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Open Problem Toolkit A comprehensive Julia toolkit for learning and implementing modern cryptographic systems. This educational platform helps university students understand and work with cutting-edge encryption techniques that protect our digital world.
Explore three revolutionary areas of cryptography:
🔐 Homomorphic Encryption - Imagine being able to perform calculations on locked data without ever unlocking it. This technology lets cloud servers process your encrypted files (like doing math on scrambled numbers) while never seeing your actual information. It's like having a sealed box where you can manipulate the contents from the outside without opening it.
Beneficial for: Healthcare providers analyzing patient data without compromising privacy, financial institutions processing transactions securely in the cloud, and researchers collaborating on sensitive datasets while maintaining confidentiality.
🛡️ Post-Quantum Cryptography - Today's encryption relies on math problems that regular computers find nearly impossible to solve. But quantum computers (super-powerful machines that work differently than regular computers) could break this protection easily. Post-quantum crypto uses different mathematical puzzles that even quantum computers can't crack, ensuring your data stays safe in the quantum future.
Beneficial for: Government agencies protecting classified information, cryptocurrency networks securing transactions against future quantum attacks, and any organization needing long-term data protection (like legal firms with 50+ year document retention requirements).
🔍 Zero-Knowledge Proofs - This mind-bending concept lets you prove you know something without revealing what you actually know. Think of it like proving you know the password to enter a club without ever saying the password out loud. You could prove you're over 18 without showing your exact birthdate, or prove you have enough money for a purchase without revealing your bank balance.
Beneficial for: Identity verification systems that protect personal information, blockchain networks enabling private transactions, voting systems that verify eligibility without revealing voter choices, and authentication services that don't store sensitive credentials.
🧮 Lattice-Based Cryptography - Uses the mathematical concept of lattices (imagine 3D grids or crystal structures) to create unbreakable codes. These geometric patterns form the foundation for many post-quantum algorithms because finding the shortest path through these mathematical mazes is incredibly difficult, even for quantum computers.
Beneficial for: Secure communication protocols resistant to both classical and quantum attacks, digital signature systems for long-term document authenticity, and key exchange mechanisms that will remain secure in the post-quantum era.
🚀 Overview
The Open Problem Toolkit provides specialized packages for modern cryptographic research and development:
📦 Package Structure
🛠️ Installation
Prerequisites
Installation Steps
git clone https://github.com/Kiara-Dev-Team/open-problem-toolkit.git cd open-problem-toolkitcd HomomorphicCryptography.jl
julia --project=. -e "using Pkg; Pkg.instantiate()"
PQCValidator.jl
cd ../PQCValidator.jl
julia --project=. -e "using Pkg; Pkg.instantiate()"
ZKPValidator.jl
cd ../ZKPValidator.jl
julia --project=. -e "using Pkg; Pkg.instantiate()"
LibOQS.jl
cd ../LibOQS.jl
julia --project=. -e "using Pkg; Pkg.instantiate()"
LatticeBasedCryptography.jl
cd ../LatticeBasedCryptography.jl
