Publications (59)
Towards practical key exchange from ordinary isogeny graphs
Luca De Feo, Jean Kieffer, Benjamin Smith
We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev-Stolbunov, long dismissed as impractical. We give algorithmic improvements that accelerate ke…
qDSA: Small and Secure Digital Signatures with Curve-based Diffie--Hellman Key Pairs
Joost Renes, Benjamin Smith
qDSA is a high-speed, high-security signature scheme that facilitates implementations with a very small memory footprint, a crucial requirement for embedded systems and IoT devices…
From Knowledge to Action: Outcomes of the 2025 Large Language Model (LLM) Hackathon for Applications in Materials Science and Chemistry
Aritra Roy, Kevin Shen, Andrew MacBride +350
Large language models (LLMs) are rapidly changing how researchers in materials science and chemistry discover, organize, and act on scientific knowledge. This paper analyzes a broa…
Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method
Benjamin Smith
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 a maximal Weil-isotropic subgroup of Jac(H)[ell], then Jac(H)/S is isomorphic to…
Factoring Safe Semiprimes with a Single Quantum Query
Frédéric Grosshans, Thomas Lawson, François Morain +1
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order…
Polyamorous Scheduling
Leszek GÄ sieniec, Benjamin Smith, Sebastian Wild
Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationship…
Creating a Cooperative AI Policymaking Platform through Open Source Collaboration
Aiden Lewington, Alekhya Vittalam, Anshumaan Singh +48
Advances in artificial intelligence (AI) present significant risks and opportunities, requiring improved governance to mitigate societal harms and promote equitable benefits. Curre…
Simple approximation algorithms for Polyamorous Scheduling
Yuriy Biktairov, Leszek GÄ sieniec, Wanchote Po Jiamjitrak +3
In Polyamorous Scheduling, we are given an edge-weighted graph and must find a periodic schedule of matchings in this graph which minimizes the maximal weighted waiting time betwee…
The supersingular isogeny problem in genus 2 and beyond
Craig Costello, Benjamin Smith
Let and be supersingular principally polarized abelian varieties of dimension . For any prime , we give…
Families of explicitly isogenous Jacobians of variable-separated curves
Benjamin Smith
We construct six infinite series of families of pairs of curves (X,Y) of arbitrarily high genus, defined over number fields, together with an explicit isogeny from the Jacobian of…
Distributions of traces of Frobenius for smooth plane curves over finite fields
Reynald Lercier, Christophe Ritzenthaler, Florent Rovetta +2
In a previous article, we obtained data on the distribution of traces of Frobenius of non-hyperelliptic genus curves over small finite fields. In the present one, we give a heu…
Debiased Estimators in High-Dimensional Regression: A Review and Replication of Javanmard and Montanari (2014)
Benjamin Smith
High-dimensional statistical settings () pose fundamental challenges for classical inference, largely due to bias introduced by regularized estimators such as the LASSO. T…
Cessation of X-ray Pulsation of GX 1+4
Wei Cui, Benjamin Smith
We report results from our weekly monitoring campaign on the X-ray pulsar GX 1+4 with the {\em Rossi X-ray Timing Explorer} satellite. The spin-down trend of GX 1+4 was continuing,…
A new version of the CABLE land surface model, incorporating land-use change, woody vegetation demography and a novel optimisation-based approach to plant coordination of photosynthesis
Vanessa Haverd, Benjamin Smith, Lars Nieradzik +4
CABLE is a land surface model (LSM) that can be applied stand-alone, as well as providing for land surface-atmosphere exchange within the Australian Community Climate and Earth Sys…
Design and initial results from the "Junior" Levitated Dipole Experiment
Craig S. Chisholm, Thomas Berry, Darren T. Garnier +43
OpenStar Technologies is a private fusion company exploring the levitated dipole concept for commercial fusion energy production. OpenStar has manufactured a new generation of levi…
Gluing Quantum Spectral Curves: A Two-Copy osp(4|2) Construction
Filipp Chernikov, Simon Ekhammar, Nikolay Gromov +1
We propose a Quantum Spectral Curve for planar string theory on AdS3*S3*S3*S1 supported by pure Ramond-Ramond flux. Our proposal is built on symmetry considerations and integrabili…
Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
Ping Ngai Chung, Craig Costello, Benjamin Smith
We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus 2 curves that operate by…
Diagonalising the LEFT
Sophie Renner, Benjamin Smith, Dave Sutherland
We organise the four-fermion vector current interactions below the weak scale -- i.e., in the low energy effective field theory (LEFT) -- into irreps of definite parity and …
Families of Explicit Isogenies of Hyperelliptic Jacobians
Benjamin Smith
We construct three-dimensional families of hyperelliptic curves of genus 6, 12, and 14, two-dimensional families of hyperelliptic curves of genus 3, 6, 7, 10, 20, and 30, and one-d…
Large Legislative Models: Towards Efficient AI Policymaking in Economic Simulations
