Phase1‐Research‐and‐Specification - chimans/PrivnetAI GitHub Wiki

🧪 Phase 1 – Research & Specification

Timeline: Q2 2025
Status: In Progress

🎯 Goal

Establish formal foundations of PrivNet.AI’s architecture by exploring cutting-edge cryptographic primitives, graph learning frameworks, and advanced mathematical structures — to enable privacy-preserving encrypted graph learning.

📊 Overview Diagram

Phase 1 Diagram

🔐 Cryptography Layer

Focus: Post-quantum secure isogeny-based cryptographic protocols

Tasks:

  • Conduct deep literature review on Supersingular Isogeny Graphs, SIDH, and SIKE
  • Define security assumptions and threat models
  • Build a toy prototype of key exchange in SageMath

🧠 Learning Layer (GNN)

Focus: Graph representation learning on encrypted structures

Tasks:

  • Define minimal encryption-preserving graph data model
  • Evaluate different GNN architectures for encrypted input (e.g., GCN, GIN, MPNN)
  • Benchmark PyTorch Geometric vs DGL for modularity and compatibility

📐 Mathematical Foundations

Focus: Algebraic Geometry, Topology & Category Theory

Tasks:

  • Study elliptic curves, isogenies, and modular forms from an algebraic geometry lens
  • Formalize graph structures using sheaf theory, simplicial complexes, and homological algebra
  • Explore connections with information geometry and functional analysis
  • Propose category-theoretic abstractions for crypto-learning operations

🧪 Evaluation & Alignment

  • Ensure theoretical soundness of all components
  • Align research with future phases (prototype integration in Phase 2)
  • Prepare internal documentation + reproducible Jupyter notebooks

📎 Resources

  • Tools: SageMath, Jupyter, LaTeX, Python 3.11
  • Frameworks: PyTorch Geometric, DGL
  • External Refs: SIKE specs, ISO draft proposals, NeurIPS/ICLR papers on GNNs & crypto