Secure Passwords Using Combinatorial Group Theory

Gilbert Baumslag; Benjamin Fine; Anja Moldenhauer; Gerhard Rosenberger

doi:10.4236/jis.2018.92011

Secure Passwords Using Combinatorial Group Theory

Gilbert Baumslag, Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger

Fairfield University

Research output: Contribution to journal › Article › peer-review

Abstract

Password security is a crucial component of modern internet security. In this paper, we present a provably secure method for password verification using combinatorial group theory. This method relies on the group randomizer system, a subset of the MAGNUS computer algebra system and corrects most of the present problems with challenge response systems, the most common types of password verification. Theoretical security of the considered method depends on several results in asymptotic group theory. We mention further that this method has applications for many other password situations including container security.

Original language	American English
Journal	Journal of Information Security
Volume	9
DOIs	https://doi.org/10.4236/jis.2018.92011
State	Published - Jan 1 2018

Keywords

Password Security
Combinatorial Group Theory
Free Group Cryptography
Group Randomizer System

Disciplines

Mathematics
Physical Sciences and Mathematics

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10.4236/jis.2018.92011License: CC BY

Secure Passwords Using Combinatorial Group TheoryFinal published version, 364 KBLicense: CC BY

Cite this

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title = "Secure Passwords Using Combinatorial Group Theory",

abstract = " Password security is a crucial component of modern internet security. In this paper, we present a provably secure method for password verification using combinatorial group theory. This method relies on the group randomizer system, a subset of the MAGNUS computer algebra system and corrects most of the present problems with challenge response systems, the most common types of password verification. Theoretical security of the considered method depends on several results in asymptotic group theory. We mention further that this method has applications for many other password situations including container security.",

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AU - Rosenberger, Gerhard

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N2 - Password security is a crucial component of modern internet security. In this paper, we present a provably secure method for password verification using combinatorial group theory. This method relies on the group randomizer system, a subset of the MAGNUS computer algebra system and corrects most of the present problems with challenge response systems, the most common types of password verification. Theoretical security of the considered method depends on several results in asymptotic group theory. We mention further that this method has applications for many other password situations including container security.

AB - Password security is a crucial component of modern internet security. In this paper, we present a provably secure method for password verification using combinatorial group theory. This method relies on the group randomizer system, a subset of the MAGNUS computer algebra system and corrects most of the present problems with challenge response systems, the most common types of password verification. Theoretical security of the considered method depends on several results in asymptotic group theory. We mention further that this method has applications for many other password situations including container security.

KW - Password Security

KW - Combinatorial Group Theory

KW - Free Group Cryptography

KW - Group Randomizer System

UR - https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/59

U2 - 10.4236/jis.2018.92011

DO - 10.4236/jis.2018.92011

M3 - Article

VL - 9

JO - Journal of Information Security

JF - Journal of Information Security

ER -

Secure Passwords Using Combinatorial Group Theory

Abstract

Keywords

Disciplines

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