Henry Gasztowtt, Benjamin Smith, Vincent Zhu +2
The improvement of economic policymaking presents an opportunity for broad societal benefit, a notion that has inspired research towards AI-driven policymaking tools. AI policymaki…
Failing to hash into supersingular isogeny graphs
Jeremy Booher, Ross Bowden, Javad Doliskani +12
An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of "hard supersingular curves" that is, equation…
Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph
Enric Florit, Benjamin Smith
We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular. We give theoretical and exp…
Ship Detection: Parameter Server Variant
Benjamin Smith
Deep learning ship detection in satellite optical imagery suffers from false positive occurrences with clouds, landmasses, and man-made objects that interfere with correct classifi…
Stronger and Faster Side-Channel Protections for CSIDH
Daniel Cervantes-Vázquez, Mathilde Chenu, Jesús-Javier Chi-DomÃnguez +3
CSIDH is a recent quantum-resistant primitive based on the difficulty of finding isogeny paths between supersingular curves. Recently, two constant-time versions of CSIDH have been…
Deterministic factoring with oracles
Fran{\c c}ois Morain, Gu{é}na{ë}l Renault, Benjamin Smith
We revisit the problem of integer factorization with number-theoretic oracles, including a well-known problem: can we factor an integer unconditionally, in deterministic polyno…
Quantum-Resistant Security for Software Updates on Low-power Networked Embedded Devices
Gustavo Banegas, Koen Zandberg, Adrian Herrmann +2
As the Internet of Things (IoT) rolls out today to devices whose lifetime may well exceed a decade, conservative threat models should consider attackers with access to quantum comp…
An atlas of the Richelot isogeny graph
Enric Florit, Benjamin Smith
We describe and illustrate the local neighbourhoods of vertices and edges in the (2, 2)-isogeny graph of principally polarized abelian surfaces, considering the action of automorph…
Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves
Benjamin Smith
We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem (DLP) from Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperell…
Multiway Powersort
William Cawley Gelling, Markus E. Nebel, Benjamin Smith +1
We present a stable mergesort variant, Multiway Powersort, that exploits existing runs and finds nearly-optimal merging orders for k-way merges with negligible overhead. This build…
Families of fast elliptic curves from Q-curves
Benjamin Smith
We construct new families of elliptic curves over \(\FF_{p^2}\) with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the…
Exploiting Load/Store Leakage of Sparse Vectors for Key Recovery in HQC
Gustavo Banegas, Benjamin Smith, Jad Zahreddine
Hamming Quasi-Cyclic (HQC) is a code-based key encapsulation mechanism selected by NIST for standardization, making its resistance to implementation attacks critically important. W…
Fast and Frobenius: Rational Isogeny Evaluation over Finite Fields
Gustavo Banegas, Valerie Gilchrist, Anaëlle Le Dévéhat +1
Consider the problem of efficiently evaluating isogenies of elliptic curves over a finite field , where the kernel is a cyclic…
Faster computation of isogenies of large prime degree
Daniel Bernstein, Luca de Feo, Antonin Leroux +1
Let be an elliptic curve, and a point in of prime order . Vélu's formulae let us compute a quotient curve $\mathca…
Higher-degree supersingular group actions
Mathilde Chenu, Benjamin Smith
We investigate the isogeny graphs of supersingular elliptic curves over equipped with a -isogeny to their Galois conjugate. These curves are interesting becau…
Montgomery curves and their arithmetic
Craig Costello, Benjamin Smith
Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them…
Wavelet: Code-based postquantum signatures with fast verification on microcontrollers
Gustavo Banegas, Thomas Debris-Alazard, Milena NedeljkoviÄ +1
This work presents the first full implementation of Wave, a postquantum code-based signature scheme. We define Wavelet, a concrete Wave scheme at the 128-bit classical security lev…
Kummer: efficient hyperelliptic signatures and key exchange on microcontrollers
Joost Renes, Peter Schwabe, Benjamin Smith +1
We describe the design and implementation of efficient signature and key-exchange schemes for the AVR ATmega and ARM Cortex M0 microcontrollers, targeting the 128-bit security leve…
Not All Timesteps Matter Equally: Selective Alignment Knowledge Distillation for Spiking Neural Networks
Kai Sun, Peibo Duan, Yongsheng Huang +4
Spiking neural networks (SNNs), which are brain-inspired and spike-driven, achieve high energy efficiency. However, a performance gap between SNNs and artificial neural networks (A…
Hash functions from superspecial genus-2 curves using Richelot isogenies
Wouter Castryck, Thomas Decru, Benjamin Smith
Last year Takashima proposed a version of Charles, Goren and Lauter's hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmeti…
Anomaly Detection with SDAE
Benjamin Smith, Kevin Cant, Gloria Wang
