2017

titre
qDSA: Small and Secure Digital Signatures with Curve-based Diffie–Hellman Key Pairs
auteur
Joost Renes, Benjamin Smith
Resume_court
qDSA is a high-speed, high-security signature scheme that facilitates implementations with a very sm .....
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-01585322/file/xkummer.pdf BibTex
titre
Montgomery curves and their arithmetic
auteur
Craig Costello, Benjamin Smith
Resume_court
Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factori .....
DOI
DOI : 10.1007/s13389-017-0157-6
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-01483768/file/Monty_arxiv.pdf BibTex
titre
Distributions of traces of Frobenius for smooth plane curves over finite fields
auteur
Christophe Ritzenthaler, Reynald Lercier, Florent Rovetta, Jeroen Sijsling, Benjamin Smith
Resume_court
In a previous article, we obtained data on the distribution of traces of Frobenius of non-hyperellip .....
DOI
DOI : 10.1080/10586458.2017.1328321
Accès au bibtex
https://arxiv.org/pdf/1510.05601 BibTex

2016

titre
Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
auteur
Sean Ballentine, Aurore Guillevic, Elisa Lorenzo García, Chloe Martindale, Maike Massierer, Benjamin Smith, Jaap Top, Elisa García
Resume_court
Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomia .....
DOI
DOI : 10.1007/978-3-319-63931-4
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-01421031/file/Isogenies_point_counting_genus2RM_17.pdf BibTex
titre
Computing cardinalities of Q-curve reductions over finite fields
auteur
François Morain, Charlotte Scribot, Benjamin Smith
Resume_court
We present a specialized point-counting algorithm for a class of elliptic curves over F_{p^2} that i .....
DOI
DOI : 10.1112/S1461157016000267
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-01320388/file/qcsea.pdf BibTex
titre
Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers
auteur
Ping Ngai Chung, Craig Costello, Benjamin Smith
Resume_court
We give one-and two-dimensional scalar multiplication algorithms for Jacobians of genus 2 curves tha .....
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https://hal.inria.fr/hal-01353480/file/recovery.pdf BibTex
titre
The Q-curve construction for endomorphism-accelerated elliptic curves
auteur
Benjamin Smith
Resume_court
We give a detailed account of the use of $\mathbb{Q}$-curve reductions to construct elliptic curves .....
DOI
DOI : 10.1007/s00145-015-9210-8
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-01064255/file/smith-qcurves.pdf BibTex
titre
Factoring Safe Semiprimes with a Single Quantum Query
auteur
Frédéric Grosshans, Thomas Lawson, Benjamin Smith, François Morain
Resume_court
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potent .....
Accès au bibtex
https://arxiv.org/pdf/1511.04385 BibTex
titre
$\mu$Kummer: efficient hyperelliptic signatures and key exchange on microcontrollers
auteur
Joost Renes, Peter Schwabe, Benjamin Smith, Lejla Batina
Resume_court
We describe the design and implementation of efficient signature and key-exchange schemes for the AV .....
DOI
DOI : 10.1007/978-3-662-53140-2_15
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-01300727/file/mukummer.pdf BibTex

2015

titre
Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians
auteur
Benjamin Smith
Resume_court
The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions usi .....
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-00874925/file/easy.pdf BibTex
titre
Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
auteur
Ping Ngai Chung, Craig Costello, Benjamin Smith
Resume_court
We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication .....
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-01214259/file/recovery.pdf BibTex

2014

titre
Faster Compact Diffie-Hellman: Endomorphisms on the x-line
auteur
Craig Costello, Huseyin Hisil, Benjamin Smith
Resume_court
We describe an implementation of fast elliptic curve scalar multiplication, optimized for Diffie--He .....
DOI
DOI : 10.1007/978-3-642-55220-5_11
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-00932952/file/main.pdf BibTex

2013

titre
Families of fast elliptic curves from Q-curves
auteur
Benjamin Smith
Resume_court
We construct new families of elliptic curves over \(\FF_{p^2}\) with efficiently computable endomorp .....
DOI
DOI : 10.1007/978-3-642-42033-7_4
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-00825287/file/qc-hal.pdf BibTex

2012

titre
Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method
auteur
Benjamin Smith
Resume_court
Let ell be a prime, and H a curve of genus 2 over a field k of characteristic not 2 or ell. If S is .....
Accès au texte intégral et bibtex
https://hal.inria.fr/inria-00632118/file/isogenies.pdf BibTex

2011

titre
Families of explicitly isogenous Jacobians of variable-separated curves
auteur
Benjamin Smith
Resume_court
We construct six infinite series of families of pairs of curves (X,Y) of arbitrarily high genus, def .....
DOI
DOI : 10.1112/S1461157010000410
Accès au texte intégral et bibtex
https://hal.inria.fr/inria-00516038/file/isogenies.pdf BibTex
titre
Counting Points on Genus 2 Curves with Real Multiplication
auteur
Pierrick Gaudry, David Kohel, Benjamin Smith
Resume_court
We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with a .....
DOI
DOI : 10.1007/978-3-642-25385-0_27
Accès au texte intégral et bibtex
https://hal.inria.fr/inria-00598029/file/paper.pdf BibTex

2009

titre
Distortion maps for supersingular genus two curves
auteur
Steven Galbraith, Christophe Ritzenthaler, Jordi Pujolas, Benjamin Smith
Resume_court
Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the .....
DOI
DOI : 10.1515/JMC.2009.001
Accès au bibtex
BibTex
titre
Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves
auteur
Benjamin Smith
Resume_court
We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem ( .....
DOI
DOI : 10.1007/s00145-009-9038-1
Accès au bibtex
https://arxiv.org/pdf/0806.2995 BibTex
titre
Families of Explicit Isogenies of Hyperelliptic Jacobians
auteur
Benjamin Smith
Resume_court
We construct three-dimensional families of hyperelliptic curves of genus 6, 12, and 14, two-dimensio .....
Accès au texte intégral et bibtex
https://hal.inria.fr/inria-00420605/file/isogenies.pdf BibTex

2008

titre
Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves
auteur
Benjamin Smith
Resume_court
We describe the use of explicit isogenies to reduce Discrete Logarithm Problems (DLPs) on Jacobians .....
DOI
DOI : 10.1007/978-3-540-78967-3_10
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BibTex

2006

titre
Discrete Logarithms in Generalized Jacobians
auteur
S. D. Galbraith, Benjamin Smith
Resume_court
Déchène has proposed generalized Jacobians as a source of groups for public-key cryptosystems base .....
Accès au bibtex
https://arxiv.org/pdf/math.NT/0610073 BibTex
titre
Efficiently Computable Endomorphisms for Hyperelliptic Curves
auteur
David Kohel, Benjamin Smith
Resume_court
Elliptic curves have a well-known and explicit theory for the construction and application of endomo .....
DOI
DOI : 10.1007/11792086_35
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BibTex