Blahaj

https://docs.rs/blahaj/0.6.0/
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Blahaj is a fast, small and secure Shamir's Secret Sharing library crate for Rust that enables...
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### Shamir's Secret Sharing Usage Examples

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/lib.rs.html

Demonstrates basic secret sharing and recovery in both standard and no_std environments.

```rust
use blahaj::{ Sharks, Share };

// Set a minimum threshold of 10 shares
let sharks = Sharks(10);
// Obtain an iterator over the shares for secret [1, 2, 3, 4]
# #[cfg(feature = "std")]
# {
let dealer = sharks.dealer(&[1, 2, 3, 4]);
// Get 10 shares
let shares: Vec<Share> = dealer.take(10).collect();
// Recover the original secret!
let secret = sharks.recover(shares.as_slice()).unwrap();
assert_eq!(secret, vec![1, 2, 3, 4]);
# }
```

```rust
use blahaj::{ Sharks, Share };
use rand_chacha::rand_core::SeedableRng;

// Set a minimum threshold of 10 shares
let sharks = Sharks(10);
// Obtain an iterator over the shares for secret [1, 2, 3, 4]
let mut rng = rand_chacha::ChaCha8Rng::from_seed([0x90; 32]);
let dealer = sharks.dealer_rng(&[1, 2, 3, 4], &mut rng);
// Get 10 shares
let shares: Vec<Share> = dealer.take(10).collect();
// Recover the original secret!
let secret = sharks.recover(shares.as_slice()).unwrap();
assert_eq!(secret, vec![1, 2, 3, 4]);
```

--------------------------------

### Generate and Recover Secret (std)

Source: https://docs.rs/blahaj/0.6.0/blahaj

Use this example when the standard library is available. It shows how to set a minimum threshold, generate shares for a secret, and then recover the original secret from those shares.

```rust
use blahaj::{ Sharks, Share };

// Set a minimum threshold of 10 shares
let sharks = Sharks(10);
// Obtain an iterator over the shares for secret [1, 2, 3, 4]
let dealer = sharks.dealer(&[1, 2, 3, 4]);
// Get 10 shares
let shares: Vec<Share> = dealer.take(10).collect();
// Recover the original secret!
let secret = sharks.recover(shares.as_slice()).unwrap();
assert_eq!(secret, vec![1, 2, 3, 4]);
```

--------------------------------

### Usage example for Sharks struct

Source: https://docs.rs/blahaj/0.6.0/blahaj/struct.Sharks.html

Demonstrates how to use the Sharks struct to set a threshold, generate shares for a secret, and recover the original secret from those shares.

```rust
// Set a minimum threshold of 10 shares
let sharks = Sharks(10);
// Obtain an iterator over the shares for secret [1, 2, 3, 4]
let dealer = sharks.dealer(&[1, 2, 3, 4]);
// Get 10 shares
let shares: Vec<Share> = dealer.take(10).collect();
// Recover the original secret!
let secret = sharks.recover(shares.as_slice()).unwrap();
assert_eq!(secret, vec![1, 2, 3, 4]);
```

--------------------------------

### Generate and Recover Secret (no std)

Source: https://docs.rs/blahaj/0.6.0/blahaj

This example is for environments where the standard library is not available. It requires a random number generator, like `rand_chacha`, to be seeded and provided for share generation.

```rust
use blahaj::{ Sharks, Share };
use rand_chacha::rand_core::SeedableRng;

// Set a minimum threshold of 10 shares
let sharks = Sharks(10);
// Obtain an iterator over the shares for secret [1, 2, 3, 4]
let mut rng = rand_chacha::ChaCha8Rng::from_seed([0x90; 32]);
let dealer = sharks.dealer_rng(&[1, 2, 3, 4], &mut rng);
// Get 10 shares
let shares: Vec<Share> = dealer.take(10).collect();
// Recover the original secret!
let secret = sharks.recover(shares.as_slice()).unwrap();
assert_eq!(secret, vec![1, 2, 3, 4]);
```

--------------------------------

### Get TypeId of self

Source: https://docs.rs/blahaj/0.6.0/blahaj/struct.Sharks.html

Retrieves the `TypeId` of the current instance. This is a standard method for trait objects.

```rust
fn type_id(&self) -> TypeId
```

