PYI: Mathematical Foundations of Cryptography

PYI：密码学的数学基础

• 批准号: 8657527
• 负责人: Shafrira Goldwasser
• 金额: $ 31.2万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-08-15 至 1993-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8657527&HistoricalAwards=false
• 关键词: PYI; Mathematical; Foundations; Cryptography

PYI: New Foundations for Cryptography Research is in progress in the general area of computational complexity. The focus of this research is on cryptography and computational number theory. During the decade of the eighties cryptography was developed into a formal discipline in which notions such as "one-way function" and "proving that a protocol is correct" have a precise yet natural meaning. Rigor was accomplished by concrete proposals which were shown to comply with the new complexity standards under a few complexity assumptions. Unfortunately, the complexity assumptions made, for example the existence of one-way functions, are likely to remain unproven for quite a while longer. This situation provides motivation for establishing a new foundation for cryptography. Instead of making intractability assumptions about functions, physical assumptions about the model in which cryptography is being done (for example the kind of channel or layout used for communication by the network participants) are being made. Unconditionally secure communication protocols for the new model are sought. Results already achieved that involve proof- systems with a "distributed" prover may have applications to fault tolerant distributed computing. Such applications are being explored. Work is continuing on interactive proof systems. Using tools developed in this area an attempt is being made to clarify the complexity of previously unclassified optimization problems. Work in computational number theory is also continuing. Simpler and faster algorithms for primality testing and other algebraic computations are sought. The P.I. has been judged to be an outstanding computer scientist by the Presidential Young Investigator Panel.

密码学的新基础 计算一般领域的研究正在进行中 复杂性 这项研究的重点是密码学和 计算数论 在八十年代的十年中，密码学发展成为一种 正式的纪律，其中的概念，如“单向功能”和 “证明协议是正确的”有一个精确而自然的 意义严格性是通过所示的具体建议来实现的 在几个复杂度下遵守新复杂度标准 假设。 不幸的是，复杂性假设， 例如单向函数的存在，很可能仍然存在 还没有被证实 这种情况提供了动力 为密码学建立新的基础。 而不是让 关于函数的难以处理的假设，关于 加密的模型（例如， 用于网络参与者通信的通道或布局） 正在制造。 无条件安全通信协议 新的模式正在寻求。已经取得的成果涉及证据- 具有“分布式”证明器的系统可能会有应用程序出错 容错分布式计算 目前正在探讨这类应用。 正在继续进行交互式证明系统的工作。 使用开发的工具 在这方面，正在努力澄清 以前未分类的优化问题。 计算工作 数论也在继续。 更简单、更快速的算法， 寻求素性测试和其它代数计算。 私家侦探被评为杰出的计算机科学家 总统青年调查员小组。