Pure mathematics
Proofs, invariants, algebraic objects, and abstraction used on concrete problems.
About Zaiku
Mathematics inside hard technical systems
Zaiku Group applies pure mathematics to software, cryptography, scientific AI, privacy technology, and applied R&D.
A project may look like ordinary software work while the hard part is mathematical. It may depend on a cryptographic assumption, a privacy claim, a modelling choice, a stability issue, or a dataset that does not support the conclusion people want to draw.
We help research and engineering groups check the maths, review assumptions, build working products, and train internal teams when the missing knowledge is mathematical.
The name Zaiku is inspired by the Japanese Yosegi-Zaiku puzzle box. Intricate construction, hidden mechanisms, and parts that only work when they fit together precisely.
Applied R&D
Modelling, working product development, evaluation, and technical review.
Privacy technology
Cryptographic and statistical methods for constrained, sensitive, or distributed data.
Scientific AI
Model behaviour, uncertainty, diagnostics, and the limits of what data can support.
OUR WORK
Sakurai
Sakurai is a platform for researchers and engineers working with mathematics, privacy-enhancing technologies, and quantum computing.
Invite-only
Sakurai Platform
A research platform for mathematical tools, privacy-enhancing technologies, and quantum computing experiments.
It brings together tools for computation, experimentation, protocol study, and mathematical training.
Access is currently invite-only. Public access will follow once the core tools are stable enough for wider use.
Request accessMathematical tools
Algebraic, analytical, and computational tools for research and engineering work.
Privacy-enhancing technologies
Federated learning, zero-knowledge proofs, homomorphic encryption, and differential privacy.
Quantum computing
Quantum algorithms, post-quantum cryptography, and the mathematical foundations needed to study them properly.
Mathematics Consulting
Consulting for mathematics-led R&D
We help teams check the mathematical claims inside a product, model, protocol, or research programme before those claims become expensive to repair.
Scientific AI & R&D Workflows
Experimental records, sensor outputs, images, logs, and spreadsheets rarely arrive ready for modelling. We help organise the problem before model selection, evaluation, anomaly detection, or failure analysis.
Post-Quantum Cryptography
Post-quantum readiness, lattice-based cryptography, migration planning, protocol review, and internal training for teams preparing for quantum-era security.
Privacy-Preserving Computation
Federated learning, zero-knowledge proofs, homomorphic encryption, differential privacy, and secure data collaboration. We treat each method as an engineering choice with mathematical constraints.
Mathematical Modelling & Scientific Computing
Modelling assumptions, optimisation, numerical methods, dynamical systems, simulation design, and analysis of technical outputs.
Advanced Data Structures & Knowledge Systems
Knowledge graphs, typed workflows, compositional systems, category-theoretic abstractions, and formal methods in software design.
Internal Mathematical Training
Workshops, reading groups, technical training, and curriculum design for teams that need stronger mathematics in-house.
INDUSTRIES
Industries we focus on
We focus on sectors where errors in modelling, security, privacy, or data analysis can have serious operational, financial, or safety consequences.
Healthcare & Life Sciences
Clinical, biomedical, and preclinical R&D produce complex data under tight constraints. We support mathematical modelling, privacy-preserving analysis, scientific AI, and evidence workflows where the data must be handled carefully.
Financial Services
Financial systems depend on models, risk assumptions, security controls, and high-integrity data flows. We support cryptography, privacy technology, mathematical risk analysis, optimisation, and model review.
Defence & Security
Security-critical systems need clear assumptions, well-reviewed protocols, and careful handling of sensitive or distributed data. We support cryptographic review, post-quantum readiness, secure computation, and technical training.
Industrial R&D & Scientific Computing
Engineering, materials, devices, and scientific workflows often combine messy data with difficult models. We help organise data, simulations, and failure analysis using suitable mathematics.
Mathematical Domains
Fields we draw on
We choose the mathematics according to the problem, whether the work calls for algebra, topology, analysis, probability, optimisation, or cryptography.
Abstract Algebra
Groups, rings, fields, representations, coding theory, and cryptographic constructions.
Algebraic Topology
Homology, cohomology, and topological invariants for structured data, networks, and higher-order relationships.
Functional Analysis
Operators, Hilbert spaces, spectral methods, inverse problems, signals, and machine learning models with analytic structure.
Differential Geometry
Manifolds, curvature, geometric structure, continuous models, simulation, and non-Euclidean optimisation.
Category Theory
Compositional systems, typed interfaces, workflows, software architecture, and knowledge representation.
Probability, Statistics & Information Theory
Uncertainty, inference, signal structure, information flow, diagnostics, and model assessment.
Optimisation
Constrained optimisation, variational methods, numerical search, design trade-offs, and operational tuning.
Cryptography
Protocol design, threat modelling, and mathematical security analysis across classical and post-quantum settings.
Quantum Formalism
Training through Quantum Formalism
QF Academy is our education arm. It teaches the mathematics behind modern tools, models, and protocols, with an emphasis on proofs, problem sheets, and guided study.