--------------------------------

### Math Module Unit Tests

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/math.rs.html

Verification tests for polynomial generation, evaluation, and secret interpolation logic.

```rust
#[cfg(test)]
mod tests {
    use super::{get_evaluator, interpolate, random_polynomial, Share, GF256};
    use alloc::{vec, vec::Vec};
    use rand_chacha::rand_core::SeedableRng;

    #[test]
    fn random_polynomial_works() {
        let mut rng = rand_chacha::ChaCha8Rng::from_seed([0x90; 32]);
        let poly = random_polynomial(GF256(1), 3, &mut rng);
        assert_eq!(poly.len(), 3);
        assert_eq!(poly[2], GF256(1));
    }

    #[test]
    fn evaluator_works() {
        let iter = get_evaluator(vec![vec![GF256(3), GF256(2), GF256(5)]]);
        let values: Vec<_> = iter.take(2).map(|s| (s.x.clone(), s.y.clone())).collect();
        assert_eq!(
            values,
            vec![(GF256(1), vec![GF256(4)]), (GF256(2), vec![GF256(13)])]
        );
    }

    #[test]
    fn interpolate_works() {
        let mut rng = rand_chacha::ChaCha8Rng::from_seed([0x90; 32]);
        let poly = random_polynomial(GF256(185), 10, &mut rng);
        let iter = get_evaluator(vec![poly]);
        let shares: Vec<Share> = iter.take(10).collect();
        let root = interpolate(&shares);
        assert_eq!(root, vec![185]);
    }
}
```

--------------------------------

### Usage of Share for secret distribution and recovery

Source: https://docs.rs/blahaj/0.6.0/blahaj/struct.Share.html

Demonstrates generating shares from a dealer and recovering a secret from serialized share bytes.

```rust
use blahaj::{Sharks, Share};
use core::convert::TryFrom;

// Transmit the share bytes to a printer
let sharks = Sharks(3);
let mut rng = rand_chacha::ChaCha8Rng::from_seed([0x90; 32]);
let dealer = sharks.dealer_rng(&[1, 2, 3], &mut rng);

// Get 5 shares and print paper keys
for s in dealer.take(5) {
    send_to_printer(Vec::from(&s));
};

// Get share bytes from an external source and recover secret
let shares_bytes: Vec<Vec<u8>> = ask_shares();
let shares: Vec<Share> = shares_bytes.iter().map(|s| Share::try_from(s.as_slice()).unwrap()).collect();
let secret = sharks.recover(&shares).unwrap();
```

--------------------------------

### Test Vec<u8> to Share Conversion

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/share.rs.html

Unit test for the `TryFrom<&[u8]> for Share` implementation, verifying that a byte slice is correctly parsed into a Share instance.

```rust
#[test]
fn share_from_u8_slice_works() {
    let bytes = [1, 2, 3];
    let share = Share::try_from(&bytes[..]).unwrap();
    assert_eq!(share.x, GF256(1));
    assert_eq!(share.y, vec![GF256(2), GF256(3)]);
}
```

--------------------------------

### Share Serialization and Conversion

Source: https://docs.rs/blahaj/0.6.0/blahaj/struct.Share.html

Methods for converting Share instances to byte vectors and reconstructing them from byte slices.

```APIDOC
## Serialization and Conversion

### Description
Methods to convert a Share instance into a byte vector or reconstruct a Share from a byte slice.

### Request Body
- **Share** (struct) - The share object containing x and y coordinates.

### Response
#### Success Response (200)
- **Vec<u8>** (byte vector) - Serialized representation of the share.
- **Share** (struct) - Reconstructed share object from bytes.

### Request Example
// Converting Share to bytes
let share_bytes: Vec<u8> = Vec::from(&share);

// Reconstructing Share from bytes
let share = Share::try_from(bytes.as_slice()).unwrap();
```

--------------------------------

### Test Share to Vec<u8> Conversion

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/share.rs.html

Unit test for the `From<&Share> for Vec<u8>` implementation, ensuring that a Share is correctly converted into its byte representation.

```rust
#[test]
fn vec_from_share_works() {
    let share = Share {
        x: GF256(1),
        y: vec![GF256(2), GF256(3)],
    };
    let bytes = Vec::from(&share);
    assert_eq!(bytes, vec![1, 2, 3]);
}
```

