Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


thesis.pdf (707.62 KB)

ETD Abstract Container

Abstract Header

Totally Symmetric and Medial Quasigroups and their Applications

Young, Benjamin M
http://orcid.org/0000-0003-1921-7253
http://rave.ohiolink.edu/etdc/view?acc_num=case1618269661285196

Abstract Details

2021, Master of Sciences, Case Western Reserve University, EECS - Computer and Information Sciences.
We prove some new results regarding binary and n-ary totally symmetric and medial (TSM) quasigroups and explore their applications to cubic curves and cryptography. We first generalize to the n-ary case Etherington’s result that a product in binary TSM quasigroup is symmetric in factors whose depths differ by a multiple of 2 in the corresponding product tree. We then demonstrate that there are an equal number of the four following labeled structures over any finite set: abelian groups, n-ary abelian groups, TSM quasigroups, and n-ary TSM quasigroups. Next we explore applications of quasigroups in cryptography and discuss how our maps between abelian groups, TSM quasigroups, and n-ary TSM quasigroups can be used to generate and easily calculate products in quasigroups for use in cryptosystems. Finally, we discuss the TSM quasigroup of points on a cubic curve and prove some properties of iterated squaring in prime-order TSM quasigroups.
Harold Connamacher (Advisor)
Shuai Xu (Committee Member)
David Singer (Committee Member)
88 p.
Computer Science; Mathematics
totally symmetric; medial; quasigroups; totally symmetric and medial quasigroups; cryptography, n-ary quasigroups; n-ary groups; abelian groups; cubic curves

Recommended Citations

Citations

  • Young, B. M. (2021). Totally Symmetric and Medial Quasigroups and their Applications [Master's thesis, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1618269661285196

    APA Style (7th edition)

  • Young, Benjamin. Totally Symmetric and Medial Quasigroups and their Applications. 2021. Case Western Reserve University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1618269661285196.

    MLA Style (8th edition)

  • Young, Benjamin. "Totally Symmetric and Medial Quasigroups and their Applications." Master's thesis, Case Western Reserve University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1618269661285196

    Chicago Manual of Style (17th edition)

case1618269661285196
450
© 2021, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.