### Install libcrypto on Ubuntu

Source: https://pub.dev/documentation/spake2plus/latest/index.html

Installs the OpenSSL development library required for the spake2plus package on Ubuntu systems. Ensure you have the Dart/Flutter SDK installed prior to this step.

```bash
sudo apt-get install libssl-dev
```

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

### Install openssl on macOS

Source: https://pub.dev/documentation/spake2plus/latest/index.html

Installs OpenSSL version 3 or later on macOS using Homebrew, a prerequisite for the spake2plus package. After installation, verify the path to libcrypto.dylib and provide it to the Spake2plus class constructor.

```bash
brew install openssl@3 # Homebrew
```

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

### ScryptParameters Constructor

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters/ScryptParameters.html

Initializes a ScryptParameters object with the provided password, salt, cost, block size, parallelization, and derived key length.

```APIDOC
## ScryptParameters Constructor

### Description
Initializes a ScryptParameters object with the provided password, salt, cost, block size, parallelization, and derived key length.

### Parameters
#### Path Parameters
- **pwd** (String) - Required - The password to be hashed.
- **salt** (String) - Required - The salt to be used in the hashing process.
- **cost** (int) - Required - The cost factor (N) for the scrypt algorithm, determining computational effort.
- **blockSize** (int) - Required - The block size (r) for the scrypt algorithm.
- **parallelization** (int) - Required - The parallelization factor (p) for the scrypt algorithm.
- **dkLen** (int) - Required - The desired length of the derived key in bytes.
```

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

### Spake2plus Constructor

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus-class.html

Initializes a new instance of the Spake2plus class.

```APIDOC
## Spake2plus Constructor

### Description
Initializes a new instance of the Spake2plus class with the provided library path and curve points.

### Parameters
- **libraryPath** (String) - The path to the Spake2plus library.
- **curvePointM** (List<int>) - The M curve point.
- **curvePointN** (List<int>) - The N curve point.
```

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

### Spake2plus Constructor

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/Spake2plus.html

Initializes a new instance of the Spake2plus class. Requires the path to the OpenSSL library and the curve points M and N as lists of integers.

```APIDOC
## Spake2plus Constructor

### Description
Initializes a new instance of the Spake2plus class.

### Parameters
- **libraryPath** (String) - Required - The file path to the OpenSSL dynamic library.
- **curvePointM** (List<int>) - Required - The curve point M as a list of integers.
- **curvePointN** (List<int>) - Required - The curve point N as a list of integers.

### Implementation
```dart
Spake2plus(String libraryPath, List<int> curvePointM, List<int> curvePointN)
    : _openssl = OpenSSL(ffi.DynamicLibrary.open(libraryPath)),
      _curvePointM = Uint8List.fromList(curvePointM),
      _curvePointN = Uint8List.fromList(curvePointN);
```
```

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

### Compute Witnesses Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/computeWitnesses.html

This is the main implementation of the computeWitnesses method. It initializes an internal context and then calls a private helper function to perform the actual witness computation.

```dart
(Uint8List, Uint8List) computeWitnesses(ScryptParameters scryptParams) {
  return _context((group, ctx, order) {
    return _computeWitnesses(scryptParams, group, ctx, order);
  });
}
```

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

### ScryptParameters Constructor Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters/ScryptParameters.html

This is the Dart implementation of the ScryptParameters constructor. It initializes the object with the provided password, salt, cost, block size, parallelization, and derived key length.

```dart
ScryptParameters(this.pwd, this.salt, this.cost, this.blockSize,
    this.parallelization, this.dkLen);
```

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

### Spake2plus Constructor Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/Spake2plus.html

Initializes the Spake2plus object by opening the OpenSSL library, and converting the provided curve points into Uint8List format.

```dart
Spake2plus(String libraryPath, List<int> curvePointM, List<int> curvePointN)
    : _openssl = OpenSSL(ffi.DynamicLibrary.open(libraryPath)),
      _curvePointM = Uint8List.fromList(curvePointM),
      _curvePointN = Uint8List.fromList(curvePointN);
```

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

### ScryptParameters Constructor

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters-class.html

Constructs a ScryptParameters object with the specified parameters.

```APIDOC
## ScryptParameters Constructor

### Description
Initializes a new instance of the `ScryptParameters` class.

### Parameters
- **pwd** (String) - The password.
- **salt** (String) - The salt.
- **cost** (int) - The cost factor (N).
- **blockSize** (int) - The block size (r).
- **parallelization** (int) - The parallelization factor (p).
- **dkLen** (int) - The desired length of the derived key in bytes.
```