--------------------------------

### Shamir's Secret Sharing Math Functions

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/math.rs.html

Core functions for interpolating secrets, generating random polynomials, and evaluating polynomials for share creation.

```rust
pub fn interpolate(shares: &[Share]) -> Vec<u8> {
    (0..shares[0].y.len())
        .map(|s| {
            shares
                .iter()
                .map(|s_i| {
                    shares
                        .iter()
                        .filter(|s_j| s_j.x != s_i.x)
                        .map(|s_j| s_j.x.clone() / (s_j.x.clone() - s_i.x.clone()))
                        .product::<GF256>()
                        * s_i.y[s].clone()
                })
                .sum::<GF256>()
                .0
        })
        .collect()
}

pub fn random_polynomial<R: rand::Rng>(s: GF256, k: u8, rng: &mut R) -> Vec<GF256> {
    let k = k as usize;
    let mut poly = Vec::with_capacity(k);
    let between = Uniform::new_inclusive(0, 255);

    for _ in 1..k {
        poly.push(GF256(between.sample(rng)));
    }
    poly.push(s);

    poly
}

pub fn get_evaluator(polys: Vec<Vec<GF256>>) -> impl Iterator<Item = Share> {
    (1..=u8::MAX).map(GF256).map(move |x| Share {
        x: x.clone(),
        y: polys
            .iter()
            .map(|p| {
                p.iter()
                    .fold(GF256(0), |acc, c| acc * x.clone() + c.clone())
            })
            .collect(),
    })
}
```

--------------------------------

### Generating Shares with dealer

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/lib.rs.html

Generates shares using the thread-local random number generator. Requires the std feature.

```rust
# use blahaj::{ Sharks, Share };
# let sharks = Sharks(3);
// Obtain an iterator over the shares for secret [1, 2]
let dealer = sharks.dealer(&[1, 2]);
// Get 3 shares
let shares: Vec<Share> = dealer.take(3).collect();
```

--------------------------------

### Test secret recovery scenarios

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/lib.rs.html

Unit tests verifying error conditions for insufficient or duplicate shares, and successful integration recovery.

```rust
#[test]
    fn test_insufficient_shares_err() {
        let sharks = Sharks(255);
        let shares: Vec<Share> = sharks.make_shares(&[1]).take(254).collect();
        let secret = sharks.recover(&shares);
        assert!(secret.is_err());
    }

    #[test]
    fn test_duplicate_shares_err() {
        let sharks = Sharks(255);
        let mut shares: Vec<Share> = sharks.make_shares(&[1]).take(255).collect();
        shares[1] = Share {
            x: shares[0].x.clone(),
            y: shares[0].y.clone(),
        };
        let secret = sharks.recover(&shares);
        assert!(secret.is_err());
    }

    #[test]
    fn test_integration_works() {
        let sharks = Sharks(255);
        let shares: Vec<Share> = sharks.make_shares(&[1, 2, 3, 4]).take(255).collect();
        let secret = sharks.recover(&shares).unwrap();
        assert_eq!(secret, vec![1, 2, 3, 4]);
    }
```

--------------------------------

### Test GF256 Product

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/field.rs.html

Confirms the product calculation for a list of GF256 values.

```rust
let values = vec![GF256(1), GF256(1), GF256(4)];
        assert_eq!(values.into_iter().product::<GF256>().0, 4);
```

