TWC: Medium: CRYPTOGRAPHIC APPLICATIONS OF CAPACITY THEORY

TWC:媒介:容量理论的密码学应用

基本信息

  • 批准号:
    1513671
  • 负责人:
  • 金额:
    $ 109.5万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2015
  • 资助国家:
    美国
  • 起止时间:
    2015-10-01 至 2021-09-30
  • 项目状态:
    已结题

项目摘要

The primary goal of this project is to develop a mathematical foundation underlying the analysis of modern cryptosystems. Cryptography is a core tool used to secure communications over the Internet. Secure and trustworthy communications and data storage are essential to national security and to the functioning of the world economy. Recent spectacular research results have enabled the development of new types of cryptography, exciting new potential applications, and hopes for stronger guarantees of cryptographic security in the long term. This project aims to increase confidence in these new constructions by unifying new methods from mathematics with cryptographic tools.Nearly all of public-key cryptography relies for its security on the assumed difficulty of solving various number theoretic problems. Recent developments in cryptography such as fully homomorphic encryption, candidate multilinear maps, and efficient post-quantum lattice-based cryptography have produced a multitude of new algebraicand number-theoretic cryptographic hardness assumptions. Many of these problems are new and largely unstudied by the computational number theory community. This project uses tools from arithmetic geometry such as capacity theory and Arakelov theory to develop a more rigorous understanding of the theoretical and computational limits to the fundamental cryptanalytic techniques used to assure cryptographic security. This project will improve the numerical and theoretical tools used in cryptanalysis, and promote a better understanding of the security of many practical cryptosystems.
这个项目的主要目标是为现代密码系统的分析建立一个数学基础。密码学是用于保护Internet上通信安全的核心工具。安全可靠的通信和数据存储对国家安全和世界经济的运转至关重要。最近惊人的研究成果使新型密码学的发展成为可能,新的潜在应用令人兴奋,并希望从长远来看,密码安全得到更强有力的保证。这个项目旨在通过将数学中的新方法与密码工具相结合来增加对这些新构造的信心。几乎所有公钥密码学的安全性都依赖于假定的解决各种数论问题的难度。密码学的最新发展,如完全同态加密、候选多线性映射和有效的基于后量子格的密码学,已经产生了大量新的代数和数论密码硬度假设。这些问题中的许多都是新问题,在很大程度上没有被计算数论社区研究过。该项目使用算术几何中的工具,如容量理论和Arakelov理论,对用于确保密码安全的基本密码分析技术的理论和计算限制进行了更严格的理解。这个项目将改进密码分析中使用的数值和理论工具,并促进对许多实用密码系统安全性的更好理解。

项目成果

期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
CacheQuote: Efficiently Recovering Long-term Secrets of SGX EPID via Cache Attacks
  • DOI:
    10.13154/tches.v2018.i2.171-191
  • 发表时间:
    2018-05
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Fergus Dall;Gabrielle De Micheli;T. Eisenbarth;Daniel Genkin;N. Heninger;A. Moghimi;Y. Yarom
  • 通讯作者:
    Fergus Dall;Gabrielle De Micheli;T. Eisenbarth;Daniel Genkin;N. Heninger;A. Moghimi;Y. Yarom
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Ted Chinburg其他文献