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

### computeWitnesses

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus-class.html

Computes witnesses using Scrypt parameters.

```APIDOC
## computeWitnesses

### Description
Computes witnesses required for the Spake2plus protocol using Scrypt parameters for key derivation.

### Parameters
- **scryptParams** (ScryptParameters) - The parameters for the Scrypt key derivation function.

### Returns
- **(Uint8List, Uint8List)** - A tuple containing two Uint8List representing the computed witnesses.
```

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

### verifierFinish Method Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/verifierFinish.html

This is the core implementation of the verifierFinish method. It validates input points, performs cryptographic calculations for Z and V, and cleans up allocated resources. Use this method when acting as the verifier in the Spake2plus protocol.

```dart
(Uint8List Z, Uint8List V)? verifierFinish(
  Uint8List w0Bytes,
  Uint8List bytesL,
  Uint8List bytesX,
  Uint8List yBytes,
) {
  return _context((group, ctx, _) {
    final X = _openssl.EC_POINT_new(group);
    _openssl.bytes2point(group, X, bytesX, ctx);
    final ok = (_openssl.EC_POINT_is_on_curve(group, X, ctx) == 1) &&
        (_openssl.EC_POINT_is_at_infinity(group, X) == 0);

    if (!ok) {
      _openssl.EC_POINT_free(X);
      return null;
    }

    final M = _openssl.EC_POINT_new(group);
    _openssl.bytes2point(group, M, _curvePointM, ctx);

    final L = _openssl.EC_POINT_new(group);
    _openssl.bytes2point(group, L, bytesL, ctx);

    final w0 = _openssl.BN_new();
    _openssl.bytes2bn(w0, w0Bytes);
    final y = _openssl.BN_new();
    _openssl.bytes2bn(y, yBytes);

    final Z = _openssl.calculateZ(group, ctx, X, M, w0, y);
    final V = _openssl.calculateV_verifier(group, ctx, L, y);

    final bytesZ = _openssl.point2bytes(group, Z, ctx);
    final bytesV = _openssl.point2bytes(group, V, ctx);

    _openssl.EC_POINT_free(V);
    _openssl.EC_POINT_free(Z);
    _openssl.EC_POINT_free(L);
    _openssl.EC_POINT_free(M);
    _openssl.EC_POINT_free(X);
    _openssl.BN_free(w0);
    _openssl.BN_free(y);

    return (bytesZ, bytesV);
  });
}
```

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

### ProverFinish Implementation in Spake2plus

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/proverFinish.html

This implementation details the prover's final step in the Spake2+ protocol. It validates the verifier's public point Y, calculates intermediate values using private keys and curve parameters, and returns the proof elements Z and V as byte arrays. Ensure all necessary OpenSSL bindings are available.

```dart
(Uint8List Z, Uint8List V)? proverFinish(Uint8List w0Bytes, Uint8List w1Bytes,
    Uint8List xBytes, Uint8List bytesY) {
  return _context((group, ctx, _) {
    final Y = _openssl.EC_POINT_new(group);
    _openssl.bytes2point(group, Y, bytesY, ctx);
    final ok = (_openssl.EC_POINT_is_on_curve(group, Y, ctx) == 1) &&
        (_openssl.EC_POINT_is_at_infinity(group, Y) == 0);

    if (!ok) {
      _openssl.EC_POINT_free(Y);
      return null;
    }

    final N = _openssl.EC_POINT_new(group);
    _openssl.bytes2point(group, N, _curvePointN, ctx);

    final x = _openssl.BN_new();
    _openssl.bytes2bn(x, xBytes);

    final w0 = _openssl.BN_new();
    _openssl.bytes2bn(w0, w0Bytes);

    final w1 = _openssl.BN_new();
    _openssl.bytes2bn(w1, w1Bytes);

    final Z = _openssl.calculateZ(group, ctx, Y, N, w0, x);
    final V = _openssl.calculateV_prover(group, ctx, Y, N, w0, w1, x);

    final bytesZ = _openssl.point2bytes(group, Z, ctx);
    final bytesV = _openssl.point2bytes(group, V, ctx);

    _openssl.EC_POINT_free(V);
    _openssl.EC_POINT_free(Z);
    _openssl.EC_POINT_free(N);
    _openssl.EC_POINT_free(Y);
    _openssl.BN_free(w1);
    _openssl.BN_free(w0);
    _openssl.BN_free(x);

    return (bytesZ, bytesV);
  });
}

