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Novel Authentication Protocols Based on Quadratic Diophantine Equations

Author

Listed:
  • Avinash Vijayarangan

    (School of Computing, SASTRA Deemed University, Thanjavur 613401, India
    These authors contributed equally to this work.)

  • Veena Narayanan

    (School of Arts, Science, Humanities and Education, SASTRA Deemed University, Thanjavur 613401, India
    These authors contributed equally to this work.)

  • Vijayarangan Natarajan

    (Travel and Hospitality-Strategic Initiative Group, TCS Ltd., Chennai 600113, India
    These authors contributed equally to this work.)

  • Srikanth Raghavendran

    (School of Arts, Science, Humanities and Education, SASTRA Deemed University, Thanjavur 613401, India
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Avinash Vijayarangan & Veena Narayanan & Vijayarangan Natarajan & Srikanth Raghavendran, 2022. "Novel Authentication Protocols Based on Quadratic Diophantine Equations," Mathematics, MDPI, vol. 10(17), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3136-:d:903796
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    References listed on IDEAS

    as
    1. Farrah Kristel Batista & Angel Martín del Rey & Araceli Queiruga-Dios, 2020. "A New Individual-Based Model to Simulate Malware Propagation in Wireless Sensor Networks," Mathematics, MDPI, vol. 8(3), pages 1-23, March.
    2. Víctor Gayoso Martínez & Luis Hernández-Álvarez & Luis Hernández Encinas, 2020. "Analysis of the Cryptographic Tools for Blockchain and Bitcoin," Mathematics, MDPI, vol. 8(1), pages 1-14, January.
    3. Luis Hernández-Álvarez & Juan José Bullón Pérez & Farrah Kristel Batista & Araceli Queiruga-Dios, 2022. "Security Threats and Cryptographic Protocols for Medical Wearables," Mathematics, MDPI, vol. 10(6), pages 1-17, March.
    Full references (including those not matched with items on IDEAS)

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