Generating More MNT Elliptic Curves

Michael Scott, Paulo S. L. M. Barreto · Des. Codes Cryptogr. · 2006

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Summary

An alternative derivation of Miyaji et al.'s results for the creation of elliptic curves of prime order with embedding degree 3, 4, or 6 is provided.

Type: article
Published: 2006-02-01
Cited by: 99
References: 17
DOI: https://doi.org/10.1007/s10623-005-0538-1
OpenAlex: https://openalex.org/W2070030672
Semantic Scholar: https://api.semanticscholar.org/CorpusID:9552969

Keywords

Elliptic curve, Mathematics, Mathematical analysis

References

The arithmetic of elliptic curvesJoseph H. Silverman — 1986
Discrete Logarithms: The Past and the FutureAndrew Odlyzko — 2000
New Explicit Conditions of Elliptic Curve Traces for FR-ReductionAtsuko Miyaji, Masaki Nakabayashi, Shunzou Takano — 2001
Elliptic Curves Suitable for Pairing Based CryptographyFriederike Brezing, Annegret Weng — 2005
Prime numbers: A computational perspectiveRichard E. Crandall, Carl Pomerance — 2002
Short Signatures from the Weil PairingDan Boneh, Ben Lynn, Hovav Shacham — 2001
Building Curves with Arbitrary Small MOV Degree over Finite Prime FieldsRégis Dupont, Andreas Enge, François Morain — 2005
Fast evaluation of logarithms in fields of characteristic twoDon Coppersmith — 1984
Elliptic curve public key cryptosystemsAlfred Menezes — 1993
Finite fieldsRudolf Lide, Harald Niederreiter — 1983
Efficient Algorithms for Pairing-Based CryptosystemsPaulo S. L. M. Barreto, Hae Yong Kim, Ben Lynn — 2002
Signcryption scheme for Identity-based CryptosystemsDivya Nalla, Karthik Reddy — 2003
AN IDENTITY BASED AUTHENTICATED KEY AGREEMENT PROTOCOL BASED ON THE WEIL PAIRINGNigel P. Smart — 2001
Prime NumbersRichard S. Crandall, Carl Pomerance — 2001
Constructing Elliptic Curves with Prescribed Embedding DegreesPaulo S. L. M. Barreto, Ben Lynn, Michael Scott — 2002
Identity-Based Encryption from the Weil PairingDan Boneh, Matthew Franklin — 2001
Implementing the Tate PairingS. Galbraith, K. Harrison, David Soldera — 2002
An Efficient Signature Scheme from Bilinear Pairings and Its ApplicationsFangguo Zhang, R. Safavi-Naini, W. Susilo — 2004

Cited by

Evaluating elliptic curve based KEMs in the light of pairingsDavid Galindo, Sebastià Martín Mollevi, Jorge L. Villar — 2004
Problèmes autour de courbes élliptiques et modulairesMin Sha — 2013
Special polynomial families for generating more suitable pairing-friendly elliptic curvesPu Duan, Shi Cui, Choong Wah Chan — 2006
Contributions to pairing-based cryptographyTsz Hon Yuen — 2010
A Java based software solution for efficient pairing cryptography.Yejun Zou — 2010
Fast Formulas for Computing Cryptographic PairingsCraig Costello — 2012
ペアリングベースの楕円曲線暗号に適した曲線の構成法(応用,数論アルゴリズムとその応用, 平成19年研究部会連合発表会)覚田中, 憲中村 — 2007
Constructing elliptic curves over finite fields using complex multiplicationØystein Øvreås Thuen — 2006
Pairing-Based Cryptography – Pairing 2013Zhenfu Cao, Fanggo Zhang — 2013
Traceability, linkability and policy hiding in attribute-based signature schemesAli El Kaafarani — 2015
On the Efficiency and Security of Cryptographic PairingsEdward Knapp — 2012
Faster Pairing Computations on Curves with High-Degree TwistsCraig Costello, Tanja Lange, Michael Naehrig — 2010
Topics in Geometry, Coding Theory and CryptographyArnaldo Garcia — 2010
Introducing Ramanujan's Class Polynomials in the Generation of Prime Order Elliptic CurvesElisavet KonstantinouAristides Kontogeorgis — 2008
Anonymous, Secure and Efficient Vehicular CommunicationsXiaoting Sun — 2007
Algebraic curves and cryptographySteven D. Galbraith⋆, Alfred Menezes — 2005
On the Efficient Generation of Prime-Order Elliptic CurvesElisavet Konstantinou, Aristides Kontogeorgis, Yannis C. Stamatiou — 2010
A Taxonomy of Pairing-Friendly Elliptic CurvesDavid Mandell Freeman, Michael Scott, Edlyn Teske — 2010
On the security of generalized Jacobian cryptosystemsIsabelle Déchène — 2007
Ordinary abelian varieties having small embedding degreeSteven D. Galbraith⋆, James McKee, P. C. Valença — 2007

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