Note on families of pairing-friendly elliptic curves with small embedding degree

DOI10.14495/jsiaml.8.61zbMath1409.11049arXiv1605.02328OpenAlexW2963254063MaRDI QIDQ3121464

Keiji Okano

Publication date: 18 March 2019

Published in: JSIAM Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.02328

zbMATH Keywords

elliptic curvespairing-based cryptographyembedding degree

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Elliptic curves (14H52) Curves over finite and local fields (11G20) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Uses Software

• ECPP
• zk-SNARK

Cites Work

• On the non-idealness of cyclotomic families of pairing-friendly elliptic curves
• A taxonomy of pairing-friendly elliptic curves
• Ordinary Abelian varieties having small embedding degree
• Elliptic curves suitable for pairing based cryptography
• Scalable Zero Knowledge via Cycles of Elliptic Curves
• Elliptic Curves and Primality Proving
• Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
• Identity-Based Encryption from the Weil Pairing
• On the ρ-values of complete families of pairing-friendly elliptic curves
• Pairing-Friendly Elliptic Curves of Prime Order

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