--------------------------------

### Galois Field 256 Pre-calculated Tables

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/field.rs.html

Logarithmic and exponential lookup tables used for field arithmetic. These constants are essential for performing multiplication and division within the field.

```rust
const LOG_TABLE: [u8; 256] = [
    0x00, 0x00, 0x01, 0x19, 0x02, 0x32, 0x1a, 0xc6, 0x03, 0xdf, 0x33, 0xee, 0x1b, 0x68, 0xc7, 0x4b,
    0x04, 0x64, 0xe0, 0x0e, 0x34, 0x8d, 0xef, 0x81, 0x1c, 0xc1, 0x69, 0xf8, 0xc8, 0x08, 0x4c, 0x71,
    0x05, 0x8a, 0x65, 0x2f, 0xe1, 0x24, 0x0f, 0x21, 0x35, 0x93, 0x8e, 0xda, 0xf0, 0x12, 0x82, 0x45,
    0x1d, 0xb5, 0xc2, 0x7d, 0x6a, 0x27, 0xf9, 0xb9, 0xc9, 0x9a, 0x09, 0x78, 0x4d, 0xe4, 0x72, 0xa6,
    0x06, 0xbf, 0x8b, 0x62, 0x66, 0xdd, 0x30, 0xfd, 0xe2, 0x98, 0x25, 0xb3, 0x10, 0x91, 0x22, 0x88,
    0x36, 0xd0, 0x94, 0xce, 0x8f, 0x96, 0xdb, 0xbd, 0xf1, 0xd2, 0x13, 0x5c, 0x83, 0x38, 0x46, 0x40,
    0x1e, 0x42, 0xb6, 0xa3, 0xc3, 0x48, 0x7e, 0x6e, 0x6b, 0x3a, 0x28, 0x54, 0xfa, 0x85, 0xba, 0x3d,
    0xca, 0x5e, 0x9b, 0x9f, 0x0a, 0x15, 0x79, 0x2b, 0x4e, 0xd4, 0xe5, 0xac, 0x73, 0xf3, 0xa7, 0x57,
    0x07, 0x70, 0xc0, 0xf7, 0x8c, 0x80, 0x63, 0x0d, 0x67, 0x4a, 0xde, 0xed, 0x31, 0xc5, 0xfe, 0x18,
    0xe3, 0xa5, 0x99, 0x77, 0x26, 0xb8, 0xb4, 0x7c, 0x11, 0x44, 0x92, 0xd9, 0x23, 0x20, 0x89, 0x2e,
    0x37, 0x3f, 0xd1, 0x5b, 0x95, 0xbc, 0xcf, 0xcd, 0x90, 0x87, 0x97, 0xb2, 0xdc, 0xfc, 0xbe, 0x61,
    0xf2, 0x56, 0xd3, 0xab, 0x14, 0x2a, 0x5d, 0x9e, 0x84, 0x3c, 0x39, 0x53, 0x47, 0x6d, 0x41, 0xa2,
    0x1f, 0x2d, 0x43, 0xd8, 0xb7, 0x7b, 0xa4, 0x76, 0xc4, 0x17, 0x49, 0xec, 0x7f, 0x0c, 0x6f, 0xf6,
    0x6c, 0xa1, 0x3b, 0x52, 0x29, 0x9d, 0x55, 0xaa, 0xfb, 0x60, 0x86, 0xb1, 0xbb, 0xcc, 0x3e, 0x5a,
    0xcb, 0x59, 0x5f, 0xb0, 0x9c, 0xa9, 0xa0, 0x51, 0x0b, 0xf5, 0x16, 0xeb, 0x7a, 0x75, 0x2c, 0xd7,
    0x4f, 0xae, 0xd5, 0xe9, 0xe6, 0xe7, 0xad, 0xe8, 0x74, 0xd6, 0xf4, 0xea, 0xa8, 0x50, 0x58, 0xaf,
];

const EXP_TABLE: [u8; 512] = [
    0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26,
    0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0,
    0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23,
    0x46, 0x8c, 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1,
    0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0,
    0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2,
    0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce,
    0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc,
    0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54,
    0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73,
    0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff,
    0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41,
    0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6,
    0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x09,
    0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0x0b, 0x16,
    0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x01,
    0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c,
    0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0, 0x9d,
    0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46,
    0x8c, 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f,
    0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0, 0xfd,
    0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9,
    0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81,
    0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85,
    0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8,
    0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6,
    0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3,
    0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82,
];
```

--------------------------------

### Convert Share to Vec<u8>

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/share.rs.html

Implements the From<&Share> trait to convert a Share instance into a byte vector. This is useful for serializing shares for storage or transmission.

```rust
impl From<&Share> for Vec<u8> {
    fn from(s: &Share) -> Vec<u8> {
        let mut bytes = Vec::with_capacity(s.y.len() + 1);
        bytes.push(s.x.0);
        bytes.extend(s.y.iter().map(|p| p.0));
        bytes
    }
}
```