Anomaly detection is a prominent data preprocessing step in learning applications for correction and/or removal of faulty data. Automating this data type with the use of autoencode…
Compressed verification for post-quantum signatures with long-term public keys
Gustavo Banegas, Anaëlle Le Dévéhat, Benjamin Smith
Many signature applications-such as root certificates, secure software updates, and authentication protocols-involve long-lived public keys that are transferred or installed once a…
Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians
Benjamin Smith
The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions using efficient endomorphisms-including Gallant-Lambert-Vanstone (GLV) and Galbrait…
Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
Sean Ballentine, Aurore Guillevic, Elisa Lorenzo GarcÃa +4
Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations…
The Price of a Large Electron Yukawa Modification
Lukas Allwicher, Matthew McCullough, Sophie Renner +2
The theoretical implications of an electron Yukawa modification are considered in the context of a possible Higgs pole run at FCC-ee, aimed at bounding this coupling. We start from…
The Q-curve construction for endomorphism-accelerated elliptic curves
Benjamin Smith
We give a detailed account of the use of -curve reductions to construct elliptic curves over with efficiently computable endomorphisms, which can be…
Efficient -isogenies on fast Kummer surfaces
Maria Corte-Real Santos, Craig Costello, Benjamin Smith
We give an alternative derivation of -isogenies between fast Kummer surfaces which complements existing works based on the theory oftheta functions. We use this framework to…
Quantum Equivalence of the DLP and CDHP for Group Actions
Steven Galbraith, Lorenz Panny, Benjamin Smith +1
In this short note we give a polynomial-time quantum reduction from the vectorization problem (DLP) to the parallelization problem (CDHP) for group actions. Combined with the trivi…
Bridging Scene Understanding and Task Execution with Flexible Simulation Environments
Zachary Ravichandran, J. Daniel Griffith, Benjamin Smith +1
Significant progress has been made in scene understanding which seeks to build 3D, metric and object-oriented representations of the world. Concurrently, reinforcement learning has…
Trustless unknown-order groups
Samuel Dobson, Steven Galbraith, Benjamin Smith
Groups of unknown order are of major interest due to their applications including time-lock puzzles, verifiable delay functions, and accumulators. In this paper we focus on trustle…
Extending the GLS endomorphism to speed up GHS Weil descent using Magma
Jesús-Javier Chi-DomÃnguez, Francisco RodrÃguez-HenrÃquez, Benjamin Smith
Let , and let be a generalized Galbraith--Lin--Scott (GLS) binary curve, with and .We show that the GLS endomorphis…
Efficient Scene Compression for Visual-based Localization
Marcela Mera-Trujillo, Benjamin Smith, Victor Fragoso
Estimating the pose of a camera with respect to a 3D reconstruction or scene representation is a crucial step for many mixed reality and robotics applications. Given the vast amoun…
Centrality in Collaboration: A Novel Algorithm for Social Partitioning Gradients in Community Detection for Multiple Oncology Clinical Trial Enrollments
Benjamin Smith, Tyler Pittman, Wei Xu
Patients at a comprehensive cancer center who do not achieve cure or remission following standard treatments often become candidates for clinical trials. Patients who participate i…
Small-time, large-time and asymptotics for the Rough Heston model
Martin Forde, Stefan Gerhold, Benjamin Smith
We characterize the behaviour of the Rough Heston model introduced by Jaisson\&Rosenbaum \cite{JR16} in the small-time, large-time and (i.e. ) limits. We show t…
Computing cardinalities of Q-curve reductions over finite fields
François Morain, Charlotte Scribot, Benjamin Smith
We present a specialized point-counting algorithm for a class of elliptic curves over F\_{p^2} that includes reductions of quadratic Q-curves modulo inert primes and, more generall…
Towards the 5/6-Density Conjecture of Pinwheel Scheduling
Leszek GÄ sieniec, Benjamin Smith, Sebastian Wild
Pinwheel Scheduling aims to find a perpetual schedule for unit-length tasks on a single machine subject to given maximal time spans (a.k.a. frequencies) between any two consecutive…
Fairmetrics: An R package for group fairness evaluation
Benjamin Smith, Jianhui Gao, Jessica Gronsbell
Fairness is a growing area of machine learning (ML) that focuses on ensuring models do not produce systematically biased outcomes for specific groups, particularly those defined by…
Pre- and post-quantum Diffie-Hellman from groups, actions, and isogenies
Benjamin Smith
Diffie-Hellman key exchange is at the foundations of public-key cryptography, but conventional group-based Diffie-Hellman is vulnerable to Shor's quantum algorithm. A range of "pos…
Distortion maps for genus two curves
Steven D. Galbraith, Jordi Pujolà s, Christophe Ritzenthaler +1
Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated since the full…
Counting Points on Genus 2 Curves with Real Multiplication
Pierrick Gaudry, David Kohel, Benjamin Smith
We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm red…