#### Document Type

Article

#### Publication Date

7-31-2009

#### First Advisor

Joshua Holden

#### Abstract

In an age of digital information, security is of utmost importance. Many encryption schemes, such as the Diffie-Hellman Key Agreement and RSA Cryptosystem, use a function which maps x to y by a modular power map with generator g. The inverse of this function - trying to find x from y - is called the discrete logarithm problem. In most cases, n is a prime number. In some cases, however, n may be a composite number. In particular, we will look at when n = p^b for a prime p. We will show different techniques of obtaining graphs of this mapping and then we look to see whether the above mapping for the described n looks like a random map, and, if it does not, observe what we can that would help in solving the discrete logarithm problem.

#### Recommended Citation

Mace, Marcus L., "Discrete Logarithm over Composite Moduli" (2009). *Mathematical Sciences Technical Reports (MSTR)*. 17.

http://scholar.rose-hulman.edu/math_mstr/17

## Comments

MSTR 09-07