--------------------------------

### GF256 Product Implementation

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/field.rs.html

Implements the `Product` trait for GF256, allowing calculation of the product of an iterator of GF256 elements using the defined multiplication operation.

```rust
impl Product for GF256 {
    fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
        iter.fold(Self(1), |acc, x| acc * x)
    }
}
```

--------------------------------

### GF256 Addition Test

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/field.rs.html

Tests the addition implementation for GF256 by comparing results against a precomputed answer table. Ensures correctness of the XOR-based addition.

```rust
#[test]
fn add_works() {
    let answers: [u8; 256] = [
        1, 2, 5, 17, 18, 18, 90, 70, 30, 229, 71, 6, 214, 239, 212, 109, 72, 252, 205, 84, 128,
        248, 5, 72, 147, 194, 111, 244, 208, 56, 44, 177, 152, 173, 43, 179, 196, 110, 155, 20,
        95, 71, 59, 173, 30, 211, 29, 102, 91, 57, 199, 119, 126, 15, 169, 25, 148, 32, 96,
        170, 244, 139, 172, 7, 89, 1, 234, 160, 255, 242, 110, 65, 135, 82, 172, 188, 14, 173,
        90, 120, 203, 55, 71, 117, 228, 64, 106, 194, 15, 51, 204, 255, 216, 142, 55, 162, 199,
        237, 245, 37, 210, 106, 58, 230, 102, 32, 28, 60, 42, 56, 221, 243, 75, 65, 165, 227,
        242, 248, 190, 184, 117, 162, 9, 105, 228, 192, 193, 155, 130, 103, 238, 171, 52, 237,
        185, 164, 40, 212, 255, 175, 181, 208, 212, 76, 75, 232, 3, 94, 116, 28, 225, 214, 88,
        214, 171, 171, 199, 245, 62, 93, 209, 238, 110, 56, 83, 45, 240, 179, 108, 98, 64, 1,
        167, 10, 79, 158, 17, 141, 120, 224, 130, 27, 63, 90, 17, 11, 87, 143, 226, 58, 239,
        227, 157, 52, 113, 188, 127, 246, 163, 120, 216, 47, 57, 12, 162, 171, 60, 80, 61, 3,
        98, 224, 80, 111, 172, 69, 56, 251, 173, 231, 23, 137, 180, 83, 217, 125, 23, 32, 161,
        211, 84, 164, 252, 6, 237, 0, 177, 254, 39, 193, 99, 246, 101, 148, 28, 14, 98, 107,
        111, 224, 152, 50, 5, 23, 214, 174,
    ];

    for (i, a) in answers.iter().enumerate() {
        assert_eq!((GF256(LOG_TABLE[i]) + GF256(EXP_TABLE[i])).0, *a);
    }
}
```

--------------------------------

### Return the argument unchanged

Source: https://docs.rs/blahaj/0.6.0/blahaj/struct.Sharks.html

A simple conversion function that returns the input value as is. This is part of the `From` trait implementation.

```rust
fn from(t: T) -> T
```

--------------------------------

### dealer Method

Source: https://docs.rs/blahaj/0.6.0/blahaj/struct.Sharks.html

Generates shares for a given secret. The maximum number of shares that can be generated is 256.

```APIDOC
## pub fn dealer(&self, secret: &[u8]) -> impl Iterator<Item = Share>

### Description
Given a `secret` byte slice, returns an `Iterator` along new shares. The maximum number of shares that can be generated is 256.

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
```rust
// Obtain an iterator over the shares for secret [1, 2]
let dealer = sharks.dealer(&[1, 2]);
// Get 3 shares
let shares: Vec<Share> = dealer.take(3).collect();
```

### Response
#### Success Response (200)
An iterator that yields `Share` items.

#### Response Example
(Iterator output, not a direct JSON response)
```

--------------------------------

### Convert Vec<u8> to Share

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/share.rs.html

Implements the TryFrom<&[u8]> trait to convert a byte slice into a Share instance. This is used for deserializing shares received from external sources. Returns an error if the byte slice is too short.

```rust
impl core::convert::TryFrom<&[u8]> for Share {
    type Error = &'static str;

    fn try_from(s: &[u8]) -> Result<Share, Self::Error> {
        if s.len() < 2 {
            Err("A Share must be at least 2 bytes long")
        } else {
            let x = GF256(s[0]);
            let y = s[1..].iter().map(|p| GF256(*p)).collect();
            Ok(Share { x, y })
        }
    }
}
```