julia --project=. -e "using Pkg; Pkg.instantiate()"" tabindex="0" role="button" style="box-sizing: border-box; position: relative; display: flex !important; padding: 0px !important; font-size: 14px; font-weight: 500; line-height: 20px; white-space: nowrap; vertical-align: middle; cursor: pointer; user-select: none; border: 0px; border-radius: 6px; appearance: none; color: rgb(9, 105, 218); background-color: rgba(0, 0, 0, 0); box-shadow: none; transition: color 80ms cubic-bezier(0.33, 1, 0.68, 1), background-color, box-shadow, border-color; justify-content: center !important; align-items: center !important; margin: 8px !important; width: 28px; height: 28px;">
🧪 Testing
Each package includes comprehensive test suites:
cd HomomorphicCryptography.jl
julia --project=. test/runtests.jl
Test PQCValidator.jl
cd ../PQCValidator.jl
julia --project=. test/runtests.jl
Test ZKPValidator.jl
cd ../ZKPValidator.jl
julia --project=. test/runtests.jl
Test LibOQS.jl
cd ../LibOQS.jl
julia --project=. test/runtests.jl
Test LatticeBasedCryptography.jl
cd ../LatticeBasedCryptography.jl
julia --project=. test/runtests.jl" tabindex="0" role="button" style="box-sizing: border-box; position: relative; display: flex !important; padding: 0px !important; font-size: 14px; font-weight: 500; line-height: 20px; white-space: nowrap; vertical-align: middle; cursor: pointer; user-select: none; border: 0px; border-radius: 6px; appearance: none; color: rgb(9, 105, 218); background-color: rgba(0, 0, 0, 0); box-shadow: none; transition: color 80ms cubic-bezier(0.33, 1, 0.68, 1), background-color, box-shadow, border-color; justify-content: center !important; align-items: center !important; margin: 8px !important; width: 28px; height: 28px;">
📊 Project Status
🎯 Use Cases
Homomorphic Encryption
Post-Quantum Cryptography
Zero-Knowledge Proofs
LibOQS Integration
Lattice-Based Cryptography Education
🤝 Contributing
We welcome contributions to all packages! Please see individual package documentation for specific contribution guidelines.
Areas for Contribution
📚 Documentation
Detailed documentation is available in each package:
📈 Recent Updates (September 21, 2025)
🆕 New: LatticeBasedCryptography.jl Package
We've added a comprehensive educational toolkit for lattice-based cryptography, featuring:
🔐 Complete Lattice-Based Encryption/Decryption System
• Key generation algorithms - Implementation of lattice-based key pair generation using techniques like LWE or NTRU • Encryption/decryption functions - Core cryptographic operations that transform plaintext to ciphertext using lattice mathematical structures • Parameter selection and security analysis - Code for choosing appropriate lattice dimensions, noise parameters, and security level configurations • Simple password protection demo - Shows how your text messages can be scrambled using math so only your friend with the right "key" can read them • Why normal encryption won't work against quantum computers - Explains how future super-computers will break today's security, but lattice math will still protect us
🔄 Interactive Lattice Reduction Algorithms
• LLL (Lenstra-Lenstra-Lovász) algorithm implementation - The foundational lattice reduction technique with step-by-step visualization • BKZ (Block Korkine-Zolotarev) variants - More advanced reduction algorithms with interactive parameter tuning • Real-time lattice visualization - 2D/3D plotting of lattice bases before and after reduction with interactive controls • Think of it like organizing messy dots into neat patterns - Visual demos showing how scattered points get rearranged into organized grids • Why finding the shortest path matters in cryptography - Interactive games showing how hard it is to find the shortest route through a lattice maze
🎓 Educational Demonstrations of LWE/Ring-LWE
