#### Presentation Title

Shor’s Algorithm: How Quantum Computing Affects Cybersecurity

#### Faculty Sponsor

Dr. Asai Asaithambi

#### Faculty Sponsor College

College of Computing, Engineering & Construction

#### Faculty Sponsor Department

Computing

#### Location

SOARS Virtual Conference

#### Presentation Website

https://unfsoars.domains.unf.edu/2021/posters/shors-algorithm-how-quantum-computing-affects-cybersecurity/

#### Keywords

SOARS (Conference) (2021 : University of North Florida) – Archives; SOARS (Conference) (2021 : University of North Florida) – Posters; University of North Florida -- Students -- Research – Posters; University of North Florida. Office of Undergraduate Research; University of North Florida. Graduate School; College students – Research -- Florida – Jacksonville – Posters; University of North Florida – Undergraduates -- Research – Posters; University of North Florida. School of Computing; Honorable Mention Award Winner

#### Abstract

Honorable Mention Winner

Almost all of today’s computer security relies on something known as the RSA cryptosystem. This system relies on a mathematical, specifically number theory, problem known as prime factorization, where a composite number is broken down into its two prime number factors. This in an ideal method for encryption because it is easy to multiply two numbers, encoding the data, but it much harder to determine which numbers were originally multiplied together, thus hard to decode the data. If this composite number is sufficiently large, there is no known algorithm for efficiently breaking it down – at least not in classical computation. Peter Shor developed an algorithm in 1994, however, which can factor integers very efficiently and thus break down RSA encryption by employing some mathematical principles of quantum mechanics, specifically quantum parallelism, which allows for an exponential speedup with some quantum algorithms. The main goal of this research is to implement these quantum principles, as well as some necessary classical components, to demonstrate Shor’s algorithm and its superior time complexity. To do this, we needed to build Shor’s algorithm in the form of a quantum circuit, which can be done using python and employing the libraries of Qiskit, a quantum computing simulation program developed by IBM. The goal of this program is to show that Shor’s algorithm successfully returns the factors of some integer and compare it to classical computation.

#### Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

#### Included in

Shor’s Algorithm: How Quantum Computing Affects Cybersecurity

SOARS Virtual Conference

Honorable Mention Winner

Almost all of today’s computer security relies on something known as the RSA cryptosystem. This system relies on a mathematical, specifically number theory, problem known as prime factorization, where a composite number is broken down into its two prime number factors. This in an ideal method for encryption because it is easy to multiply two numbers, encoding the data, but it much harder to determine which numbers were originally multiplied together, thus hard to decode the data. If this composite number is sufficiently large, there is no known algorithm for efficiently breaking it down – at least not in classical computation. Peter Shor developed an algorithm in 1994, however, which can factor integers very efficiently and thus break down RSA encryption by employing some mathematical principles of quantum mechanics, specifically quantum parallelism, which allows for an exponential speedup with some quantum algorithms. The main goal of this research is to implement these quantum principles, as well as some necessary classical components, to demonstrate Shor’s algorithm and its superior time complexity. To do this, we needed to build Shor’s algorithm in the form of a quantum circuit, which can be done using python and employing the libraries of Qiskit, a quantum computing simulation program developed by IBM. The goal of this program is to show that Shor’s algorithm successfully returns the factors of some integer and compare it to classical computation.

https://digitalcommons.unf.edu/soars/2021/spring_2021/96