--------------------------------

### Generating Shares with dealer_rng

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/lib.rs.html

Generates shares using a provided random number generator, suitable for no_std environments.

```rust
# use blahaj::{ Sharks, Share };
# use rand_chacha::rand_core::SeedableRng;
# let sharks = Sharks(3);
// Obtain an iterator over the shares for secret [1, 2]
let mut rng = rand_chacha::ChaCha8Rng::from_seed([0x90; 32]);
let dealer = sharks.dealer_rng(&[1, 2], &mut rng);
// Get 3 shares
let shares: Vec<Share> = dealer.take(3).collect();
```

--------------------------------

### GF256 Multiplication Implementation

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/field.rs.html

Implements the `Mul` trait for GF256. Multiplication uses precomputed logarithm and exponentiation tables for efficiency. Handles multiplication by zero.

```rust
impl Mul for GF256 {
    type Output = Self;

    fn mul(self, other: Self) -> Self::Output {
        let log_x = LOG_TABLE[self.0 as usize] as usize;
        let log_y = LOG_TABLE[other.0 as usize] as usize;

        if self.0 == 0 || other.0 == 0 {
            Self(0)
        } else {
            Self(EXP_TABLE[log_x + log_y])
        }
    }
}
```

--------------------------------

### GF256 Addition Implementation

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/field.rs.html

Implements the `Add` trait for GF256. Addition in GF(256) is equivalent to the bitwise XOR operation.

```rust
impl Add for GF256 {
    type Output = GF256;

    fn add(self, other: Self) -> Self::Output {
        Self(self.0 ^ other.0)
    }
}
```

--------------------------------

### Generate shares for a secret

Source: https://docs.rs/blahaj/0.6.0/blahaj/struct.Sharks.html

Generates shares for a given secret. The maximum number of shares that can be generated is 256. This is a typical usage scenario for share generation.

```rust
// Obtain an iterator over the shares for secret [1, 2]
let dealer = sharks.dealer(&[1, 2]);
// Get 3 shares
let shares: Vec<Share> = dealer.take(3).collect();
```

--------------------------------

### Sharks Struct Usage

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/lib.rs.html

Basic usage of the Sharks struct to generate and recover shares.

```rust
# use blahaj::{ Sharks, Share };
// Set a minimum threshold of 10 shares
let sharks = Sharks(10);
// Obtain an iterator over the shares for secret [1, 2, 3, 4]
# #[cfg(feature = "std")]
# {
let dealer = sharks.dealer(&[1, 2, 3, 4]);
// Get 10 shares
let shares: Vec<Share> = dealer.take(10).collect();
// Recover the original secret!
let secret = sharks.recover(shares.as_slice()).unwrap();
assert_eq!(secret, vec![1, 2, 3, 4]);
# }
```

--------------------------------

### Recovering Secrets from Shares

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/lib.rs.html

Recovers the original secret from a collection of shares.

```rust
# use blahaj::{ Sharks, Share };
# use rand_chacha::rand_core::SeedableRng;
# let sharks = Sharks(3);
# let mut rng = rand_chacha::ChaCha8Rng::from_seed([0x90; 32]);
# let mut shares: Vec<Share> = sharks.dealer_rng(&[1], &mut rng).take(3).collect();
// Recover original secret from shares
let mut secret = sharks.recover(&shares);
// Secret correctly recovered
```

--------------------------------

### GF256 Division Implementation

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/field.rs.html

Implements the `Div` trait for GF256. Division uses precomputed logarithm and exponentiation tables. Handles division by zero by returning zero.

```rust
impl Div for GF256 {
    type Output = Self;

    fn div(self, other: Self) -> Self::Output {
        let log_x = LOG_TABLE[self.0 as usize] as usize;
        let log_y = LOG_TABLE[other.0 as usize] as usize;

        if self.0 == 0 {
            Self(0)
        } else {
            Self(EXP_TABLE[log_x + 255 - log_y])
        }
    }
}
```

