Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Rose-Hulman Institute of Technology

2009

Cryptography

Articles 1 - 1 of 1

Full-Text Articles in Physical Sciences and Mathematics

Statistical Investigation Of Structure In The Discrete Logarithm, Andrew Hoffman Jul 2009

Statistical Investigation Of Structure In The Discrete Logarithm, Andrew Hoffman

Mathematical Sciences Technical Reports (MSTR)

The absence of an efficient algorithm to solve the Discrete Logarithm Problem is often exploited in cryptography. While exponentiation with a modulus is extremely fast with a modern computer, the inverse is decidedly not. At the present time, the best algorithms assume that the inverse mapping is completely random. Yet there is at least some structure, and to uncover additional structure that may be useful in constructing or refining algorithms, statistical methods are employed to compare modular exponential mappings to random mappings. More concretely, structure will be defined by representing the mappings as functional graphs and using parameters from graph …