• Learning With Errors problem setup - Interactive examples showing how LWE instances are constructed and why they're hard to solve • Ring-LWE polynomial arithmetic - Demonstrations of polynomial ring operations and their cryptographic applications • Security parameter exploration - Tools to experiment with different noise levels and see their impact on security vs. efficiency • Adding random noise to hide secrets - Shows how adding "mathematical static" to equations makes them impossible to solve backwards • Like trying to solve algebra with typos - Demonstrates why equations with small random errors become incredibly hard puzzles to crack
🔒 Cryptographic Protocol Implementations
• Key exchange protocols - Implementation of lattice-based key agreement schemes with interactive parameter selection • Digital signature schemes - Code for lattice-based signatures like Dilithium or FALCON with verification demos • Post-quantum security analysis - Tools to analyze and compare the quantum resistance of different lattice-based approaches • How two people can agree on a secret over the internet - Interactive simulations of secure communication without ever sharing the actual password • Digital signatures that prove "this really came from me" - Demos showing how mathematical proofs can verify who sent a message without revealing private keys
🛠️ Technical Implementation Details
オープン問題ツールキット 現代暗号システムの学習と実装のための包括的なJuliaツールキット。この教育プラットフォームは、大学生がデジタル世界を守る最先端の暗号化技術を理解し、実際に使用できるよう支援します。
暗号学の3つの革命的分野を探索してください：
🔐 準同型暗号 - ロックされたデータを解除することなく計算を実行できることを想像してみてください。この技術により、クラウドサーバーは実際の情報を見ることなく、暗号化されたファイルを処理できます（スクランブルされた数字で計算を行うようなものです）。外側から箱の中身を操作できる密封された箱のようなものです。
メリットを受ける対象： プライバシーを損なうことなく患者データを分析する医療提供者、クラウドで安全に取引を処理する金融機関、機密性を維持しながら機密データセットで協力する研究者。
🛡️ ポスト量子暗号 - 現在の暗号化は、通常のコンピュータでは解決がほぼ不可能な数学問題に依存しています。しかし、量子コンピュータ（通常のコンピュータとは異なる働きをする超強力なマシン）は、この保護を簡単に破ることができます。ポスト量子暗号は、量子コンピュータでも解読できない異なる数学パズルを使用し、量子の未来においてもデータの安全性を確保します。
メリットを受ける対象： 機密情報を保護する政府機関、将来の量子攻撃に対してトランザクションを保護する暗号通貨ネットワーク、長期的なデータ保護が必要な組織（50年以上の文書保存要件を持つ法律事務所など）。
🔍 ゼロ知識証明 - 実際に知っていることを明かすことなく、何かを知っていることを証明できるという驚異的な概念です。クラブに入るためのパスワードを知っていることを、実際にパスワードを声に出さずに証明するようなものと考えてください。正確な生年月日を示すことなく18歳以上であることを証明したり、銀行残高を明かすことなく購入に十分なお金があることを証明したりできます。
メリットを受ける対象： 個人情報を保護する身元確認システム、プライベートな取引を可能にするブロックチェーンネットワーク、有権者の選択を明かすことなく資格を確認する投票システム、機密の認証情報を保存しない認証サービス。
🧮 格子ベース暗号 - 格子の数学的概念（3Dグリッドや結晶構造を想像してください）を使用して、解読不可能なコードを作成します。これらの幾何学的パターンは多くのポスト量子アルゴリズムの基盤となっています。なぜなら、これらの数学的迷路を通る最短経路を見つけることは、量子コンピュータにとってさえも非常に困難だからです。
メリットを受ける対象： 古典的攻撃と量子攻撃の両方に耐性のある安全な通信プロトコル、長期的な文書の真正性のためのデジタル署名システム、ポスト量子時代においても安全性を維持する鍵交換メカニズム。
Open Problem Toolkit A comprehensive Julia toolkit for learning and implementing modern cryptographic systems. This educational platform helps university students understand and work with cutting-edge encryption techniques that protect our digital world.Explore three revolutionary areas of cryptography:
🔐 Homomorphic Encryption - Imagine being able to perform calculations on locked data without ever unlocking it. This technology lets cloud servers process your encrypted files (like doing math on scrambled numbers) while never seeing your actual information. It's like having a sealed box where you can manipulate the contents from the outside without opening it.
Beneficial for: Healthcare providers analyzing patient data without compromising privacy, financial institutions processing transactions securely in the cloud, and researchers collaborating on sensitive datasets while maintaining confidentiality.
🛡️ Post-Quantum Cryptography - Today's encryption relies on math problems that regular computers find nearly impossible to solve. But quantum computers (super-powerful machines that work differently than regular computers) could break this protection easily. Post-quantum crypto uses different mathematical puzzles that even quantum computers can't crack, ensuring your data stays safe in the quantum future.
