Publications HAL de Benjamin,Smith du labo/EPI GRACE;TANC;SMS;RHUL

2024

titre: Efficient $(3,3)$-isogenies on fast Kummer surfaces
auteur: Maria Corte-Real Santos, Craig Costello, Benjamin Smith
Resume_court: We give an alternative derivation of $(N,N)$-isogenies between fast Kummer surfaces which complement .....
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2023

titre: Fast and Frobenius: Rational Isogeny Evaluation over Finite Fields
auteur: Gustavo Banegas, Valerie Gilchrist, Anaëlle Le Dévéhat, Benjamin Smith
Resume_court: Consider the problem of efficiently evaluating isogenies $\phi: E \to E/H$ of elliptic curves over a .....
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titre: WAVE
auteur: Gustavo Banegas, Kevin Carrier, André Chailloux, Alain Couvreur, Thomas Debris-Alazard, Philippe Gaborit, Pierre Karpman, Johanna Loyer, Ruben Niederhagen, Nicolas Sendrier, Benjamin Smith, Jean-Pierre Tillich
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titre: Deterministic factoring with oracles
auteur: François Morain, Guénaël Renault, Benjamin Smith
Resume_court: We revisit the problem of integer factorization with number-theoretic oracles, including a well-know .....
DOI: DOI : 10.1007/s00200-021-00521-8
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titre: Advances in asymmetric cryptographic algorithms
auteur: Benjamin Smith
Resume_court: This document gives a synthetic overview of my research since 2006. It is focused on algorithms for .....
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2022

titre: An atlas of the Richelot isogeny graph
auteur: Enric Florit, Benjamin Smith
Resume_court: We describe and illustrate the local neighbourhoods of vertices and edges in the (2, 2)-isogeny grap .....
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titre: Higher-degree supersingular group actions
auteur: Mathilde Chenu, Benjamin Smith
Resume_court: We investigate the isogeny graphs of supersingular elliptic curves over $\mathbb{F}_{p^2}$ equipped .....
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titre: Efficient supersingularity testing over F_p and CSIDH key validation
auteur: Gustavo Banegas, Valerie Gilchrist, Benjamin Smith
Resume_court: Many public-key cryptographic protocols, notably non-interactive key exchange (NIKE), require incomi .....
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titre: Quantum-Resistant Software Update Security on Low-Power Networked Embedded Devices
auteur: Gustavo Banegas, Koen Zandberg, Emmanuel Baccelli, Adrian Herrmann, Benjamin Smith
DOI: DOI : 10.1007/978-3-031-09234-3_43
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titre: Failing to hash into supersingular isogeny graphs
auteur: Jeremy Booher, Ross Bowden, Javad Doliskani, Tako Boris Fouotsa, Steven Galbraith, Sabrina Kunzweiler, Simon-Philipp Merz, Christophe Petit, Benjamin Smith, Katherine E. Stange, Yan Bo Ti, Christelle Vincent, José Felipe Voloch, Charlotte Weitkämper, Lukas Zobernig
Resume_court: An important open problem in supersingular isogeny-based cryptography is to produce, without a trust .....
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titre: Trustless unknown-order groups
auteur: Samuel Dobson, Steven Galbraith, Benjamin Smith
Resume_court: Groups of unknown order are of major interest due to their applications including time-lock puzzles, .....
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2021

