7 citations · 21 across the 16 of their papers we have counts for
16 papers
Decidability of the Orbit Problem Over
Joshua Holden, Alexa Renner
The orbit problem is the problem of whether, given and an matrix , there exists an such that . In 1980, Kannan and…
Resource Guide for Teaching Post-Quantum Cryptography
Joshua Holden
Public-key cryptography has become a popular way to motivate the teaching of concepts in elementary number theory, abstract algebra, and introduction to proof courses, as well as i…
Counting fixed points and rooted closed walks of the singular map modulo powers of a prime
Joshua Holden, Pamela A. Richardson, Margaret M. Robinson
The "self-power" map modulo and its generalized form modulo are of considerable interest for both theoretical reasons and for potential…
Statistics for fixed points of the self-power map
Matthew Friedrichsen, Joshua Holden
The map x -> x^x modulo p is related to a variation of the digital signature scheme in a similar way to the discrete exponentiation map, but it has received much less study. We exp…
Counting Fixed Points, Two-Cycles, and Collisions of the Discrete Exponential Function using p-adic Methods
Joshua Holden, Margaret M. Robinson
Brizolis asked for which primes p greater than 3 does there exist a pair (g, h) such that h is a fixed point of the discrete exponential map with base g, or equivalently h is a fix…
Mapping the Discrete Logarithm
Daniel R. Cloutier, Joshua Holden
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,…