Beneficial for: Government agencies protecting classified information, cryptocurrency networks securing transactions against future quantum attacks, and any organization needing long-term data protection (like legal firms with 50+ year document retention requirements).
🔍 Zero-Knowledge Proofs - This mind-bending concept lets you prove you know something without revealing what you actually know. Think of it like proving you know the password to enter a club without ever saying the password out loud. You could prove you're over 18 without showing your exact birthdate, or prove you have enough money for a purchase without revealing your bank balance.
Beneficial for: Identity verification systems that protect personal information, blockchain networks enabling private transactions, voting systems that verify eligibility without revealing voter choices, and authentication services that don't store sensitive credentials.
🧮 Lattice-Based Cryptography - Uses the mathematical concept of lattices (imagine 3D grids or crystal structures) to create unbreakable codes. These geometric patterns form the foundation for many post-quantum algorithms because finding the shortest path through these mathematical mazes is incredibly difficult, even for quantum computers.
Beneficial for: Secure communication protocols resistant to both classical and quantum attacks, digital signature systems for long-term document authenticity, and key exchange mechanisms that will remain secure in the post-quantum era.
🚀 Overview
The Open Problem Toolkit provides specialized packages for modern cryptographic research and development:
🔐 HomomorphicCryptography.jl - Standards-compliant homomorphic encryption implementations
🛡️ PQCValidator.jl - Post-quantum cryptography validation for TLS 1.3
🔍 ZKPValidator.jl - Zero-knowledge proof protocol validation framework
🔒 LibOQS.jl - Julia bindings for the Open Quantum Safe library
🧮 LatticeBasedCryptography.jl - Interactive lattice-based cryptography educational toolkit
📦 Package Structure
open-problem-toolkit/
├── HomomorphicCryptography.jl/ # Homomorphic encryption library
├── PQCValidator.jl/ # Post-quantum crypto validator
├── ZKPValidator.jl/ # Zero-knowledge proof validator
├── LibOQS.jl/ # Open Quantum Safe Julia bindings
└── LatticeBasedCryptography.jl/ # Lattice cryptography educational toolkit
├── playground/
│ └── pluto/ # Interactive Pluto notebooks
└── src/ # Core implementations
🛠️ Installation
Prerequisites
Julia 1.10 or later
Git
Installation Steps
Clone the repository:
git clone https://github.com/Kiara-Dev-Team/open-problem-toolkit.git
cd open-problem-toolkit
Install individual packages:
HomomorphicCryptography.jl
cd HomomorphicCryptography.jl
julia --project=. -e "using Pkg; Pkg.instantiate()"
PQCValidator.jl
cd ../PQCValidator.jl
julia --project=. -e "using Pkg; Pkg.instantiate()"
ZKPValidator.jl
cd ../ZKPValidator.jl
julia --project=. -e "using Pkg; Pkg.instantiate()"
LibOQS.jl
cd ../LibOQS.jl
julia --project=. -e "using Pkg; Pkg.instantiate()"
LatticeBasedCryptography.jl
cd ../LatticeBasedCryptography.jl
julia --project=. -e "using Pkg; Pkg.instantiate()"
🧪 Testing
Each package includes comprehensive test suites:
Test HomomorphicCryptography.jl (parallel execution)
cd HomomorphicCryptography.jl
julia --project=. test/runtests.jl
Test PQCValidator.jl
cd ../PQCValidator.jl
julia --project=. test/runtests.jl
Test ZKPValidator.jl
cd ../ZKPValidator.jl
julia --project=. test/runtests.jl
Test LibOQS.jl
cd ../LibOQS.jl
julia --project=. test/runtests.jl
Test LatticeBasedCryptography.jl
cd ../LatticeBasedCryptography.jl
julia --project=. test/runtests.jl
📊 Project Status
