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+# Athena: Predictive Complexity Model for Poseidon Cryptanalysis using Gröbner Basis Attacks
+- **Team Name:** MeCuadra
+- **Payment Address:** 0xea99B3C34aE77A8CC49aB8Ffc4a388ec882952B9 (ERC20 USDC)
+- **Level:** 2
+## Project Overview :page_facing_up:
+### Overview
+- **Tag line:** First empirically-grounded security model for Poseidon hash functions against Gröbner basis attacks
+- **Brief description:** This research develops "Athena," a predictive complexity model for Poseidon cryptanalysis using Gröbner basis attacks. The project addresses a critical gap in security analysis for ZK-friendly hash functions, directly supporting the Ethereum Foundation's Poseidon Cryptanalysis Initiative.
+- **Integration with Substrate/Polkadot/Kusama:** While Poseidon is primarily used in Ethereum, this research contributes to the broader zero-knowledge proof ecosystem that is increasingly important for Polkadot parachains and Substrate-based applications requiring efficient ZK-proofs.
+- **Team interest:** As a Master's student in Mathematical Sciences with specialization in Cryptography at the University of Havana, I am passionate about advancing cryptographic security through rigorous mathematical analysis and empirical validation.
+- **Research type:** This is academic research intended for publication in peer-reviewed venues, specifically targeting cryptographic conferences and journals.
+
+### Project Details
+
+**Problems to investigate:**
+- Current security analysis of Poseidon hash functions lacks empirical validation of Gröbner basis attack complexity
+- Theoretical complexity bounds for Gröbner basis attacks are often much higher than practical observations
+- No predictive model exists to estimate attack costs based on Poseidon parameters (RF, RP, t)
+- The Ethereum Foundation's Poseidon Cryptanalysis Initiative identifies this as a critical research gap
+
+**Research questions/hypothesis:**
+- **Primary Hypothesis:** The practical complexity of Gröbner basis attacks against Poseidon, measured by the regularity degree (Dreg), exhibits linear growth with the number of rounds
+- **Research Questions:**
+  1. How does the regularity degree scale with Poseidon parameters in practice?
+  2. Can we develop a predictive model for attack complexity?
+  3. What are the practical security margins for current Poseidon deployments?
+
+**Methodology:**
+1. **Systematic Experimental Analysis:** Implement the three-step Gröbner basis attack methodology (DRL computation → LEX conversion → univariate resolution)
+2. **Empirical Data Collection:** Measure regularity degrees and computational costs across different Poseidon configurations
+3. **Statistical Modeling:** Develop regression models to predict attack complexity based on round parameters
+4. **Validation:** Test the model against the Ethereum Foundation's 40-bit security challenge
+
+**Data collection and analysis procedures:**
+- Use computational algebra systems (Magma/Sage) for Gröbner basis computations
+- Implement high-performance Poseidon variants in Rust for efficient experimental validation
+- Use Lean theorem prover for formal verification of mathematical properties and attack complexity bounds
+- Measure regularity degrees, memory usage, and computation time for various Poseidon configurations
+- Apply statistical analysis to identify scaling relationships
+- Validate predictions against known attack results using both experimental and formal methods
+
+**Expected results and verification:**
+- **Deliverable 1:** Empirical complexity measurements for Poseidon variants
+- **Deliverable 2:** Athena predictive model with mathematical formulation
+- **Deliverable 3:** Validation against Ethereum Foundation challenge
+- **Verification:** All code and data will be open-source, with detailed documentation for reproducibility
+
+**Relevant related work:**
+- Grassi et al. (2019): HADES design strategy for Poseidon
+- Koschatko et al. (2024): Gröbner basis cryptanalysis of algebraic hash functions
+- Ethereum Foundation (2024): Poseidon Cryptanalysis Initiative
+- Canteaut et al. (2020): Security analysis of STARK-friendly hash functions
+
+**Intended publication venue:**
+- **Primary:** [Journal of the University of Havana](https://revistas.uh.cu/rcm/) (indexed in zbMATH Open, Google Scholar, and other academic databases)
+- **Secondary:** Cryptology ePrint Archive
+- **Timeline:** Submit to conferences within 6 months of completion, with additional publication in university journal
+
+**What this project will NOT provide:**
+- It will not provide business or commercial applications
+- It will not include tokenomics or economic analysis
+
+### Ecosystem Fit
+- **Where does your project fit into the ecosystem?** This research directly supports the security of zero-knowledge proof systems used across the Polkadot ecosystem. As parachains increasingly adopt ZK-proofs for privacy and scalability, understanding the security of underlying hash functions becomes critical.
