New Explicit Conditions of Elliptic Curve Traces for FR-Reduction

Keywords

Hessian form of an elliptic curve, Elliptic curve point multiplication, Tripling-oriented Doche–Icart–Kohel curve, Schoof's algorithm, Jacobian curve

References

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Cited by

• Constructing Families of Pairing-Friendly Elliptic CurvesDavid Mandell Freeman — 2005
• New paradigms in signature schemesDan Boneh, Hovav Shacham — 2005
• AC ertificateless Signature Scheme based on Bilinear Pairing FunctionsRouto Terada, Denise Goya — 2007
• 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
• Applications of elliptic curve pairings in cryptographyColin Boyd — 2008
• Pairings in Cryptology: efficiency, security and applicationsManuel Charlemagne — 2010
• Contributions to pairing-based cryptographyTsz Hon Yuen — 2010
• Faster Pairing ComputationChristophe Arène, Tanja Lange, Michael Naehrig — 2009
• Implementing cryptographic pairingsMichael Scott — 2007
• Attribute-Based Traitor TracingYongtao Wang, Kefei Chen, Jianhong Chen — 2011
• Fault Attack, Countermeasures on Pairing Based CryptographySantosh Ghosh, Debdeep Mukhopadhyay, Dipanwita Roy Chowdhury — 2011
• Developing an Automatic Generation Tool for Cryptographic Pairing FunctionsD. Royo Pérez, Luis Felipe de Julián — 2011
• Security and privacy in RFID systems. (Sécurité et protection de la vie privée dans les systèmes RFID)Kaoutar Elkhiyaoui — 2012
• On small degree extension fields in cryptologyRobert Granger — 2005
• Investigating power and fault analysis with specific application to bilinear pairingsClaire Whelan — 2007
• Fast Formulas for Computing Cryptographic PairingsCraig Costello — 2012
• Toward Efficient Certificateless Signcryption from (and without) Bilinear PairingsPaulo S. L. M. Barreto, Alexandre Machado Deusajute, Eduardo de Souza Cruz — 2008
• Efficient Arithmetic on Low-Genus CurvesPeter Birkner — 2008
• L' anonymat dans les protocoles cryptographiquesMalika Izabachène — 2009

Related papers

• Cryptosystems based on pairingM. Kasahara — 2000
• Pairing-Friendly Elliptic Curves of Prime OrderPaulo S. L. M. Barreto, Michael Naehrig — 2005
• Elliptic curve public key cryptosystemsAlfred Menezes — 1993
• The Eta Pairing RevisitedF. Hess, Nigel P. Smart, Fréderik Vercauteren — 2006
• A remark concerning m -divisibility and the discrete logarithm in the divisor class group of curvesGerhard Frey, Hans-Georg Rück — 1994
• The Improbability That an Elliptic Curve Has Subexponential Discrete Log Problem under the Menezes—Okamoto—Vanstone AlgorithmR. Balasubramanian, Neal Koblitz — 1998
• A Taxonomy of Pairing-Friendly Elliptic CurvesDavid Mandell Freeman, Michael Scott, Edlyn Teske — 2010