#### Date of Award

Summer 8-10-2017

#### Degree Type

Creative Project

#### Degree Name

Master of Mathematics (MMath)

#### Department

Mathematics and Statistics

#### First Advisor

David Brown

#### Abstract

Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log_{2}(α)^{3} + 16.5log_{2}(α)^{2} + 6log_{2}(α) whereas previous work on the subject has only produced systems in which at least one of the polynomials has an ordered binary decision diagram representation with size exponential in log_{2}(α). Using a different approach based on the Chinese remainder theorem we prove that for α ≥ 4 there is an alternative system of boolean equations whose solutions correspond to nontrivial factorizations of α such that there exists a C > 0, independent of α, such that for any order σ on the variables in the system every function in the system can be represented by a σ-OBDD with size less than C log_{2}(log_{2}(α))^{2}log_{2}(α)^{4} .

#### Recommended Citation

Skidmore, David, "Efficiently representing the integer factorization problem using binary decision diagrams" (2017). *All Graduate Plan B and other Reports*. 1043.

http://digitalcommons.usu.edu/gradreports/1043

#### Included in

Algebra Commons, Discrete Mathematics and Combinatorics Commons, Information Security Commons, Number Theory Commons, Other Computer Sciences Commons, Other Mathematics Commons

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