+- **Target audience:** ZK-proof developers, parachain teams implementing privacy features, cryptographic researchers, and security auditors working with zero-knowledge systems.
+- **What need(s) does your project meet?** Provides empirical security analysis for Poseidon, enabling informed decisions about parameter selection and security margins in ZK-proof applications.
+- **Similar projects:** No similar projects exist in the Polkadot/Substrate ecosystem. Related work exists in Ethereum ecosystem but lacks the empirical focus and predictive modeling approach of this research.
+
+## Team :busts_in_silhouette:
+### Team members
+- B.Sc Enmanuel Cabrera (Team Leader)
+- M.Sc Frank Ernesto (Supervisor)
+### Contact
+- **Contact Name:** Enmanuel Cabrera
+- **Contact Email:** manudevcabrera@gmail.com
+- **X (Twitter):** https://x.com/manudev97
+### Legal Structure
+- **Registered Address:** Universidad de La Habana, Facultad de Matemática y Computación, Edificio Felipe Poey, San Lázaro y L, Vedado, Plaza de la Revolución, La Habana, Cuba, CP 10400
+- **Registered Legal Entity:** Universidad de La Habana
+### Team's experience
+Enmanuel Cabrera is a Master's student in Mathematical Sciences with specialization in Cryptography at the University of Havana. He has published research on zk-SNARKs for blockchain developers in the journal "Ciencias Matemáticas" (Vol. 38, No. 2, 2024), demonstrating expertise in zero-knowledge proof systems and cryptographic implementations. His academic background includes advanced coursework in algebraic geometry, computational algebra, and cryptographic protocols.
+**Previous publications:**
+- ["zk-SNARK para desarrolladores blockchain"](https://revistas.uh.cu/rcm/article/view/10616) - Ciencias Matemáticas, Vol. 38, No. 2, 2024
+### Team Code Repos
+- https://github.com/me-cuadra
+- https://github.com/manudev97/
+### Team LinkedIn Profiles
+- https://www.linkedin.com/in/manudev97
+## Development Status :open_book:
+This project builds upon my ongoing Master's thesis research at the University of Havana. I have already completed:
+- **Comprehensive literature review** on Poseidon hash functions and Gröbner basis attacks
+- **Initial research document** (available at [here](https://github.com/manudev97/athena/blob/main/docs/s1/athena.pdf))
+- **Theoretical framework** for the Athena predictive model
+- **Academic foundation** with peer-reviewed references and methodology
+**Current progress:**
+- Literature review and theoretical framework completed
+- Research proposal and methodology established
+- Initial experimental setup in progress
+- Strong academic foundation with university supervision
+
+## Development Roadmap :nut_and_bolt:
+
+### Overview
+- **Total Estimated Duration:** 12 months
+- **Full-Time Equivalent (FTE):** 2.0
+- **Total Costs:** 15,000 USD
+
+### Milestone 1 — Experimental Setup and Initial Analysis
+- **Estimated duration:** 3 months
+- **FTE:** 2.0
+- **Costs:** 3,750 USD
+
+| Number | Deliverable | Specification |
+| -----: | ----------- | ------------- |
+| **0a.** | Copyright and Licenses | Apache 2.0 |
+| **0b.** | Documentation/Tutorial | Complete setup guide for Gröbner basis computations with Magma/Sage, including Docker containers for reproducible experiments |
+| **0c.** | Methodology | Detailed explanation of the three-step attack methodology and experimental procedures |
+| **0d.** | Infrastructure | Docker containers with Magma/Sage, Rust development environment, Lean theorem prover setup, computational requirements documentation, and cloud computing infrastructure |
+| **0e.** | Article | Research article explaining the experimental setup and initial complexity measurements for small-scale Poseidon variants |
+| 1. | Experimental Framework | Complete implementation of the three-step Gröbner basis attack methodology |
+| 2. | Rust Implementation | High-performance Rust implementation of Poseidon variants for experimental validation |
+| 3. | Lean Formal Verification | Initial Lean proofs for mathematical properties and complexity bounds |
+| 4. | Initial Measurements | Complexity measurements for Poseidon variants with small parameters (t=3, RF=2, RP=3-5) |
+| 5. | Statistical Analysis | Preliminary analysis of complexity scaling with round parameters |
+
+### Milestone 2 — Systematic Data Collection
+- **Estimated Duration:** 4 months
