Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mapping the Discrete Logarithm   The discrete logarithm is a problem that surfaces frequently in the field of
cryptography as a result of using the transformation g^a mod n. This paper
focuses on a prime modulus, p, for which it is shown that the basic structure
of the functional graph is largely dependent on an interaction between g and
p-1. In fact, there are precisely as many different functional graph structures
as there are divisors of p-1. This paper extracts two of these structures,
permutations and binary functional graphs. Estimates exist for the shape of a
random permutation, but similar estimates must be created for the binary
functional graphs. Experimental data suggests that both the permutations and
binary functional graphs correspond well to the theoretical data which provides
motivation to extend this to larger divisors of p-1 and study the impact this
forced structure has on the many cryptographic algorithms that rely on the
discrete logarithm for their security. This is especially applicable to those
algorithms that require a "safe" prime (p=2q+1, where q is prime) modulus since
all non-trivial functional graphs generated using a safe prime modulus can be
analyzed by the framework presented here.

35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat