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认证码的构造及其相关组合问题的研究
  • 项目名称：认证码的构造及其相关组合问题的研究
  • 项目类别：面上项目
  • 批准号：61179026
  • 申请代码：F010103
  • 项目来源：国家自然科学基金
  • 研究期限：2012-01-01-2015-12-31
  • 项目负责人：高有
  • 依托单位：中国民航大学
  • 批准年度：2011
中文摘要：

本项目将充分运用典型群上的几何学和组合设计等有关工具研究认证码的构造以及与其相关的组合问题。具体研究认证系统的组合结构以及与其相关的组合设计问题；基于有限域上典型群作用下的几何空间构造几何格、带仲裁的认证码、区组设计和结合方案，利用所得到的区组设计和结合方案构造带仲裁的认证码；作为传统认证码的扩张，基于有限域上典型群作用下的几何空间构造多发送多重认证码与多接收多重认证码；基于有限域上典型群作用下的几何空间构造（t,n）门限密钥共享认证系统（即 (t,n) threshold SGA-system）；基于有限域上典型群作用下的几何空间构造具有保密功能的认证码，研究具有保密功能的认证码与组合设计之间的关系。项目的最终目的是获得一批最优的或完善的各种类型认证码，进而推动典型群上的几何学、组合设计和密码学理论的进一步发展。

中文主题词： 密码认证；认证码；具有保密功能的认证码；组合设计；有限典型群的几何学
英文摘要：

cryptogram authentication；authentication code；authentication codes with secrecy；combinatorial design；geometry of finite classical groups

英文主题词： cryptogram authentication；authentication code；authentication codes with secrecy；combinatorial design；geometry of finite classical groups
结论摘要：

项目充分运用典型群上的几何学和组合设计等有关工具研究认证码的构造以及与其相关的组合问题。取得的主要研究成果基于有限域上典型群作用下的几何空间构造了一系列结合方案，进而得到一系列具有保密功能的认证码，研究了具有保密功能的认证码与结合方案之间的关系；基于有限域上典型群作用下的几何空间构造具有仲裁的认证码以及具有多个仲裁人的认证码；基于有限域上典型群作用下的几何空间构造多接收认证码、多接收多重认证码及多发送认证码；研究了（t,n）门限密钥共享认证系统的构造问题；基于有限域上奇异典型群作用下的几何空间构造几何格与组合设计；构造了三类完善认证码，研究了无条件安全认证码及线性认证码的构造问题；研究了有限域上典型群作用下的几何学在子空间码构造方面的应用。

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 51
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期刊论文
Lattices generated by orbits of ？ats under ？nite affine-singular symplectic groups
A New Construction of Multi-sender Authentication Codes from Pseudo-Symplectic Geometry over Finite
Authentication Codes from Free modules: Bounds and Constructions
Association schemes based on the subspaces of type (m,s,0) in singular symplectic space over finite
Lattices Generated by Two Orbits of Subspaces under Finite Singular symplectic Groups
Two Constructions of Optimal Authentication Codes from Unitary Geometry over Finite Fields
A New Group-oriented Publicly Verifiable Threshold Signcrytion Scheme
The Construction of A3-Code from Projective Spaes over Finite Fields
Two Constructions of Multi-sender Authentication Codes with Arbitration based linear codes
Constructicticon of Multi-receiver Multi-fold Authentication Codes from Singular Symplectic Geometry
Some New Constructions of Authentication Codes with Arbitration and Multi-Receiver from Singular Sym
A New Construction of A2 Authentication Codes from Singular Pseudo-Symplectic Geometry over Finite F
利用有限域上交错矩阵构造带仲裁的认证码
Lattices Generated by Totally Isotropic Subspaces under Symplectic Group over a Finite Field
A New Construction of Multisender Authentication Codes from Symplectic Geometry over Finite Fields
A New Construction of Authentication Code with Arbitration from (2v+2+l)-dimensional Singular Pseudo
Three Constructions of Authentication Codes from Power Function over Finite Fields with Perfect Secr
A New Construction of Multi receiver Authentication Codes from Pseudo-Symplectic Geometry over Fihit
利用有限域上的酉几何构作带仲裁的认证码
Lattices generated by orbits of subspaces under finite singular orthogonal groups II
Error-correcting codes in attenuated space over finite fields
Association schemes based on the subspaces of type (2, 1, 0)in singular symplectic space over finite
The Construction of A3-code from Singular Pseudo-symplectic Geometry over Finite Fields
Two Constructions of Multireceiver Authentication Codes from Singular Symplectic Geometry over Finit
Association schemes based on the subspaces of type (2,0,1) in singular symplectic space over finite
Two Constructions of Authentication Codes with Multiple Arbiters
Pooling designs with singular linear space and its tighter bound
Bounds on Subspace Codes Based on Subspaces of Type (m,1) in Singular Linear Space
A New Construction of Multi-receiver Authentication Codes from Pseudo-Symplectic Geometry over Finit
A Construction of Multi-sender Authentication Codes from Pseudo-Symplectic Geometry of Finite fields
Constructing Error-correcting Pooling Designs with Singular Linear Space
Two New Constructions of Multi-receiver Authentication Codes from Singular Pseudo- Symplectic Geomet
Association schemes based on singular symplectic geometry over ？nite ？elds and its application
Association schemes based on singular linear spaces and its applications
Constructions for Key Distribution Pattern using Resolvable Designs
A Construction of Multisender Authentication Codes with Sequential Model from Symplectic Geometry ov
Key Pre-distribution Schemes based on Symplectic Geometry for Wireless Sensor Networks
A Construction of Authentication Codes with Double Arbiters over Symplectic Geometry
Three constructions of perfect authentication codes from projective geometry over finite fields
Constructing error-correcting pooling designs with singular symplectic space
Linear authentication Code over Finite local Rings
A New Construction of Multi-sender Authentication Codes from Polynomials over Finite Fields
A New Construction of Multisender Authentication Codes with Simultaneous Model from Singular Symplec
New error-correcting pooling designs with vector spaces over finite field
利用有限域上奇异辛几何构造一个新的带仲裁的认证码
有限奇异辛群作用下（m，0，k）型子空间的子轨道
有限局部环上的线性认证码
奇异线性空间上的Pooling设计及其紧界
基于奇异酉空间的具有容错纠错能力的Pooling设计的构造
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