Pure mathematics
Proofs, algebraic structures and invariants for cryptography, topology and verification.
About Zaiku
Mathematics in software and cryptography
Mathematical choices affect the security, accuracy and stability of software.
We work on cryptographic systems, privacy-preserving methods, scientific software and machine-learning evaluation. We also prepare mathematical training for engineering and research teams.
The name Zaiku comes from Japanese Yosegi-Zaiku puzzle boxes, whose internal mechanisms depend on carefully fitted parts.
Mathematical software
Modelling, simulation and numerical experiments.
Privacy-preserving computation
Cryptographic and statistical methods for sensitive or distributed data.
AI evaluation
Measurement of machine-learning behaviour, uncertainty and sources of error.
OUR WORK
Sakurai
Sakurai is Zaiku Group's invite-only platform for mathematical computation and cryptographic experiments.
Invite-only
Sakurai Platform
The current version includes symbolic and numerical tools, privacy experiments and material on quantum algorithms.
Access is currently limited.
Request accessMathematical computation
Symbolic, numerical and structural calculations.
Privacy experiments
Secure computation and cryptographic privacy methods.
Quantum computing
Quantum algorithms and post-quantum cryptography.
Mathematics Consulting
Consulting on cryptography and scientific software
We provide consulting in cryptography, scientific computing and machine-learning evaluation.
AI Evaluation & Research Software
We organise experimental data and code, then test performance, uncertainty, anomalies and known sources of error.
Post-Quantum Cryptography
We assess migration plans, scheme selection, implementation choices and parameters for lattice-based cryptography.
Privacy-Preserving Computation
We compare federated learning, zero-knowledge proofs, homomorphic encryption and differential privacy across security, accuracy and computational cost.
Mathematical Modelling & Scientific Computing
We test simulations, numerical methods and optimisation procedures for stability and sensitivity to inputs.
Data Structures & Knowledge Systems
We check interfaces and composition in knowledge graphs and typed data systems.
Internal Mathematical Training
We prepare training programmes using examples and exercises from the team's own software and methods.
Collaborative Venture Building
Developing research into software and new ventures
Zaiku works with researchers, engineers and industry specialists to develop mathematical results into software, prototypes and grant-funded work.
Working with researchers
We adapt theorems, algorithms and modelling results to specific technical problems.
Software prototypes
We implement the mathematics in code and test it through experiments.
Working with industry
Industry collaborators provide the data, requirements and constraints.
Grants and teams
We prepare grant applications, identify missing technical roles and plan the initial software.
INDUSTRIES
Industries we focus on
We work mainly in sectors that rely on secure computation, sensitive data or scientific modelling.
Healthcare & Life Sciences
We work on privacy-preserving analysis, reproducibility and the relation between biomedical evidence and conclusions.
Financial Services
We work on cryptographic controls, risk calculations, optimisation and privacy constraints on financial data.
Defence & Security
We work on post-quantum migration, secure computation and the security analysis of cryptographic schemes.
Industrial R&D & Scientific Computing
We use simulations and experimental data to investigate numerical and implementation errors.
Mathematical Domains
Mathematical fields
Our work uses methods from pure and applied mathematics.
Abstract Algebra
Groups, rings, fields and representations used in coding theory and cryptography.
Algebraic Topology
Homology, cohomology and invariants used to study topological structure.
Functional Analysis
Operators, Hilbert spaces and spectral methods for inverse problems and signal analysis.
Differential Geometry
Manifolds and curvature for continuous systems and optimisation on non-Euclidean spaces.
Category Theory
Categories and functors for compositional software, type systems and knowledge representation.
Probability, Statistics & Information Theory
Probability, inference and information-theoretic methods for uncertainty and diagnostics.
Optimisation
Constrained and variational methods for parameter fitting, numerical search and design trade-offs.
Cryptography
Protocol design, threat models and security analysis for classical and post-quantum systems.
QF Academy
QF Academy
QF Academy, Zaiku Group's education arm, uses proofs and problem sets to teach quantum computing, cryptography and related mathematics.