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Tomáš Novotný

Bachelor's thesis

Cycles of pairing-friendly elliptic curves and their applications in cryptography

Cycles of pairing-friendly elliptic curves and their applications in cryptography
Abstract:
Moderní zero-knowledge protokoly zk-SNARKs využívají 2-cykly eliptických křivek, kde často požadujeme, aby příslušné křivky byly pairing-friendly a měly vysokou 2-adicitu. Jediné známé pairing-friendly cykly pocházejí z rodin MNT4 a MNT6; ty však nejsou dostatečně efektivní. V práci ukazujeme, že 2-cyklus obsahující MNT3 křivku nemůže být pairing-friendly; pro další rodiny máme podobný výsledek pro …more
Abstract:
Modern zk-SNARK protocols use 2-cycles of elliptic curves, where we often require that the curves are pairing-friendly and have a high 2-adicity. The only known pairing-friendly cycles come from the MNT4 and MNT6 families; however, they are ineffective. This work shows that a 2-cycle containing an MNT3 curve cannot be pairing-friendly; for other families, we have a similar result for cryptographically …more
 

Keywords

elliptic curve elliptic curve cycle family of elliptic curves cyclotomic polynomial zk-SNARK
 
Language used: English
Date on which the thesis was submitted / produced: 25. 5. 2021
Identifier: https://is.muni.cz/th/dsib4/

Thesis defence

  • Date of defence: 29. 6. 2021
  • Supervisor: RNDr. Vladimír Sedláček
  • Reader: Mgr. Marek Sýs, Ph.D.

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Institution archiving the thesis and making it accessible: Masarykova univerzita, Fakulta informatiky
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Masaryk University

Faculty of Informatics

Bachelor programme / field:
Informatics / Mathematical Informatics

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