a binary DCF scheme based on the“two-layer binary tree”structure.In a binary tree structure,each node computes the seed of its child nodes based on its own seed.The key technique is to realize the transition transfer of seeds by using oblivious transfer,to connect two unary structures.Theoretical analysis and experimental results show that our binary scheme changes from single-round communication in the original definition to multiround communication,and has great advantages in communication cost and computation efficiency.For the security parameterλand input length n,the key size is reduced from to O(λn^(2))to O(λn)In addition,we explore the extensions and applications of the above method.In the batch computation,this paper uses oblivious transfer(OT)extension to realize the one-time transmission of multiple pairs of seeds and optimize its communication efficiency.By extending the structure from“two-layer”to“multi-layer”,a secret sharing scheme of multivariate mixed basic function is proposed based on the serial thought.Furthermore,by employing the parallel thought,a general 2-layer FSS structure from OT for multivariate mixed basic functions is explored to enhance the efficiency,where the first layer is composed of d parallel binary trees with d representing the input dimension,and the second layer is one binary tree of depth d.And the applications of our schemes in multi-keyword private information retrieval are presented.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11601227and 11701034。
文摘In this paper,the regression function comparison for paired data is studied.The proposed test statistic is based on the weighted integral of characteristic function marked by the difference of responses.There are several merits of the proposed statistic.For instance,it takes a simple V-statistic form.No bandwidth is needed.No moment conditions are required for covariates.It can be applied to covariates of any fixed dimension.The asymptotic results are also developed.It is proven that n times the proposed test statistic converges to a finite limit under the null hypothesis and the test is consistent against any fixed alternatives.Local alternative hypotheses which converge to the null hypothesis at the rate of n-1/2 are also detected.A suitable Bootstrap algorithm is also proposed for the implementation of the proposed test statistic.Simulation studies are carried out to illustrate the merits of the proposed method.A real data example is also used to illustrate the proposed testing procedures.
基金supported by National Key R&D Program of China(No.2022ZD0161901)the National Natural Science Foundation of China(Grant No.62072023)+3 种基金Beijing Natural Science Foundation(No.4242024)the Open Project Fund of the State Key Laboratory of Cryptology,China(No.MMKFKT202120)the Exploratory Optional Project Fund of the State Key Laboratory of Complex&Critical Software Environment(No.SKLCCSE-2025ZX-XX)the Fundamental Research Funds of Beihang University,China(Nos.YWF-21-BJ-J-1041 and YWF-23-L-1033).
文摘Function secret sharing(FSS)is a secret sharing technique for functions in a specific function class,mainly including distributed point function(DPF)and distributed comparison function(DCF).As an important basis for function secret sharing,DPF and DCF are the foundation for the extension of this technique to other more general and complex function classes.However,the function classes corresponding to the current DPF and DCF schemes are almost all unary function classes,and there is no efficient construction for multivariate function classes.The applications of FSS can be extended with the development of a multivariate scheme,e.g.,a multi-keyword private information retrieval scheme can be constructed.To solve this problem,this paper presents a binary DCF scheme based on the“two-layer binary tree”structure.In a binary tree structure,each node computes the seed of its child nodes based on its own seed.The key technique is to realize the transition transfer of seeds by using oblivious transfer,to connect two unary structures.Theoretical analysis and experimental results show that our binary scheme changes from single-round communication in the original definition to multiround communication,and has great advantages in communication cost and computation efficiency.For the security parameterλand input length n,the key size is reduced from to O(λn^(2))to O(λn)In addition,we explore the extensions and applications of the above method.In the batch computation,this paper uses oblivious transfer(OT)extension to realize the one-time transmission of multiple pairs of seeds and optimize its communication efficiency.By extending the structure from“two-layer”to“multi-layer”,a secret sharing scheme of multivariate mixed basic function is proposed based on the serial thought.Furthermore,by employing the parallel thought,a general 2-layer FSS structure from OT for multivariate mixed basic functions is explored to enhance the efficiency,where the first layer is composed of d parallel binary trees with d representing the input dimension,and the second layer is one binary tree of depth d.And the applications of our schemes in multi-keyword private information retrieval are presented.
