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Researcher profile

Benjamin Smith

Benjamin Smith contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.NTCryptography and SecurityArtificial IntelligenceMachine Learningcond-mat.mtrl-sciData Structures and Algorithmshep-ph

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Published work

17 published item(s)

preprint2026arXiv

Diagonalising the LEFT

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 $SU(N)$ flavour symmetry. Their coefficients are thus arranged into small subsets with distinct phenomenology, which are significantly smaller than traditional groupings of operators by individual fermion number. As these small subsets only mix among themselves, we show that the renormalisation group evolution is soluble semi-analytically, and examine the resulting eigenvalues and eigenvectors of the one- and two-loop running. This offers phenomenological insights, for example into the radiative stability of lepton flavour non-universality. We use these to study model-independent implications for $b\to s ττ$ decays, as well as setting indirect bounds on flavour changing four-quark interactions.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

From Knowledge to Action: Outcomes of the 2025 Large Language Model (LLM) Hackathon for Applications in Materials Science and Chemistry

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 broad set of community-developed LLM applications in an effort to identify emerging patterns in how these systems can be used across the scientific research lifecycle. We organize the projects into two complementary categories: Knowledge Infrastructure, systems that structure, retrieve, synthesize, and validate scientific information; and Action Systems, systems that execute, coordinate, or automate scientific work across computational and experimental environments. The submissions reveal a shift from single-purpose LLM tools toward integrated, multi-agent workflows that combine retrieval, reasoning, tool use, and domain-specific validation. Prominent themes include retrieval-augmented generation as grounding infrastructure, persistent structured knowledge representations, multimodal and multilingual scientific inputs, and early progress toward laboratory-integrated closed-loop systems. Together, these results suggest that LLMs are evolving from general-purpose assistants into composable infrastructure for scientific reasoning and action. This work provides a community snapshot of that transition and a practical taxonomy for understanding emerging LLM-enabled workflows in materials science and chemistry.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Not All Timesteps Matter Equally: Selective Alignment Knowledge Distillation for Spiking Neural Networks

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 (ANNs) still remains. Knowledge distillation (KD) is commonly adopted to improve SNN performance, but existing methods typically enforce uniform alignment across all timesteps, either from a teacher network or through inter-temporal self-distillation, implicitly assuming that per-timestep predictions should be treated equally. In practice, SNN predictions vary and evolve over time, and intermediate timesteps need not all be individually correct even when the final aggregated output is correct. Under such conditions, effective distillation should not force every timestep toward the same supervision target, but instead provide corrective guidance to erroneous timesteps while preserving useful temporal dynamics. To address this issue, we propose Selective Alignment Knowledge Distillation (SeAl-KD), which selectively aligns class-level and temporal knowledge by equalizing competing logits at erroneous timesteps and reweighting temporal alignment based on confidence and inter-timestep similarity. Extensive experiments on static image and neuromorphic event-based datasets demonstrate consistent improvements over existing distillation methods. The code is available at https://github.com/KaiSUN1/SeAl

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Multiway Powersort

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 builds on Powersort (Munro & Wild, ESA2018), which has recently replaced Timsort's suboptimal merge policy in the CPython reference implementation of Python, as well as in PyPy and further libraries. Multiway Powersort reduces the number of memory transfers, which increasingly determine the cost of internal sorting (as observed with Multiway Quicksort (Kushagra et al., ALENEX 2014; Aumüller & Dietzfelbinger, TALG 2016; Wild, PhD thesis 2016) and the inclusion of Dual-Pivot Quicksort in the Java runtime library). We demonstrate that our 4-way Powersort implementation can achieve substantial speedups over standard (2-way) Powersort and other stable sorting methods without compromising the optimally run-adaptive performance of Powersort.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph

We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular. We give theoretical and experimental results on the spectral and statistical properties of (2, 2)-isogeny graphs of superspecial abelian surfaces, including stationary distributions for random walks, bounds on eigenvalues and diameters, and a proof of the connectivity of the Jacobian subgraph of the (2, 2)-isogeny graph. Our results improve our understanding of the performance and security of some recently-proposed cryptosystems, and are also a concrete step towards a better understanding of general superspecial isogeny graphs in arbitrary dimension.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Anomaly Detection with SDAE