```

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

### Compute Share V Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/computeShareV.html

This is the core implementation of the computeShareV method. It utilizes OpenSSL bindings to perform cryptographic operations necessary for the Spake2+ protocol. Ensure the OpenSSL library is correctly linked and initialized before calling this method.

```dart
Uint8List computeShareV(Uint8List w0Bytes, Uint8List yBytes) {
  return _context((group, ctx, _) {
    final w0 = _openssl.BN_new();
    _openssl.bytes2bn(w0, w0Bytes);

    final N = _openssl.EC_POINT_new(group);
    _openssl.bytes2point(group, N, _curvePointN, ctx);

    final y = _openssl.BN_new();
    _openssl.bytes2bn(y, yBytes);

    final Y = _openssl.calculatePoint(group, ctx, y, N, w0);

    final bytesY = _openssl.point2bytes(group, Y, ctx);

    _openssl.BN_free(y);
    _openssl.BN_free(w0);
    _openssl.EC_POINT_free(Y);
    _openssl.EC_POINT_free(N);

    return bytesY;
  });
}
```

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

### verifierFinish

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/verifierFinish.html

Completes the Spake2+ verification process. It takes the verifier's initial secret (w0), the commitment point L, the verifier's ephemeral secret X, and the verifier's ephemeral public key y as input. It returns the calculated Z and V values, which are essential for the final verification step.

```APIDOC
## verifierFinish

### Description
Completes the Spake2+ verification process by calculating the Z and V values.

### Parameters
- **w0Bytes** (Uint8List) - The verifier's initial secret.
- **bytesL** (Uint8List) - The commitment point L.
- **bytesX** (Uint8List) - The verifier's ephemeral secret X.
- **yBytes** (Uint8List) - The verifier's ephemeral public key y.

### Returns
- **(Uint8List, Uint8List)?** - A tuple containing the byte representations of Z and V, or null if an error occurs during point validation.
```

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

### ScryptParameters Methods

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters-class.html

Methods available for the ScryptParameters class.

```APIDOC
## ScryptParameters Methods

### toString()
- Returns: String
- Description: Returns a string representation of the ScryptParameters object.
```

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

### proverFinish

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus-class.html

Completes the Spake2plus protocol from the prover's side.

```APIDOC
## proverFinish

### Description
Completes the Spake2plus protocol execution from the prover's perspective, generating the final proof.

### Parameters
- **w0Bytes** (Uint8List) - Prover's secret share w0.
- **w1Bytes** (Uint8List) - Prover's secret share w1.
- **xBytes** (Uint8List) - Prover's public value X.
- **bytesY** (Uint8List) - Verifier's public value Y.

### Returns
- **(Uint8List, Uint8List)?** - A tuple containing the proof and potentially other data, or null if an error occurs.
```

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

### proverFinish Method

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/proverFinish.html

The proverFinish method is used by the prover in the Spake2plus protocol to finalize the proof. It takes several byte arrays as input, representing cryptographic values, and returns a tuple of byte arrays representing the calculated Z and V values.

```APIDOC
## proverFinish Method

### Description
This method finalizes the Spake2plus proof on the prover's side. It takes the prover's secret values and the verifier's public information to compute the proof elements.

### Signature
(Uint8List, Uint8List)? proverFinish(
  1. Uint8List w0Bytes,
  2. Uint8List w1Bytes,
  3. Uint8List xBytes,
  4. Uint8List bytesY
)

### Parameters
*   **w0Bytes** (Uint8List) - The prover's first secret value as bytes.
*   **w1Bytes** (Uint8List) - The prover's second secret value as bytes.
*   **xBytes** (Uint8List) - The prover's public value x as bytes.
*   **bytesY** (Uint8List) - The verifier's public value Y as bytes.

### Returns
A tuple of two Uint8List containing the calculated Z and V values if successful, otherwise null.
```

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

### Spake2+ Cost Property Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters/cost.html

Shows the declaration of the final integer 'cost' property.

```java
final int cost;

