We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,thi...We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,this method saves most of the multiplications in the price of little increase of additions comparing to Horner's method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.展开更多
In this note a simple iterative method for simultaneously finding all zeros of a polynomial is established.The method does not require repeated evaluation of the polynomial or its deriva-tives,and is globally converge...In this note a simple iterative method for simultaneously finding all zeros of a polynomial is established.The method does not require repeated evaluation of the polynomial or its deriva-tives,and is globally convergent for quadratic polynomials.展开更多
To enhance the expressive power and the declarative ability of a deductive database, various CWA (Closed World Assumption) formalizations including the naive CWA, the generalized CWA and the careful CWA are extended ...To enhance the expressive power and the declarative ability of a deductive database, various CWA (Closed World Assumption) formalizations including the naive CWA, the generalized CWA and the careful CWA are extended to multi-valued logics. The basic idea is to embed logic formulas into some polynomial ring. The extensions can be applied in a uniform manner to any finitely multi-valued logics. Therefore they are also of computational significance.展开更多
Oblivious polynomial evaluation(OPE)is a two-party protocol that allows a receiver,R to learn an evaluation f(α),of a sender,S's polynomial(f(x)),whilst keeping both a and f(x)private.This protocol has attracted ...Oblivious polynomial evaluation(OPE)is a two-party protocol that allows a receiver,R to learn an evaluation f(α),of a sender,S's polynomial(f(x)),whilst keeping both a and f(x)private.This protocol has attracted a lot of attention recently,as it has wide ranging applications in the field of cryptography.In this article we review some of these applications and,additionally,take an in-depth look at the special case of information theoretic OPE.Specifically,we provide a current and critical review of the existing information theoretic OPE protocols in the literature.We divide these protocols into two distinct cases(three-party and distributed OPE)allowing for the easy distinction and classification of future information theoretic OPE protocols.In addition to this work,we also develop several modifications and extensions to existing schemes,resulting in increased security,flexibility and efficiency.Lastly,we also identify a security flaw in a previously published OPE scheme.展开更多
隐私保护集合交集(private set intersection,PSI)计算属于安全多方计算领域的特定应用问题,不仅具有重要的理论意义也具有很强的应用背景,在大数据时代,对该问题的研究更是符合人们日益强烈的在享受各种服务的同时达到隐私保护的需求....隐私保护集合交集(private set intersection,PSI)计算属于安全多方计算领域的特定应用问题,不仅具有重要的理论意义也具有很强的应用背景,在大数据时代,对该问题的研究更是符合人们日益强烈的在享受各种服务的同时达到隐私保护的需求.对安全多方计算基础理论进行了简要介绍,并重点介绍了目前主流的安全多方计算框架下2类PSI研究技术:传统的基于公钥加密机制,混乱电路,不经意传输的PSI协议和新型的云辅助的PSI协议,并对各类协议的过程、适用性、复杂性进行简要分析总结.同时,也对隐私保护集合交集问题的应用场景进行详细说明,进一步体现对该问题的实际研究价值.随着对该问题的不断深入研究,目前已经设计了在半诚实模型下快速完成上亿元素规模的隐私集合求交集协议.展开更多
基金Supported by the Graduate Starting Seed Fund of Northwestern Polytechnical University(Z2012030)
文摘We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,this method saves most of the multiplications in the price of little increase of additions comparing to Horner's method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.
基金The Project is supported by the National Natural Science Foundation of China and by Natural Science Foundation of Zhejiang Province.
文摘In this note a simple iterative method for simultaneously finding all zeros of a polynomial is established.The method does not require repeated evaluation of the polynomial or its deriva-tives,and is globally convergent for quadratic polynomials.
文摘To enhance the expressive power and the declarative ability of a deductive database, various CWA (Closed World Assumption) formalizations including the naive CWA, the generalized CWA and the careful CWA are extended to multi-valued logics. The basic idea is to embed logic formulas into some polynomial ring. The extensions can be applied in a uniform manner to any finitely multi-valued logics. Therefore they are also of computational significance.
文摘Oblivious polynomial evaluation(OPE)is a two-party protocol that allows a receiver,R to learn an evaluation f(α),of a sender,S's polynomial(f(x)),whilst keeping both a and f(x)private.This protocol has attracted a lot of attention recently,as it has wide ranging applications in the field of cryptography.In this article we review some of these applications and,additionally,take an in-depth look at the special case of information theoretic OPE.Specifically,we provide a current and critical review of the existing information theoretic OPE protocols in the literature.We divide these protocols into two distinct cases(three-party and distributed OPE)allowing for the easy distinction and classification of future information theoretic OPE protocols.In addition to this work,we also develop several modifications and extensions to existing schemes,resulting in increased security,flexibility and efficiency.Lastly,we also identify a security flaw in a previously published OPE scheme.
文摘隐私保护集合交集(private set intersection,PSI)计算属于安全多方计算领域的特定应用问题,不仅具有重要的理论意义也具有很强的应用背景,在大数据时代,对该问题的研究更是符合人们日益强烈的在享受各种服务的同时达到隐私保护的需求.对安全多方计算基础理论进行了简要介绍,并重点介绍了目前主流的安全多方计算框架下2类PSI研究技术:传统的基于公钥加密机制,混乱电路,不经意传输的PSI协议和新型的云辅助的PSI协议,并对各类协议的过程、适用性、复杂性进行简要分析总结.同时,也对隐私保护集合交集问题的应用场景进行详细说明,进一步体现对该问题的实际研究价值.随着对该问题的不断深入研究,目前已经设计了在半诚实模型下快速完成上亿元素规模的隐私集合求交集协议.