Cup products on curves over finite fields
有限域曲线上的杯积
  • DOI:
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Frauke M. Bleher;Ted Chinburg
  • 通讯作者:
    Ted Chinburg
On representations of math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg" class="math"mrowmi mathvariant="normal"Gal/mi/mrowmo stretchy="false"(/momover accent="true"mrowmi mathvariant="double-struck"Q/mi/mrowmo‾/mo/movermo stretchy="false"//momi mathvariant="double-struck"Q/mimo stretchy="false")/mo/math, math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg" class="math"mover accent="true"mrowmiG/mimiT/mi/mrowmrowmoˆ/mo/mrow/mover/math and math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg" class="math"mrowmi mathvariant="normal"Aut/mi/mrowmo stretchy="false"(/momsubmrowmover accent="true"mrowmiF/mi/mrowmrowmoˆ/mo/mrow/mover/mrowmrowmn2/mn/mrow/msubmo stretchy="false")/mo/math
  • DOI:
    10.1016/j.jalgebra.2021.06.005
  • 发表时间:
    2022-10-01
  • 期刊:
  • 影响因子:
    0.800
  • 作者:
    Frauke M. Bleher;Ted Chinburg;Alexander Lubotzky
  • 通讯作者:
    Alexander Lubotzky
The geometry of finite dimensional algebras with vanishing radical square
  • DOI:
    10.1016/j.jalgebra.2014.11.010
  • 发表时间:
    2015-03-01
  • 期刊:
  • 影响因子:
  • 作者:
    Frauke M. Bleher;Ted Chinburg;Birge Huisgen-Zimmermann
  • 通讯作者:
    Birge Huisgen-Zimmermann
Topological properties of Eschenburg spaces and 3-Sasakian manifolds
  • DOI:
    10.1007/s00208-007-0102-6
  • 发表时间:
    2007-04-19
  • 期刊:
  • 影响因子:
    1.400
  • 作者:
    Ted Chinburg;Christine Escher;Wolfgang Ziller
  • 通讯作者:
    Wolfgang Ziller

Ted Chinburg的其他文献

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{{ truncateString('Ted Chinburg', 18)}}的其他基金

SaTC: CORE: Medium: Collaborative: An Algebraic Approach to Secure Multilinear Maps for Cryptography
SaTC:核心:媒介:协作:保护密码学多线性映射的代数方法
  • 批准号:
    1701785
  • 财政年份:
    2017
  • 资助金额:
    $ 109.5万
  • 项目类别:
    Standard Grant
FRG: Collaborative Research: Chern classes in Iwasawa Theory
FRG:合作研究:岩泽理论中的陈省身课程
  • 批准号:
    1360767
  • 财政年份:
    2014
  • 资助金额:
    $ 109.5万
  • 项目类别:
    Continuing Grant
FRG: Collaborative Research: Lifting Problems and Galois Theory
FRG:协作研究:提升问题和伽罗瓦理论
  • 批准号:
    1265290
  • 财政年份:
    2013
  • 资助金额:
    $ 109.5万
  • 项目类别:
    Continuing Grant
Euler Characteristics,Qquadratic Invariants, Arithmetic Groups and Lifting Problems
欧拉特性、Q二次不变量、算术群和提升问题
  • 批准号:
    1100355
  • 财政年份:
    2011
  • 资助金额:
    $ 109.5万
  • 项目类别:
    Standard Grant
Euler characteristics, length spectra, deformations and lifting problems
欧拉特征、长度谱、变形和提升问题
  • 批准号:
    0801030
  • 财政年份:
    2008
  • 资助金额:
    $ 109.5万
  • 项目类别:
    Standard Grant
Euler Characteristics and Lifting Problems in Arithmetic Geometry
算术几何中的欧拉特性和提升问题
  • 批准号:
    0500106
  • 财政年份:
    2005
  • 资助金额:
    $ 109.5万
  • 项目类别:
    Standard Grant
Collaborative Research: FRG: Class numbers, Hyperbolic Manifolds and Dynamics
合作研究:FRG:类数、双曲流形和动力学
  • 批准号:
    0139816
  • 财政年份:
    2002
  • 资助金额:
    $ 109.5万
  • 项目类别:
    Standard Grant
Galois Structure and Arithmetic Geometry
伽罗瓦结构与算术几何
  • 批准号:
    0070433
  • 财政年份:
    2000
  • 资助金额:
    $ 109.5万
  • 项目类别:
    Standard Grant
The Galois Structure of DeRham Cohomology and Motives
DeRham 上同调的伽罗瓦结构和动机
  • 批准号:
    9701411
  • 财政年份:
    1997
  • 资助金额:
    $ 109.5万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Galois Structures, Capacity Theory and Intersection Theory
数学科学:伽罗瓦结构、容量论和交集论
  • 批准号:
    9400748
  • 财政年份:
    1994
  • 资助金额:
    $ 109.5万
  • 项目类别:
    Continuing Grant

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协作研究:SaTC:核心:中:加密累加器和凭证撤销
  • 批准号:
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