secp256k1 Remaining Variants

Archive of Elliptic Curve Cryptography Research Explorations

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Comprehensive archive of research explorations into the secp256k1 elliptic curve used in Bitcoin. Contains over 390 Python scripts organized by approach, covering parameter analysis, endomorphism properties, hash pipeline behavior, genetic algorithm search variants, and geometric structure investigations.

This repository represents the broader research program from which focused repositories were extracted. Scripts range from early exploratory analysis to structured experimental frameworks.

Repository Structure

secp256k1-remaining-variants/
├── backdoor_investigation/     # XOR and pattern analysis of curve parameters
├── cascade_attacks/            # Multi-stage cryptanalytic attack frameworks
├── curve_analysis/             # Parameter relationship and modular arithmetic studies
│   ├── backdoor_analysis/      #   Curve constant analysis
│   ├── gpu_benchmarks/         #   GPU kernel benchmarks for ECC operations
│   ├── hash160_analysis/       #   Hash160 pipeline modular studies
│   └── modular_analysis/       #   Keypair modular arithmetic investigations
├── ecc_analysis/               # Algebraic structure, torus topology, and parameter search
├── edge_series/                # Bitcoin pipeline edge case and boundary testing
├── fiber_manifold/             # Fiber bundle and manifold structure exploration
├── ga_variants/                # Genetic algorithm variants for hash160 search
├── hash160_analysis/           # SHA-256/RIPEMD-160 pipeline statistical analysis
├── misc_crypto/                # Miscellaneous cryptographic utilities and solvers
├── mtgox_gox/                  # Mt. Gox key recovery formula iterations
├── mu_endomorphism/            # GLV endomorphism (mu = lambda + 1) decomposition research
├── multi_curve/                # Cross-curve constraint analysis (NIST, secp256k1)
├── null_zero_resonance/        # Zero-byte and null-key edge case testing
├── research_iterations/        # Iterative research across multiple approaches
│   ├── misc_research/          #   Geometry, topology, and shape mapping
│   ├── pattern_analysis/       #   ECC shape discovery and manifold analysis
│   └── structure_investigation/#   Structural investigation of curve internals
└── sgm_variants/               # SGM (Sparse Gradient Memory) network experiments

Technical Summary

• Endomorphism analysis: Investigates the GLV decomposition using the cube root of unity (lambda) and derived mu = lambda + 1, including 6th-root-of-unity structure and BSGS recovery
• Hash pipeline analysis: Statistical testing of the SHA-256 to RIPEMD-160 pipeline for information leakage and byte-position correlations
• Genetic algorithms: Population-based search with hex-aware mutation, adaptive pressure, and multi-target fitness functions
• Geometric methods: Torus mapping, fiber bundle decomposition, manifold embedding, and cross-curve geometric constraints
• SGM variants: Sparse Gradient Memory network experiments including continual learning, coalition locking, and transformer integration

Requirements

• Python 3.10+
• Core: numpy, hashlib, ecdsa or coincurve
• Optional: gmpy2, pycryptodome, cupy, matplotlib, scikit-learn

Author

Andrew Dorman Independent Researcher -- Southlake, TX GitHub: ACD421