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 autoencoders could increase the quality of the dataset by isolating anomalies that were missed through manual or basic statistical analysis. A Simple, Deep, and Supervised Deep Autoencoder were trained and compared for anomaly detection over the ASHRAE building energy dataset. Given the restricted parameters under which the models were trained, the Deep Autoencoder perfoms the best, however, the Supervised Deep Autoencoder outperforms the other models in total anomalies detected when considerations for the test datasets are given.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Faster computation of isogenies of large prime degree

Let $\mathcal{E}/\mathbb{F}_q$ be an elliptic curve, and $P$ a point in $\mathcal{E}(\mathbb{F}_q)$ of prime order $\ell$. Vélu's formulae let us compute a quotient curve $\mathcal{E}' = \mathcal{E}/\langle{P}\rangle$ and rational maps defining a quotient isogeny $ϕ: \mathcal{E} \to \mathcal{E}'$ in $\tilde{O}(\ell)$ $\mathbb{F}_q$-operations, where the $\tilde{O}$ is uniform in $q$.This article shows how to compute $\mathcal{E}'$, and $ϕ(Q)$ for $Q$ in $\mathcal{E}(\mathbb{F}_q)$, using only $\tilde{O}(\sqrt{\ell})$ $\mathbb{F}_q$-operations, where the $\tilde{O}$ is again uniform in $q$.As an application, this article speeds up some computations used in the isogeny-based cryptosystems CSIDH and CSURF.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The supersingular isogeny problem in genus 2 and beyond

Let $A/\overline{\mathbb{F}}\_p$ and $A'/\overline{\mathbb{F}}\_p$ be supersingular principally polarized abelian varieties of dimension $g>1$. For any prime $\ell \ne p$, we give an algorithm that finds a path $ϕ\colon A \rightarrow A'$ in the $(\ell, \dots , \ell)$-isogeny graph in $\widetilde{O}(p^{g-1})$ group operations on a classical computer, and $\widetilde{O}(\sqrt{p^{g-1}})$ calls to the Grover oracle on a quantum computer. The idea is to find paths from $A$ and $A'$ to nodes that correspond to products of lower dimensional abelian varieties, and to recurse down in dimension until an elliptic path-finding algorithm (such as Delfs--Galbraith) can be invoked to connect the paths in dimension $g=1$. In the general case where $A$ and $A'$ are any two nodes in the graph, this algorithm presents an asymptotic improvement over all of the algorithms in the current literature. In the special case where $A$ and $A'$ are a known and relatively small number of steps away from each other (as is the case in higher dimensional analogues of SIDH), it gives an asymptotic improvement over the quantum claw finding algorithms and an asymptotic improvement over the classical van Oorschot--Wiener algorithm.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

$μ$Kummer: efficient hyperelliptic signatures and key exchange on microcontrollers

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 level. Our algorithms are based on an efficient Montgomery ladder scalar multiplication on the Kummer surface of Gaudry and Schost's genus-2 hyperelliptic curve, combined with the Jacobian point recovery technique of Costello, Chung, and Smith. Our results are the first to show the feasibility of software-only hyperelliptic cryptography on constrained platforms, and represent a significant improvement on the elliptic-curve state-of-the-art for both key exchange and signatures on these architectures. Notably, our key-exchange scalar-multiplication software runs in under 9740k cycles on the ATmega, and under 2650k cycles on the Cortex M0.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes

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 projecting to the x-line or Kummer surface, where we can exploit faster and more uniform pseudomultiplication, before recovering the proper "signed" output back on the curve or Jacobian. This extends the work of L{ó}pez and Dahab, Okeya and Sakurai, and Brier and Joye to genus 2, and also to two-dimensional scalar multiplication. Our results show that many existing fast pseudomultiplication implementations (hitherto limited to applications in Diffie--Hellman key exchange) can be wrapped with simple and efficient pre-and post-computations to yield competitive full scalar multiplication algorithms, ready for use in more general discrete logarithm-based cryptosystems, including signature schemes. This is especially interesting for genus 2, where Kummer surfaces can outperform comparable elliptic curve systems. As an example, we construct an instance of the Schnorr signature scheme driven by Kummer surface arithmetic.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

