Modifying twist algorithms for determining the key length of a Vigenère cipher

Abstract

In this article, we analyze and improve upon the twist-based algorithms introduced by Barr–Simoson and Park–Kim–Cho–Yum for determining the key length of a Vigenère cipher. We provide an in-depth discussion on how the domain of the twist index affects the accuracy of these algorithms along with supporting experimental evidence. We also introduce a new twist-based algorithm, the twist${}^{++}$ algorithm, and show this algorithm is more accurate than the twist${}^{+}$ algorithm for a wide range of key lengths and text lengths.

Keywords:

• Index of coincidence
• key length
• twist algorithm
• Vigenère cipher

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are openly available in Zenodo at https://doi.org/10.5281/zenodo.8373071.

Additional information

Funding

This work was financially supported by the Furman University Department of Mathematics via the Summer Mathematics Undergraduate Research Fellowships.

Notes on contributors

Christian Millichap

Christian Millichap is an Associate Professor of Mathematics at Furman University in Greenville, SC. His research interests are in geometric topology and knot theory. He has also enjoyed teaching a variety of classes in cryptology for high school students and undergraduates.

Yeeka Yau

Yeeka Yau is an Assistant Professor of Mathematics at the University of North Carolina Asheville. His research interests are in Coxeter groups, combinatorial and geometric group theory, cryptology, and machine learning.

Alyssa Pate

Alyssa Pate is a student at Furman University. She is studying Applied Mathematics and Data Analytics with hopes of going into the Data Analytics field. With friend and fellow collaborator, Morgan Carns, she participated in the 2023 Kryptos Competition. She enjoys learning more about Cryptology and hopes to continue to discover more in the future.

Morgan Carns

Morgan Carns is a student at Furman University getting her Bachelor of Science in Applied Mathematics with a Data Analytics Minor. Her cryptology experience started with the Kryptos competition held by Central Washington University where she placed as an amateur codebreaker for solving one of three challenges. She then continued her exploration in cryptology by completing summer research through the Furman Mathematics Department in the summer of 2023. She hopes to continue her cryptology experience throughout the rest of her life.