```

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

### Scrypt Key Derivation Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Scrypt/deriveScryptKey.html

This Dart code implements the Scrypt key derivation function using FFI to call the underlying C library. Ensure proper memory management by freeing allocated native memory after use.

```dart
ffi.Pointer<ffi.UnsignedChar> deriveScryptKey(
    String pwd, String salt, int cost, int blockSize, int parallel, int dkLen,
    [int scryptMaxLen = 128 * 1024 * 1024]) {
  final dk = calloc<ffi.UnsignedChar>(dkLen);

  final pwdBytes = pwd.toNativeUtf8();
  final pwdlen = utf8.encode(pwd).length;

  final saltBytes = salt.toNativeUtf8();
  final saltlen = utf8.encode(salt).length;

  EVP_PBE_scrypt(
    pwdBytes.cast(),
    pwdlen,
    saltBytes.cast(),
    saltlen,
    cost,
    blockSize,
    parallel,
    scryptMaxLen,
    dk,
    dkLen,
  );

  calloc.free(saltBytes);
  calloc.free(pwdBytes);

  return dk;
}
```

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

### computeWitnesses Method

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/computeWitnesses.html

Computes the cryptographic witnesses required for the Spake2+ protocol. This method takes Scrypt parameters as input and returns a tuple of Uint8Lists representing the computed witnesses.

```APIDOC
## computeWitnesses Method

### Description
Computes the cryptographic witnesses for the Spake2+ protocol using the provided Scrypt parameters.

### Signature
```dart
(Uint8List, Uint8List) computeWitnesses(ScryptParameters scryptParams)
```

### Parameters
#### Path Parameters
- **scryptParams** (ScryptParameters) - Required - The Scrypt parameters used for key derivation.

### Returns
- **(Uint8List, Uint8List)** - A tuple containing two Uint8Lists representing the computed witnesses.
```

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

### deriveScryptKey

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Scrypt/deriveScryptKey.html

Derives a cryptographic key using the Scrypt algorithm. This function takes a password, salt, and Scrypt parameters to generate a derived key of a specified length.

```APIDOC
## deriveScryptKey

### Description
Derives a cryptographic key using the Scrypt algorithm. This function takes a password, salt, and Scrypt parameters to generate a derived key of a specified length.

### Signature
```dart
Pointer<UnsignedChar> deriveScryptKey(
  String pwd,
  String salt,
  int cost,
  int blockSize,
  int parallel,
  int dkLen,
  [int scryptMaxLen = 128 * 1024 * 1024]
)
```

### Parameters
- **pwd** (String) - The password to use for key derivation.
- **salt** (String) - The salt to use for key derivation.
- **cost** (int) - The cost factor (N) for Scrypt.
- **blockSize** (int) - The block size (r) for Scrypt.
- **parallel** (int) - The parallelization factor (p) for Scrypt.
- **dkLen** (int) - The desired length of the derived key in bytes.
- **scryptMaxLen** (int, optional) - The maximum memory to use for Scrypt. Defaults to 128MB.
```

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

### Implement digestSha256 Method

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/digestSha256.html

This is the implementation of the digestSha256 method. It takes a Uint8List transcript as input and returns a Uint8List hash.

```dart
Uint8List digestSha256(Uint8List transcript) {
  return _digest(SN_sha256, transcript);
}
```

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

### verifierFinish

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus-class.html

Completes the Spake2plus protocol from the verifier's side.

```APIDOC
## verifierFinish

### Description
Completes the Spake2plus protocol execution from the verifier's perspective, verifying the proof and generating session keys.

### Parameters
- **w0Bytes** (Uint8List) - Prover's secret share w0.
- **bytesL** (Uint8List) - The computed record L value.
- **bytesX** (Uint8List) - Prover's public value X.
- **yBytes** (Uint8List) - Verifier's public value Y.

### Returns
- **(Uint8List, Uint8List)?** - A tuple containing the session keys or other verification data, or null if verification fails.
```

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

### Compute Share P in Spake2+

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/computeShareP.html

This function computes the share P using the provided w0bytes and xBytes. It utilizes internal cryptographic functions for BigInt and Elliptic Curve operations. Ensure the input byte arrays are correctly formatted according to the Spake2+ protocol specifications.

```dart
Uint8List computeShareP(Uint8List w0bytes, Uint8List xBytes) {
  return _context((group, ctx, order) {
    final w0 = _openssl.BN_new();
    _openssl.bytes2bn(w0, w0bytes);

    final M = _openssl.EC_POINT_new(group);
    _openssl.bytes2point(group, M, _curvePointM, ctx);

    final x = _openssl.BN_new();
    _openssl.bytes2bn(x, xBytes);

    final X = _openssl.calculatePoint(group, ctx, x, M, w0);

    final bytesX = _openssl.point2bytes(group, X, ctx);

    _openssl.EC_POINT_free(X);
    _openssl.BN_free(x);
    _openssl.EC_POINT_free(M);
    _openssl.BN_free(w0);

    return bytesX;
  });
}
```

