Pure mathematics
Proofs, algebraic structures and invariants used in cryptography, topology and verification.
About Zaiku
Mathematics in software, models and protocols
Software, models and protocols rely on claims about security, privacy, stability, optimisation, uncertainty and what the data can support.
We review cryptographic assumptions and privacy guarantees, test models and protocols against their stated claims, and analyse choices in optimisation and numerical computation.
We also write mathematical and scientific software, and create internal training for engineers and researchers who need to understand the mathematics used by their project.
The name Zaiku comes from the Japanese Yosegi-Zaiku puzzle box, whose internal mechanism depends on precisely fitted parts.
Mathematical software
Code for modelling, simulation, numerical analysis and scientific experiments.
Privacy-preserving computation
Cryptographic and statistical controls for sensitive or distributed data.
AI evaluation
Analysis of model behaviour, uncertainty, diagnostics and failure modes.
OUR WORK
Sakurai
Sakurai is an invite-only project for mathematical computation, privacy protocol experiments and the study of quantum algorithms.
Invite-only
Sakurai Platform
The current build combines symbolic and numerical software with experiments in secure computation and study material for quantum algorithms and post-quantum cryptography.
Access remains limited while these components are tested and extended.
Request accessMathematical computation
Symbolic, numerical and structural calculations in a shared software environment.
Privacy experiments
Implementations for examining secure computation, privacy guarantees and protocol behaviour.
Quantum computing
Worked material on quantum algorithms, post-quantum cryptography and the mathematics behind both.
Mathematics Consulting
Consulting on mathematical software, models and protocols
We review cryptographic protocols and privacy claims, build numerical models, evaluate machine-learning models and design mathematical software.
AI Evaluation & R&D Workflows
We organise experimental data and computational workflows, then examine model performance, uncertainty, anomalies and failure modes.
Post-Quantum Cryptography
We review post-quantum migration plans and cryptographic protocols. For lattice-based schemes, we examine parameter selection and implementation choices.
Privacy-Preserving Computation
We design data workflows using federated learning, zero-knowledge proofs, homomorphic encryption or differential privacy, and compare their security, accuracy and operating costs.
Mathematical Modelling & Scientific Computing
We formulate and test models, simulations, numerical methods and optimisation procedures. We check stability, sensitivity to inputs and how the outputs should be interpreted.
Data Structures & Knowledge Systems
We build knowledge graphs, typed workflows and compositional data structures. Formal and category-theoretic tools make relationships explicit and expose inconsistencies.
Internal Mathematical Training
We create mathematics training programmes for engineering and research teams. Examples and exercises come from the protocols, models or software the team is building.
Collaborative Venture Building
Building software from mathematics and research
Zaiku works with mathematicians and academic researchers, as well as engineers, founders and industry specialists. A collaboration might start with a theorem or algorithm, a problem raised by an organisation, or software that is still at prototype stage. The result is not always a company: it might be joint research, working software, an internal product or a grant-funded project. Some projects do later become new companies. We take on projects when Zaiku can contribute mathematics or software.
Working with researchers
We examine whether a theorem, algorithm or modelling result can be adapted for software or a specific industry problem.
Building and testing software
We turn the mathematics into code, run experiments and build prototypes for researchers or potential users to test.
Working with industry
Industry collaborators define the problem and provide the relevant data, constraints, regulation and user needs.
Growing the project
We find mathematicians, engineers or industry specialists to fill gaps and prepare grant applications. If the project later becomes a company, we help assemble the first team and plan the software.
INDUSTRIES
Industries we focus on
Across these sectors, we review models and security claims, design privacy-preserving data workflows and build numerical software.
Healthcare & Life Sciences
We build mathematical models, design privacy-preserving analyses and evaluate biomedical data. We also check whether results can be reproduced and whether the evidence supports the stated conclusion.
Financial Services
We analyse cryptographic controls, risk models and optimisation problems, and design privacy-preserving ways to use financial data.
Defence & Security
We review cryptographic protocols and security assumptions, examine post-quantum migration plans and design secure computation workflows.
Industrial R&D & Scientific Computing
We build simulations and numerical models, organise experimental data and analyse failure modes in engineering and scientific programmes.
Mathematical Domains
Mathematical fields used in our projects
A cryptography project may use algebra and probability; modelling and scientific software may instead call for analysis, geometry or optimisation.
Abstract Algebra
Groups, rings, fields and representations. These structures underlie coding theory and many cryptographic constructions.
Algebraic Topology
Homology, cohomology and topological invariants used to study shape, structured data and higher-order relationships.
Functional Analysis
Operators, Hilbert spaces and spectral methods used in inverse problems, signal analysis and mathematical models.
Differential Geometry
Manifolds, curvature and geometry for continuous models, simulation and optimisation on non-Euclidean spaces.
Category Theory
Categories, functors and compositional structures for typed workflows, software interfaces and knowledge representation.
Probability, Statistics & Information Theory
Probability and statistical inference for uncertainty, model diagnostics and information flow.
Optimisation
Constrained and variational optimisation for numerical search, model fitting and design trade-offs.
Cryptography
Protocol design, threat modelling and mathematical security analysis in classical and post-quantum settings.
QF Academy
QF Academy
QF Academy is Zaiku Group's education arm. Its programmes use proofs and problem sets to teach the mathematics of quantum computing, cryptography and related subjects.