The Q-curve construction for endomorphism-accelerated elliptic curves

We give a detailed account of the use of $\mathbb{Q}$-curve reductions to construct elliptic curves over $\mathbb{F}\_{p^2}$ with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as Gallant--Lambert--Vanstone (GLV) and Galbraith--Lin--Scott (GLS) endomorphisms. Like GLS (which is a degenerate case of our construction), we offer the advantage over GLV of selecting from a much wider range of curves, and thus finding secure group orders when \(p\) is fixed for efficient implementation. Unlike GLS, we also offer the possibility of constructing twist-secure curves. We construct several one-parameter families of elliptic curves over $\mathbb{F}\_{p^2}$ equipped with efficient endomorphisms for every $p \textgreater{} 3$, and exhibit examples of twist-secure curves over $\mathbb{F}\_{p^2}$ for the efficient Mersenne prime $p = 2^{127}-1$.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians

The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions using efficient endomorphisms-including Gallant-Lambert-Vanstone (GLV) and Galbraith-Lin-Scott (GLS) multiplication, as well as higher-dimensional and higher-genus constructions-is to produce a short basis of a certain integer lattice involving the eigenvalues of the endomorphisms. The shorter the basis vectors, the shorter the decomposed scalar coefficients, and the faster the resulting scalar multiplication. Typically, knowledge of the eigenvalues allows us to write down a long basis, which we then reduce using the Euclidean algorithm, Gauss reduction, LLL, or even a more specialized algorithm. In this work, we use elementary facts about quadratic rings to immediately write down a short basis of the lattice for the GLV, GLS, GLV+GLS, and Q-curve constructions on elliptic curves, and for genus 2 real multiplication constructions. We do not pretend that this represents a significant optimization in scalar multiplication, since the lattice reduction step is always an offline precomputation---but it does give a better insight into the structure of scalar decompositions. In any case, it is always more convenient to use a ready-made short basis than it is to compute a new one.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Families of fast elliptic curves from Q-curves

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 same way as Gallant-Lambert-Vanstone (GLV) and Galbraith-Lin-Scott (GLS) endomorphisms. Our construction is based on reducing \(\QQ\)-curves-curves over quadratic number fields without complex multiplication, but with isogenies to their Galois conjugates-modulo inert primes. As a first application of the general theory we construct, for every \(p > 3\), two one-parameter families of elliptic curves over \(\FF_{p^2}\) equipped with endomorphisms that are faster than doubling. Like GLS (which appears as a degenerate case of our construction), we offer the advantage over GLV of selecting from a much wider range of curves, and thus finding secure group orders when \(p\) is fixed. Unlike GLS, we also offer the possibility of constructing twist-secure curves. Among our examples are prime-order curves equipped with fast endomorphisms, with almost-prime-order twists, over \(\FF_{p^2}\) for \(p = 2^{127}-1\) and \(p = 2^{255}-19\).

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method

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 the Jacobian of some (possibly reducible) curve X. We investigate the Dolgachev--Lehavi method for constructing the curve X, simplifying their approach and making it more explicit. The result, at least for ell=3, is an efficient and easily programmable algorithm suitable for number-theoretic calculations.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Counting Points on Genus 2 Curves with Real Multiplication

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 reduces the complexity of genus 2 point counting over a finite field (\F_{q}) of large characteristic from (\widetilde{O}(\log^8 q)) to (\widetilde{O}(\log^5 q)). Using our algorithm we compute a 256-bit prime-order Jacobian, suitable for cryptographic applications, and also the order of a 1024-bit Jacobian.

0 citations0 reviewsNo code linkedOpen access
preprint2009arXiv

Families of Explicit Isogenies of Hyperelliptic Jacobians

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-dimensional families of hyperelliptic curves of genus 5, 10 and 15, all of which are equipped with an an explicit isogeny from their Jacobian to another hyperelliptic Jacobian. We show that the Jacobians are generically absolutely simple, and describe the kernels of the isogenies. The families are derived from Cassou--Noguès and Couveignes' explicit classification of pairs $(f,g)$ of polynomials such that $f(x_1) - g(x_2)$ is reducible.

0 citations0 reviewsNo code linkedOpen access