Special Meeting: Fields Cryptography Program - International U.S. Participation

密码学和加密协议已成为信息系统的关键要素，保护数据和通信以确保数据的机密性、完整性和真实性。虽然大多数对称密钥系统具有相对适中的数学要求，但非对称或公钥系统以及加密协议在数学上已变得越来越复杂。这种系统的安全性依赖于特定数学问题的难度，例如整数因式分解和模离散对数问题。对于这些系统中的任何一个，都没有给出严格的安全数学证明。这些问题的困难通常是通过专家们频繁而不成功的尝试来确定的，这些问题在计算上有效地解决了这些问题。事实上，几个被认为非常困难的问题最近被证明没有之前认为的那么棘手。此外，量子计算变得实用的可能性将极大地改变这一局面。如果实现，公钥密码系统的安全性所依赖的大多数问题从指数复杂性下降到多项式，使目前部署的密码系统变得毫无用处。虽然这种情况在短期内发生的可能性很小，但这是一个令人兴奋的研究领域，很可能导致计算和安全信息通信方面的革命性进步。这次特别会议将试图在这些和其他相关问题上取得进展。该计划将在菲尔德研究所举行，该研究所将在2006年6月至12月期间开展一项关于密码学的强化计划。该计划将参与并促进密码学和数学界之间的互动。NSF的资助将使年轻的美国研究人员能够参与这一计划，这样做将使年轻的研究人员在数学和密码应用程序之间的界面上接触到广泛的问题。它将增加密码学家和理论家在解决领域之间边界上的重要问题方面的合作程度，并将对密码学理论和实践产生影响。

Cryptography and cryptographic protocols have become a key element of information systems, protecting data and communications to ensure confidentiality, integrity and authenticity of data. While most symmetric key systems have relatively modest mathematical requirements, asymmetric or public key systems, as well as cryptographic protocols, have become increasingly mathematically sophisticated. Such systems rely for their security on the difficulty of specific mathematical problems such as integer factorization and the modular discrete logarithm problem. No rigorous mathematical proof of security has ever been given for any of these systems. The difficulty of these problems is usually established anecdotally through frequent and unsuccessful attempts by specialists to provide computationally efficient solutions to them. Indeed, several problems thought to be very difficult have recently been shown to be less intractable than previously believed. Furthermore, the possibility of quantum computing becoming practical would change this picture dramatically. If realized, most of the problems on which the security of public key cryptosystems rely drop from exponential complexity to polynomial, rendering currently deployed cryptographic systems useless. While the likelihood of this occurring in the short term is remote, this is an exciting area of research which may well lead to revolutionary advances in computation and secure information communication. This special meeting will attempt to make progress on these and other related problems.The program will take place at the Fields Institute, which will mount an intensive program on Cryptography during the period June - December 2006. This program will engage and stimulate interaction between the cryptographic and mathematical communities. NSF funding will enable young U.S. researchers to participate in this program, and in doing so it will expose young researchers to a wide range of problems at the interface between mathematics and cryptographic applications. It will increase the degree of collaboration between cryptographers and theoreticians in attacking the important problems at the boundaries between the fields, and will impact on both cryptographic theory and practice.