Algorithms for discrete logarithm cryptography

数字通信的广泛使用大大增加了黑客和其他对手拦截和滥用数字通信的可能性。保护数字基础设施需要了解如何一般地保护网络，以及了解如何保护网络中各个链路上的通信。密码学使用数学和计算机科学来帮助保护网络通信免受攻击。实际上，密码系统的有效性取决于实现的细节——例如，可用于实现或攻击系统的算法的速度和计算复杂性。最近，一些政府已经强制要求在保护高安全性通信的密码系统中使用椭圆曲线。这些举措导致了这些系统的大规模部署，因此影响这些密码系统的更好的算法将具有实际意义。本文特别讨论了对这些密码系统的研究，以及对网络安全性的研究。所提出的研究的总体长期目标是进一步研究与离散对数密码学相关的乘法映射算法的使用。这项研究可能的结果包括更快或更便宜的通信设备或更安全的网络。

The widespread use of digital communications has much increased the possibility for their   interception and misuse by hackers and other adversaries.  Defending digital infrastructure requires understanding how to defend networks generally as well as understanding how to protect communications along individual links in the network. Cryptography uses mathematics and computer science to help protect network communications from adversaries.  The effectiveness of a cryptosystem in practice depends on the details of the implementation -- for example the speed and computational complexity of the algorithms available to implement or attack the system.  Recently several governments have mandated using elliptic curves for cryptosystems protecting high security communications.  These initiatives are resulting in large deployments of these systems, so better algorithms affecting these cryptosystems will  have practical significance.  This proposal discusses research into these cryptosystems specifically, and research into security in networks generally.   The general long-term objective of the proposed research is to further investigate uses of multiplicative maps in algorithms relating to discrete logarithm cryptography. Conceivable outcomes of this research include faster or cheaper communications equipment or more secure networks.