titre: Quantum-Resistant Security for Software Updates on Low-power Networked Embedded Devices
auteur: Gustavo Banegas, Koen Zandberg, Adrian Herrmann, Emmanuel Baccelli, Benjamin Smith
Resume_court: As the Internet of Things (IoT) rolls out today to devices whose lifetime may well exceed a decade, .....
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titre: CTIDH: Faster constant-time CSIDH
auteur: Gustavo Banegas, Daniel J. Bernstein, Fabio Campos, Tung Chou, Tanja Lange, Michael Meyer, Benjamin Smith, Jana Sotáková
Resume_court: This paper introduces a new key space for CSIDH and a new algorithm for constant-time evaluation of .....
DOI: DOI : 10.46586/tches.v2021.i4.351-387
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titre: Extending the GLS endomorphism to speed up GHS Weil descent using Magma
auteur: Jesús-Javier Chi-Domínguez, Francisco Rodríguez-Henríquez, Benjamin Smith
Resume_court: Let $q = 2^n$, and let $E / \mathbb{F}_{q^{\ell}}$ be a generalized Galbraith--Lin--Scott (GLS) bina .....
DOI: DOI : 10.1016/j.ffa.2021.101891
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titre: Quantum Equivalence of the DLP and CDHP for Group Actions
auteur: Steven Galbraith, Lorenz Panny, Benjamin Smith, Frederik Vercauteren
Resume_court: In this short note we give a polynomial-time quantum reduction from the vectorization problem (DLP) .....
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titre: Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph
auteur: Enric Florit, Benjamin Smith
Resume_court: We investigate special structures due to automorphisms in isogeny graphs of principally polarized ab .....
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titre: Wavelet: Code-based postquantum signatures with fast verification on microcontrollers
auteur: Gustavo Banegas, Thomas Debris-Alazard, Milena Nedeljković, Benjamin Smith
Resume_court: This work presents the first full implementation of Wave, a postquantum code-based signature scheme. .....
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2020

titre: The supersingular isogeny problem in genus 2 and beyond
auteur: Craig Costello, Benjamin Smith
Resume_court: Let $A/\overline{\mathbb{F}}_p$ and $A'/\overline{\mathbb{F}}_p$ be supersingular principally polari .....
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titre: Hash functions from superspecial genus-2 curves using Richelot isogenies
auteur: Wouter Castryck, Thomas Decru, Benjamin Smith
Resume_court: Last year Takashima proposed a version of Charles, Goren and Lauter's hash function using Richelot i .....
DOI: DOI : 10.1515/jmc-2019-0021
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titre: Faster computation of isogenies of large prime degree
auteur: Daniel J. Bernstein, Luca de Feo, Antonin Leroux, Benjamin Smith
Resume_court: Let $\mathcal{E}/\mathbb{F}_q$ be an elliptic curve, and $P$ a point in $\mathcal{E}(\mathbb{F}_q)$ .....
DOI: DOI : 10.2140/obs.2020.4.39
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2019

titre: Distributions of traces of Frobenius for smooth plane curves over finite fields
auteur: Reynald Lercier, Christophe Ritzenthaler, 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
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titre: Stronger and Faster Side-Channel Protections for CSIDH
auteur: Daniel Cervantes-Vázquez, Mathilde Chenu, Jesús-Javier Chi-Domínguez, Luca de Feo, Francisco Rodríguez-Henríquez, Benjamin Smith
Resume_court: CSIDH is a recent quantum-resistant primitive based on the difficulty of finding isogeny paths betwe .....
DOI: DOI : 10.1007/978-3-030-30530-7_9
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2018

titre: Towards practical key exchange from ordinary isogeny graphs
auteur: Luca de Feo, Jean Kieffer, Benjamin Smith
Resume_court: We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev-Stolbunov, lo .....
DOI: DOI : 10.1007/978-3-030-03332-3_14
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titre: Pre- and post-quantum Diffie-Hellman from groups, actions, and isogenies
auteur: Benjamin Smith
Resume_court: Diffie-Hellman key exchange is at the foundations of public-key cryptography, but conventional group .....
DOI: DOI : 10.1007/978-3-030-05153-2_1
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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 .....
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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
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2016

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
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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
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_3
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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 .....
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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
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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
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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 .....
DOI: DOI : 10.1007/978-3-319-69453-5_25
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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 .....
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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 .....
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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
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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
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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 .....
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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
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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
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2009

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 .....
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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
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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
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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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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 .....
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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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