Package Status Compliance Use Case
HomomorphicCryptography.jl 🧪 Experimental ISO/IEC 18033-6:2019 Privacy-preserving computation
PQCValidator.jl 🧪 Experimental TLS 1.3 PQC Post-quantum security validation
ZKPValidator.jl 🧪 Experimental Draft standards Zero-knowledge proof research
LibOQS.jl 🧪 Experimental NIST PQC Standards Quantum-safe cryptographic algorithms
LatticeBasedCryptography.jl 🚀 Active Development Educational Standards Interactive lattice cryptography learning
🎯 Use Cases
Homomorphic Encryption
Privacy-preserving analytics - Compute on encrypted data
Secure voting systems - Tally votes without revealing individual choices
Financial privacy - Perform calculations on encrypted financial data
Medical research - Analyze encrypted patient data
Post-Quantum Cryptography
TLS security assessment - Validate PQC implementations in web services
Migration planning - Test quantum-resistant cryptographic transitions
Compliance checking - Ensure adherence to post-quantum standards
Zero-Knowledge Proofs
Identity verification - Prove identity without revealing personal information
Credential validation - Verify qualifications without exposing details
Blockchain privacy - Enable private transactions and smart contracts
LibOQS Integration
Algorithm evaluation - Test NIST-standardized post-quantum algorithms
Cryptographic research - Experiment with quantum-safe key exchange and signatures
Protocol development - Build applications using standardized PQC primitives
Lattice-Based Cryptography Education
Interactive learning - Hands-on exploration of lattice mathematics and cryptography
Algorithm visualization - Real-time demonstrations of lattice reduction techniques
Post-quantum education - Understanding the mathematics behind quantum-resistant cryptography
🤝 Contributing
We welcome contributions to all packages! Please see individual package documentation for specific contribution guidelines.
Areas for Contribution
Algorithm implementations - New cryptographic schemes
Performance optimizations - Hardware acceleration, algorithmic improvements
Standards compliance - Implementation of emerging standards
Documentation - Examples, tutorials, and API documentation
Testing - Additional test cases and validation scenarios
📚 Documentation
Detailed documentation is available in each package:
HomomorphicCryptography.jl README
⚠️ Security Notice: These tools are intended for research and educational purposes. For production use, ensure proper security review and follow current best practices for cryptographic implementations.
PQCValidator.jl README
ZKPValidator.jl README
LibOQS.jl README
LatticeBasedCryptography.jl README
📈 Recent Updates (September 21, 2025)
🆕 New: LatticeBasedCryptography.jl Package
We've added a comprehensive educational toolkit for lattice-based cryptography, featuring:
🔐 Complete Lattice-Based Encryption/Decryption System
• Key generation algorithms - Implementation of lattice-based key pair generation using techniques like LWE or NTRU • Encryption/decryption functions - Core cryptographic operations that transform plaintext to ciphertext using lattice mathematical structures • Parameter selection and security analysis - Code for choosing appropriate lattice dimensions, noise parameters, and security level configurations • Simple password protection demo - Shows how your text messages can be scrambled using math so only your friend with the right "key" can read them • Why normal encryption won't work against quantum computers - Explains how future super-computers will break today's security, but lattice math will still protect us
🔄 Interactive Lattice Reduction Algorithms