+- **FTE:** 2.0
+- **Costs:** 5,000 USD
+
+| Number | Deliverable | Specification |
+| -----: | ----------- | ------------- |
+| **0a.** | Copyright and Licenses | Apache 2.0 |
+| **0b.** | Documentation/Tutorial | Comprehensive tutorial on reproducing all experimental results and statistical analysis |
+| **0c.** | Methodology | Detailed statistical methodology for complexity analysis and model development |
+| **0d.** | Infrastructure | Extended computational infrastructure with Rust implementations, Lean formal verification setup, performance monitoring, and data management systems |
+| **0e.** | Article | Research article presenting systematic complexity measurements and initial scaling relationships |
+| 1. | Comprehensive Dataset | Complete complexity measurements for Poseidon variants across parameter space |
+| 2. | Statistical Models | Initial regression models for complexity prediction |
+| 3. | Validation Framework | Methodology for validating predictions against known results |
+
+### Milestone 3 — Athena Model Development and Validation
+- **Estimated Duration:** 3 months
+- **FTE:** 2.0
+- **Costs:** 3,750 USD
+
+| Number | Deliverable | Specification |
+| -----: | ----------- | ------------- |
+| **0a.** | Copyright and Licenses | Apache 2.0 |
+| **0b.** | Documentation/Tutorial | Complete user guide for the Athena model with examples and case studies |
+| **0c.** | Methodology | Full mathematical formulation of the Athena model with theoretical justification |
+| **0d.** | Infrastructure | Production-ready Rust implementation with Lean formal verification, API documentation, and comprehensive testing suite |
+| **0e.** | Article | Final research article presenting the Athena model and validation results |
+| 1. | Athena Model | Complete predictive model for Poseidon attack complexity |
+| 2. | Validation Results | Validation against Ethereum Foundation's 40-bit security challenge |
+| 3. | Security Recommendations | Practical security guidelines for Poseidon parameter selection |
+
+### Milestone 4 — Publication and Community Integration
+- **Estimated Duration:** 2 months
+- **FTE:** 2.0
+- **Costs:** 2,500 USD
+
+| Number | Deliverable | Specification |
+| -----: | ----------- | ------------- |
+| **0a.** | Copyright and Licenses | Apache 2.0 |
+| **0b.** | Documentation/Tutorial | Final documentation package with academic paper, technical report, and community resources |
+| **0c.** | Methodology | Complete methodology documentation for academic publication |
+| **0d.** | Infrastructure | Final infrastructure with all tools and data publicly available |
+| **0e.** | Article | Academic paper submitted to cryptographic conference with acknowledgment of Web3 Foundation support |
+| 1. | Academic Publication | Paper submitted to [RCM](https://revistas.uh.cu/rcm)/EPRINT/EUROCRYPT |
+| 2. | University Journal Publication | Article published in Ciencias Matemáticas (Universidad de La Habana) |
+| 3. | Open Source Release | Complete codebase and data published on GitHub |
+| 4. | Community Presentation | Presentation at cryptographic conference or workshop |
+
+## Future Plans
+**Short-term plans:**
+- Complete Master's thesis and defend successfully
+- Publish research results in top-tier cryptographic conferences
+- Publish additional article in Ciencias Matemáticas (Universidad de La Habana)
+- Make all code and data publicly available for community use
+- Present findings at international cryptographic conferences
+**Long-term plans:**
+- Continue research in cryptographic security analysis
+- Develop additional tools for ZK-proof security analysis
+- Collaborate with industry partners on cryptographic implementations
+- Mentor future students in cryptographic research
+## Additional Information :heavy_plus_sign:
+**How did you hear about the Grants Program?** Web3 Foundation Website
+**Additional information:**
+- This research is conducted under the supervision of M.Sc Frank Ernesto at the University of Havana
+- The project aligns with the Ethereum Foundation's Poseidon Cryptanalysis Initiative 2024-2026
+- All findings will be published and made available to the community
+- The research addresses a critical gap identified by the cryptographic community
+- Previous work on zk-SNARKs demonstrates relevant expertise in zero-knowledge proof systems