Grant: Discovery Grants Program - Individual

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.