--------------------------------

### recover(shares)

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/lib.rs.html

Attempts to reconstruct the original secret from a provided collection of shares. It validates that all shares have consistent lengths and that a sufficient number of unique shares are provided.

```APIDOC
## recover(shares)

### Description
Reconstructs the original secret from a set of shares. The method verifies that the number of unique shares meets the threshold defined by the Sharks instance.

### Parameters
#### Request Body
- **shares** (IntoIterator<Item = &Share>) - Required - An iterator of shares to be used for recovery.

### Response
#### Success Response (200)
- **Result<Vec<u8>, &str>** - Returns the recovered secret as a byte vector on success.

#### Error Response
- **Err(&str)** - Returns an error message if shares have inconsistent lengths, or if there are insufficient unique shares to recover the secret.
```

--------------------------------

### GF256 Multiplication Test

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/field.rs.html

Tests the multiplication implementation for GF256 by comparing results against a precomputed answer table. Verifies the correctness of the logarithm-based multiplication.

```rust
#[test]
fn mul_works() {
    let answers: [u8; 256] = [
        0, 0, 4, 200, 32, 14, 206, 179, 39, 134, 169, 160, 32, 59, 184, 50, 45, 121, 69, 43,
        102, 43, 139, 169, 18, 94, 107, 84, 18, 157, 159, 51, 211, 1, 52, 13, 51, 128, 31, 219,
        240, 230, 212, 219, 197, 19, 11, 135, 93, 163, 237, 53, 91, 177, 135, 124, 240, 224, 6,
        158, 167, 155, 155, 38, 223, 144, 70, 54, 50, 45, 134, 170, 126, 223, 103, 207, 253,
        176, 75, 98, 137, 87, 59, 50, 208, 116, 29, 200, 128, 82, 13, 138, 107, 53, 42, 34,
        123, 203, 65, 174, 111, 101, 19, 78, 165, 62, 115, 108, 175, 139, 126, 107, 55, 196,
        30, 209, 126, 8, 15, 211, 57, 191, 37, 254, 24, 136, 30, 111, 188, 30, 209, 208, 49,
        132, 181, 22, 207, 241, 28, 2, 97, 58, 244, 179, 190, 120, 249, 174, 99, 6, 215, 232,
    ];

    for (i, a) in answers.iter().enumerate() {
        assert_eq!((GF256(LOG_TABLE[i]) * GF256(EXP_TABLE[i])).0, *a);
    }
}
```

--------------------------------

### Test GF256 Summation

Source: https://docs.rs/blahaj/0.6.0/src/blahaj/field.rs.html

Verifies the summation of GF256 values, ensuring the result is correct.

```rust
let values = vec![GF256(0x53), GF256(0xCA), GF256(0)];
        assert_eq!(values.into_iter().sum::<GF256>().0, 0x99);
```

--------------------------------

### recover Method

Source: https://docs.rs/blahaj/0.6.0/blahaj/struct.Sharks.html

Recovers the original secret from a collection of shares. Returns an error if the number of distinct shares is less than the minimum threshold.

```APIDOC
## pub fn recover<'a, T>(&self, shares: T) -> Result<Vec<u8>, &str>
where T: IntoIterator<Item = &'a Share>,
      T::IntoIter: Iterator<Item = &'a Share>,

### Description
Given an iterable collection of shares, recovers the original secret. If the number of distinct shares is less than the minimum threshold an `Err` is returned, otherwise an `Ok` containing the secret.

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
- **shares** (T): An iterable collection of `Share` references.

### Request Example
```rust
// Recover original secret from shares
let mut secret = sharks.recover(&shares);
// Secret correctly recovered
assert!(secret.is_ok());
// Remove shares for demonstration purposes
shares.clear();
secret = sharks.recover(&shares);
// Not enough shares to recover secret
assert!(secret.is_err());
```

### Response
#### Success Response (200)
- **Vec<u8>** - A vector of bytes representing the recovered secret.

#### Error Response (400)
- **&str** - An error message indicating insufficient shares.

#### Response Example
```json
{
  "secret": [1, 2, 3, 4]
}
```

```json
{
  "error": "Not enough shares to recover secret"
}
```
```
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