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

### deriveScryptKey

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Scrypt.html

Derives a cryptographic key using the Scrypt algorithm. This method is available on OpenSSL and provided by the Scrypt extension.

```APIDOC
## deriveScryptKey

### Description
Derives a cryptographic key using the Scrypt algorithm. This method is available on OpenSSL and provided by the Scrypt extension.

### Signature
deriveScryptKey(String pwd, String salt, int cost, int blockSize, int parallel, int dkLen, [int scryptMaxLen = 128 * 1024 * 1024]) → Pointer<UnsignedChar>

### Parameters
- **pwd** (String) - The password to use for key derivation.
- **salt** (String) - The salt to use for key derivation.
- **cost** (int) - The cost factor (N) for Scrypt.
- **blockSize** (int) - The block size (r) for Scrypt.
- **parallel** (int) - The parallelization factor (p) for Scrypt.
- **dkLen** (int) - The desired length of the derived key.
- **scryptMaxLen** (int, optional) - The maximum length for Scrypt, defaults to 128MB.
```

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

### computeRecordL

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus-class.html

Computes the record L value.

```APIDOC
## computeRecordL

### Description
Computes the record L value, likely used in a cryptographic protocol.

### Parameters
- **w1Bytes** (Uint8List) - The input byte array w1.

### Returns
- **Uint8List** - The computed record L value.
```

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

### ScryptParameters Properties

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters-class.html

Properties of the ScryptParameters class.

```APIDOC
## ScryptParameters Properties

### blockSize
- Type: int
- Description: The block size (r) for Scrypt.

### cost
- Type: int
- Description: The cost factor (N) for Scrypt.

### dkLen
- Type: int
- Description: The desired length of the derived key in bytes.

### parallelization
- Type: int
- Description: The parallelization factor (p) for Scrypt.

### pwd
- Type: String
- Description: The password used for key derivation.

### salt
- Type: String
- Description: The salt used for key derivation.
```

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

### Implement digestSha512 Method

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/digestSha512.html

This is the implementation of the digestSha512 method. It utilizes an internal _digest function with the SN_sha512 constant.

```dart
Uint8List digestSha512(Uint8List transcript) {
  return _digest(SN_sha512, transcript);
}
```

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

### ScryptParameters Operators

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters-class.html

Operators available for the ScryptParameters class.

```APIDOC
## ScryptParameters Operators

### operator ==(Object other)
- Returns: bool
- Description: Compares this ScryptParameters object with another object for equality.
```

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

### Implement deriveHkdfSha256 Method

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/deriveHkdfSha256.html

This is the implementation of the deriveHkdfSha256 method, which internally calls a private _deriveHkdf function with the SHA256 digest algorithm.

```dart
Uint8List deriveHkdfSha256(
  int L,
  Uint8List salt,
  Uint8List key,
  Uint8List info,
) {
  return _deriveHkdf(_openssl.EVP_sha256(), L, salt, key, info);
}
```

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

### computeRecordL

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/computeRecordL.html

Computes the record L value. This method takes a Uint8List representing w1 and returns a Uint8List representing L.

```APIDOC
## computeRecordL Method

### Description
Computes the record L value using the provided `w1Bytes`.

### Signature
`Uint8List computeRecordL(Uint8List w1Bytes)`

### Parameters
#### Path Parameters
- **w1Bytes** (Uint8List) - Required - The byte representation of w1.

### Request Example
```dart
// Assuming w1Bytes is a Uint8List
Uint8List resultL = computeRecordL(w1Bytes);
```

### Response
#### Success Response
- **bytesL** (Uint8List) - The computed record L value as a byte array.
```

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

### Compute Record L using OpenSSL Bindings

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/computeRecordL.html

This function computes the L value by multiplying an input byte array (w1Bytes) with the generator point G using OpenSSL's EC_POINT_mul. Ensure the OpenSSL bindings are correctly initialized.

```dart
Uint8List computeRecordL(Uint8List w1Bytes) {
  return _context((group, ctx, _) {
    final w1 = _openssl.BN_new();
    final L = _openssl.EC_POINT_new(group);

    _openssl.bytes2bn(w1, w1Bytes);
    _openssl.EC_POINT_mul(
        group, L, w1, ffi.nullptr, ffi.nullptr, ctx); // w1 * G

    final bytesL = _openssl.point2bytes(group, L, ctx);

    _openssl.BN_free(w1);
    _openssl.EC_POINT_free(L);

    return bytesL;
  });
}
```

