PYI: Mathematical Foundations of Cryptography

PYI：密码学研究的新基础在计算复杂性的一般领域正在进行中。本研究的重点是密码学和计算数论。在80年代的十年中，密码学发展成为一门正式的学科，其中诸如“单向函数”和“证明协议是正确的”之类的概念具有精确而自然的含义。通过在一些复杂性假设下符合新的复杂性标准的具体建议来实现严谨性。不幸的是，所做的复杂性假设，例如单向函数的存在，可能在相当长的一段时间内仍未得到证实。这种情况为建立密码学的新基础提供了动力。我们不再对功能做出棘手的假设，而是对正在进行加密的模型做出物理假设（例如，网络参与者用于通信的通道或布局的类型）。为新模型寻求无条件安全的通信协议。已经取得的结果涉及到证明——具有“分布式”证明器的系统可以应用于容错分布式计算。这些应用正在探索中。交互式证明系统的工作仍在继续。利用这一领域开发的工具，人们试图澄清以前未分类的优化问题的复杂性。计算数论方面的工作也在继续。在素数检验和其他代数计算中寻求更简单、更快的算法。他被总统青年调查委员会评为杰出的计算机科学家。

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.