Shamir Threshold File Encryption

A compact implementation of Shamir's Secret Sharing for splitting a 32-byte symmetric key that encrypts a file. The code shows the full path from finite-field math to practical key handling and file encryption.

• Shamir secret sharing over a prime field with BigInt arithmetic and Lagrange interpolation
• AEAD file encryption using a randomly generated 32-byte key
• Parameterized n, t, and p with safe defaults for experimentation
• End-to-end flow: encrypt, split, reconstruct, decrypt

• src/main.rs - orchestration and demo entry points
• src/utils/key_generation.rs - RNG key generation
• src/utils/key_ops.rs - Shamir split/reconstruct, modular arithmetic
• src/utils/file_operations.rs - encryption/decryption and shard IO

Let the secret be s in a prime field F_p. Choose random coefficients a_1, ..., a_(t-1) and define:

$$ f(x) = s + a_1 x + a_2 x^2 + \cdots + a_{t-1} x^{t-1} \pmod p $$

A shard is $(x_i, y_i)$ where $y_i = f(x_i)$. Given any $t$ shards, reconstruct:

$$ s = \sum_{i=1}^{t} y_i \cdot \prod_{j \ne i} \frac{-x_j}{x_i - x_j} \pmod p $$

The implementation uses extended Euclid for modular inversion and BigInt for safe arithmetic across the field.

There is no CLI yet. The demo flow is invoked from src/main.rs.

1. Choose an input file path and update the encrypt_file call
2. Run:

cargo run

3. Use the generated shards plus the stored prime to reconstruct the key and decrypt

Example flow (edit main, then run):

encrypt_file("path/to/input.txt".to_string(), None, None, None)?;
decrypt_file("path/to/encrypted_output".to_string(), "path/to/shards_dir")?;

• This is a research/demo implementation and is not audited for production use
• Output naming and shard directory layout are fixed in code
• (Being Worked On) Polynomial coefficients are sampled from 128-bit randomness and reduced mod p, which is not uniform when p is large
• Not verifiable secret sharing yet; corrupted shards are not detected
• Test cases

• num-bigint for finite-field arithmetic
• rand for randomness
• aes-gcm for AEAD file encryption