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September 2020

Researching how algorithms ‘fail’ at the University of Hawai’i at Mānoa

At a glance
The intern

Taylor Markham, Bachelor of Science, University of Calgary.

Hosted by

Annie Carter, Temporary Assistant Professor, Department of Mathematics and Statistics, University of Hawaiʻi at Mānoa, U.S.A.

The research

Study of the underlying theoretical concepts of factoring algorithms widely used with encryption systems. Understanding conditions under which the algorithm would fail could have implications for secure digital communication.

As cryptographic systems gain popularity, University of Calgary student embarks on international collaboration to discover if widely accepted algorithms fail with particular classes of numbers.

During her undergrad studies at the University of Calgary, Taylor Markham found her passion for mathematics and how cryptography demonstrates the use of mathematical concepts in everyday life applications.

In 2019, she was the first Faculty of Science student at the University of Calgary to apply for the Mitacs Globalink Research Award. Through this program, Markham spent her final summer as an undergrad student conducting research at the University of Hawai’i at Mānoa, where she was supervised by Annie Carter in the Department of Mathematics and Statistics.

Markham shared that “the Mitacs Globalink Research Award experience ended up being one of the highlights of my undergraduate degree and I found it to be incredibly valuable.”

At the University of Hawai’i, Markham researched integer factorization — which is part of an area of mathematics called number theory — and its relation to widely used encryption systems.

The objective of the project was to learn the underlying theoretical concepts of specific factoring algorithms believed to be the most efficient for working with large integers. Her work consisted in looking for necessary or sufficient conditions where the algorithm would fail.

Shared skills development: from knowledge translation to mentorship

In a field historically male-dominated, Markham welcomed the opportunity to conduct her research alongside Annie Carter. According to Carter, Markham developed a number of skills that are highly important to a mathematics researcher.

In addition to formulating research questions, developing project proposals and carrying out appropriate background research, Markham also developed her skills at communicating the results of their research — not always an easy task in advanced mathematics.

During her internship, Markham presented to both technical and non-technical audiences through departmental seminars, and also at the university’s undergraduate research symposium. “I had the opportunity to give multiple talks about my research project, which gave me more experience and confidence while presenting to audiences of various backgrounds,” Markham said.

Carter appreciated the opportunity to work with a Globalink research intern throughout the planning and implementation of the research project and highly recommends the Mitacs program to other researchers. Mentoring an intern allowed her to explore new areas of research directed by Markham’s own interest in the topic.

“It was exciting to see the way her interests could broaden the scope of my own work in the field,” Carter shared. “My experience working with her will help me to be a better mentor to future students.”

Exploring the possibilities of a diverse mathematics community

Markham is very grateful for the mentorship of both Carter and Mark Bauer, her supervisor at her home university, and the contribution to her professional development that this project provided. She gained a new perspective on mathematics and was able to experience the difference between engaging in research and doing course work.

In fact, this experience reinforced her decision to continue her education with a graduate program in mathematics and statistics in the Faculty of Science at the University of Calgary, under the supervision of Mark Bauer.

“There are a lot of great opportunities and experiences in the field of mathematics,” Markham shared. “I hope that through experiences like this one, other girls and women will see that there is a diverse mathematics community. I hope that it helps them to feel welcomed and encourages them to follow their interest in the field.”


Mitacs’s programs receive funding from valued partners across Canada. We thank the Government of Canada, the Government of Alberta, the Government of British Columbia, Research Manitoba, the Government of New Brunswick, the Government of Newfoundland and Labrador, the Government of Nova Scotia, the Government of Ontario, Innovation PEI, the Government of Quebec, Fonds de recherche du Québec – Nature et technologies, the Government of Saskatchewan, and the Government of Yukon for supporting us to foster innovation and economic growth throughout the country.

We are also grateful to our international partners. In 2020-2021, Mitacs is pleased to work with partners in Australia, Brazil, China, France, Germany, Hong Kong, India, Mexico, Taiwan, Tunisia, Ukraine, United Kingdom, and United States to support Globalink (see full list of Globalink partners).