• LLL (Lenstra-Lenstra-Lovász) algorithm implementation - The foundational lattice reduction technique with step-by-step visualization • BKZ (Block Korkine-Zolotarev) variants - More advanced reduction algorithms with interactive parameter tuning • Real-time lattice visualization - 2D/3D plotting of lattice bases before and after reduction with interactive controls • Think of it like organizing messy dots into neat patterns - Visual demos showing how scattered points get rearranged into organized grids • Why finding the shortest path matters in cryptography - Interactive games showing how hard it is to find the shortest route through a lattice maze
🎓 Educational Demonstrations of LWE/Ring-LWE
• Learning With Errors problem setup - Interactive examples showing how LWE instances are constructed and why they're hard to solve • Ring-LWE polynomial arithmetic - Demonstrations of polynomial ring operations and their cryptographic applications • Security parameter exploration - Tools to experiment with different noise levels and see their impact on security vs. efficiency • Adding random noise to hide secrets - Shows how adding "mathematical static" to equations makes them impossible to solve backwards • Like trying to solve algebra with typos - Demonstrates why equations with small random errors become incredibly hard puzzles to crack
🔒 Cryptographic Protocol Implementations
• Key exchange protocols - Implementation of lattice-based key agreement schemes with interactive parameter selection • Digital signature schemes - Code for lattice-based signatures like Dilithium or FALCON with verification demos • Post-quantum security analysis - Tools to analyze and compare the quantum resistance of different lattice-based approaches • How two people can agree on a secret over the internet - Interactive simulations of secure communication without ever sharing the actual password • Digital signatures that prove "this really came from me" - Demos showing how mathematical proofs can verify who sent a message without revealing private keys
🛠️ Technical Implementation Details
585 lines of new Pluto notebook code added for interactive demonstrations
Comprehensive Julia implementation with educational focus for high school and university students
Real-time visualizations using Pluto.jl's reactive notebook environment
Hands-on learning approach making complex lattice mathematics accessible
オープン問題ツールキット 現代暗号システムの学習と実装のための包括的なJuliaツールキット。この教育プラットフォームは、大学生がデジタル世界を守る最先端の暗号化技術を理解し、実際に使用できるよう支援します。
暗号学の3つの革命的分野を探索してください：
🔐 準同型暗号 - ロックされたデータを解除することなく計算を実行できることを想像してみてください。この技術により、クラウドサーバーは実際の情報を見ることなく、暗号化されたファイルを処理できます（スクランブルされた数字で計算を行うようなものです）。外側から箱の中身を操作できる密封された箱のようなものです。
メリットを受ける対象： プライバシーを損なうことなく患者データを分析する医療提供者、クラウドで安全に取引を処理する金融機関、機密性を維持しながら機密データセットで協力する研究者。
🛡️ ポスト量子暗号 - 現在の暗号化は、通常のコンピュータでは解決がほぼ不可能な数学問題に依存しています。しかし、量子コンピュータ（通常のコンピュータとは異なる働きをする超強力なマシン）は、この保護を簡単に破ることができます。ポスト量子暗号は、量子コンピュータでも解読できない異なる数学パズルを使用し、量子の未来においてもデータの安全性を確保します。
メリットを受ける対象： 機密情報を保護する政府機関、将来の量子攻撃に対してトランザクションを保護する暗号通貨ネットワーク、長期的なデータ保護が必要な組織（50年以上の文書保存要件を持つ法律事務所など）。
🔍 ゼロ知識証明 - 実際に知っていることを明かすことなく、何かを知っていることを証明できるという驚異的な概念です。クラブに入るためのパスワードを知っていることを、実際にパスワードを声に出さずに証明するようなものと考えてください。正確な生年月日を示すことなく18歳以上であることを証明したり、銀行残高を明かすことなく購入に十分なお金があることを証明したりできます。
メリットを受ける対象： 個人情報を保護する身元確認システム、プライベートな取引を可能にするブロックチェーンネットワーク、有権者の選択を明かすことなく資格を確認する投票システム、機密の認証情報を保存しない認証サービス。
🧮 格子ベース暗号 - 格子の数学的概念（3Dグリッドや結晶構造を想像してください）を使用して、解読不可能なコードを作成します。これらの幾何学的パターンは多くのポスト量子アルゴリズムの基盤となっています。なぜなら、これらの数学的迷路を通る最短経路を見つけることは、量子コンピュータにとってさえも非常に困難だからです。
メリットを受ける対象： 古典的攻撃と量子攻撃の両方に耐性のある安全な通信プロトコル、長期的な文書の真正性のためのデジタル署名システム、ポスト量子時代においても安全性を維持する鍵交換メカニズム。
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