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Efficient generation of pairing friendly elliptic curves

Matjaž Praprotnik (2016) Efficient generation of pairing friendly elliptic curves. MSc thesis.

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    Pairings on elliptic curves have become very popular in the decade due to the possibility of implementing modern cryptographic schemes and protocols based on the pairings. For pairings to be effective, special kind of elliptic curves are required. Construction of such curves combines knowledge from algebraic geometry, number theory and cryptography. This is the main reason, that pairings are not implemented as often as they could be. The purpose of this thesis is to present elliptic curves and pairings on elliptic curves, constructing of pairing friendly elliptic curves and researching their use and efficient implementation. The thesis also contains required preliminaries from algebraic geometry and number theory. The thesis contains four parts divided in to eight chapters. The first surveys the history of pairings in Chapter 1; Chapter 2 defines pairings, types of pairings and describes bilinear Diffie-Hellman's problem. Algebraic geometry and basic theory on elliptic curves, required for understanding are presented in the second part. It contains definition of algebraic varieties and their properties in Chapter 3 and elliptic curves and their properties in Chapter 4. The third part of the thesis introduces pairings on elliptic curves: Chapter 5 presents pairings and related algorithms, Chapter 6 includes examples of the use of pairings in cryptography. The main part of the thesis is Chapter 7. It includes the definition of pairing friendly curves and all known constructions of pairing friendly curves together with the proofs of these constructions. It also contains recommendations for further implementation and optimization. Conclusion lists some open problems regarding pairings and pairing friendly curves. Mathematical preliminaries required throughout the thesis and examples of pairing friendly curves can be found in the Appendices.

    Item Type: Thesis (MSc thesis)
    Keywords: Elliptic Curves, Pairing, Pairing Friendly Elliptic Curves, Public-Key Cryptography, Efficient Implementation
    Number of Pages: 175
    Language of Content: Slovenian
    Mentor / Comentors:
    Name and SurnameIDFunction
    prof. dr. Aleksandar Jurišić1118Mentor
    doc. dr. Anita BuckleyComentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1537130691)
    Institution: University of Ljubljana
    Department: Faculty of Computer and Information Science
    Item ID: 3591
    Date Deposited: 14 Sep 2016 12:52
    Last Modified: 22 Sep 2016 09:41
    URI: http://eprints.fri.uni-lj.si/id/eprint/3591

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