Novel Authentication Protocols Based on Quadratic Diophantine Equations

Avinash Vijayarangan, Veena Narayanan (), Vijayarangan Natarajan and Srikanth Raghavendran
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Avinash Vijayarangan: School of Computing, SASTRA Deemed University, Thanjavur 613401, India
Veena Narayanan: School of Arts, Science, Humanities and Education, SASTRA Deemed University, Thanjavur 613401, India
Vijayarangan Natarajan: Travel and Hospitality-Strategic Initiative Group, TCS Ltd., Chennai 600113, India
Srikanth Raghavendran: School of Arts, Science, Humanities and Education, SASTRA Deemed University, Thanjavur 613401, India

Mathematics, 2022, vol. 10, issue 17, 1-10

Abstract: The Diophantine equation is a strong research domain in number theory with extensive cryptography applications. The goal of this paper is to describe certain geometric properties of positive integral solutions of the quadratic Diophantine equation x 1 2 + x 2 2 = y 1 2 + y 2 2 ( x 1 , x 2 , y 1 , y 2 > 0 ) , as well as their use in communication protocols. Given one pair ( x 1 , y 1 ) , finding another pair ( x 2 , y 2 ) satisfying x 1 2 + x 2 2 = y 1 2 + y 2 2 is a challenge. A novel secure authentication mechanism based on the positive integral solutions of the quadratic Diophantine which can be employed in the generation of one-time passwords or e-tokens for cryptography applications is presented. Further, the constructive cost models are applied to predict the initial effort and cost of the proposed authentication schemes.

Keywords: Diophanitne equation; trapdoor functions; authentication communication protocols (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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