A Cryptosystem Based on the Weil Pairing on an Elliptic Curve

Paxton, Laura Gioanna (2024) A Cryptosystem Based on the Weil Pairing on an Elliptic Curve. Bachelor's Thesis, Mathematics.

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Abstract

This thesis extends Lawrence C. Washington’s Cryptosystem based on Boneh and Franklins Identity-Based Encryption (IBE) to novel parameters such as the elliptic curve, the endomorohims belonging to it and the finite fields that determine the algebraic structures. The research aims to mathematically dissect the cryptosystem’s functionality and security through a detailed analysis of these new parameters. The study focuses on constructing a modified Weil pairing that meets the requirements of the cryptosystem in question. Key findings include the identification of specific conditions for the primes p and ℓ to ensure compatibility of the elliptic curve and endomorphism with the modified Weil pairing. The thesis provides a comprehensive blueprint for future cryptographic research and implementations by detailing the necessary conditions for integrating new parameters. It also suggests potential for adapting parameters from other sources for future work. Organized into five chapters, the thesis begins with an overview of elliptic curve cryptography and IBE schemes, followed by an outline of the proposed cryptosystem and its requirements. It then presents an analysis of the new parameters and concludes with an implementation using Magma. The findings offer a robust mathematical framework for the cryptosystem and pave the way for further advancements.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Top, J. and Salgado Guimaraes da Silva, C.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	08 Aug 2024 14:36
Last Modified:	08 Aug 2024 14:36
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/33910

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