Morphia

A Rust implementation of the Paillier partially homomorphic encryption scheme, featuring secure key management and CLI operations.

Features

Core Cryptosystem

• Key Generation: Configurable prime sizes (default: 512-bit primes).
• Secure Prime Generation: Utilizes the RSA crate.
• Homomorphic Operations:
  • Addition of ciphertexts.
  • Multiplication by constants.
• Semantic Security: Achieved through random parameter r in encryption.

CLI Tools

Commands

# Generate new key pair
cargo run -- keygen [--bits <key-size>]

# Encrypt a number
cargo run -- encrypt --message <number> [--output <output-file>]

# Homomorphically add two ciphertexts
cargo run -- add --cipher1-file <file1> --cipher2-file <file2> [--output <output-file>]

# Decrypt result
cargo run -- decrypt --ciphertext <ciphertext-file>

# Demo the entire process
cargo run -- demo --value1 <number1> --value2 <number2> --constant <number>

Key Management

• Timestamped Key Directories: e.g., keys_20250413_152217.
• Master Registry: Tracks active keys.
• Automatic Key Selection: Uses the latest keys by default.
• Manual Overrides: Specify keys using the --dir parameter.
• Secure Serialization: Keys and ciphertexts serialized with JSON.

Installation

# Clone repository
git clone https://github.com/yourusername/morphia.git
cd morphia

# Build with Cargo
cargo build --release

Usage

Basic Workflow

1. Generate Keys

cargo run -- keygen

• Generates public and private keys in a timestamped directory.
• Updates the key registry.

2. Encrypt Values

cargo run -- encrypt --message 42

• Encrypts using the latest key in the registry.
• Saves ciphertext to a timestamped file automatically.
• Use --output to specify a custom output file.

3. Homomorphic Addition

cargo run -- add --cipher1-file ciphertext/20250412_210851.json --cipher2-file ciphertext/20250413_152511.json

• Adds two ciphertexts homomorphically.
• Saves the result to a timestamped file in the ciphertext directory.
• Optionally, specify output with --output.

4. Decrypt Result

cargo run -- decrypt --ciphertext ciphertext/sum_20250413_161409.json

• Uses the latest key to decrypt.
• Automatically handles small value detection for usability.

Demo Mode

cargo run -- demo --value1 5 --value2 7 --constant 3

• Demonstrates:
  • decrypt(add(encrypt(a), encrypt(b))) == a + b
  • decrypt(multiply_by_constant(encrypt(a), k)) == a * k

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Technical Details

Paillier Parameters

Parameter	Formula	Description
n	p * q	Modulus (product of primes)
g	n + 1	Generator
λ	lcm(p-1, q-1)	Carmichael function
μ	λ⁻¹ mod n	Decryption coefficient

Homomorphic Properties

Given ciphertexts:

* E(m₁) = gᵐ¹ · r₁ⁿ mod n²
* E(m₂) = gᵐ² · r₂ⁿ mod n²

Addition:

E(m₁) · E(m₂) mod n² = E(m₁ + m₂ mod n)

Scalar Multiplication:

E(m)ᵏ mod n² = E(k·m mod n) 

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License

MIT License - See LICENSE for details.