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

### computeShareV

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus-class.html

Computes the share V value.

```APIDOC
## computeShareV

### Description
Computes the share V value, possibly related to a verification or commitment in a protocol.

### Parameters
- **w0Bytes** (Uint8List) - The input byte array w0.
- **yBytes** (Uint8List) - The input byte array y.

### Returns
- **Uint8List** - The computed share V value.
```

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

### Derive HKDF SHA512 Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/deriveHkdfSha512.html

This is the Dart implementation of the deriveHkdfSha512 method. It utilizes an internal _deriveHkdf function with the SHA512 digest.

```dart
Uint8List deriveHkdfSha512(
  int L,
  Uint8List salt,
  Uint8List key,
  Uint8List info,
) {
  return _deriveHkdf(_openssl.EVP_sha512(), L, salt, key, info);
}
```

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

### HMAC-SHA512 Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/hmacSha512.html

This snippet shows the Dart implementation of the HMAC-SHA512 function, which takes a key and data as Uint8List and returns a 64-byte hash. It utilizes an internal OpenSSL binding and manages memory allocation and deallocation.

```dart
Uint8List hmacSha512(Uint8List key, Uint8List data) {
  final hmac = _openssl.hmacSha512(key, data);
  final ret =
      Uint8List.fromList((hmac as ffi.Pointer<ffi.Uint8>).asTypedList(64));
  calloc.free(hmac);
  return ret;
}
```

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

### deriveHkdfSha512

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/deriveHkdfSha512.html

Derives a key using the HKDF-SHA512 algorithm. This function takes the desired length of the output key, a salt, a secret key, and an optional info context as input.

```APIDOC
## deriveHkdfSha512

### Description
Derives a key using the HKDF-SHA512 algorithm. This function takes the desired length of the output key, a salt, a secret key, and an optional info context as input.

### Parameters
- **L** (int) - The desired length of the output key in bytes.
- **salt** (Uint8List) - The salt to be used in the derivation process.
- **key** (Uint8List) - The secret key to be used.
- **info** (Uint8List) - Optional context information.

### Implementation
```dart
Uint8List deriveHkdfSha512(
  int L,
  Uint8List salt,
  Uint8List key,
  Uint8List info,
) {
  return _deriveHkdf(_openssl.EVP_sha512(), L, salt, key, info);
}
```
```

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

### computeShareP

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus-class.html

Computes the share P value.

```APIDOC
## computeShareP

### Description
Computes the share P value, potentially part of a secret sharing scheme.

### Parameters
- **w0bytes** (Uint8List) - The input byte array w0.
- **xBytes** (Uint8List) - The input byte array x.

### Returns
- **Uint8List** - The computed share P value.
```

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

### hmacSha512

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/hmacSha512.html

Computes the HMAC-SHA512 hash of the provided data using the given key. The function returns a 64-byte Uint8List.

```APIDOC
## hmacSha512

### Description
Computes the HMAC-SHA512 hash of the provided data using the given key. The function returns a 64-byte Uint8List.

### Parameters
#### Path Parameters
- None

#### Query Parameters
- None

#### Request Body
- None

### Method Signature
`Uint8List hmacSha512(Uint8List key, Uint8List data)`

### Parameters
- **key** (Uint8List) - The secret key to use for HMAC computation.
- **data** (Uint8List) - The data to be hashed.

### Returns
- **Uint8List** - A 64-byte array representing the HMAC-SHA512 hash.

### Example
```dart
import 'dart:typed_data';

// Assuming _openssl and calloc are properly initialized and imported

Uint8List hmacSha512(Uint8List key, Uint8List data) {
  final hmac = _openssl.hmacSha512(key, data);
  final ret = Uint8List.fromList((hmac as ffi.Pointer<ffi.Uint8>).asTypedList(64));
  calloc.free(hmac);
  return ret;
}
```
```

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

### Declare Parallelization Property

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters/parallelization.html

This snippet shows the declaration of the `parallelization` property as a final integer.

```java
final int parallelization;

```

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

### Declare pwd property

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters/pwd.html

This snippet shows the declaration of the 'pwd' property as a final String.

```dart
final String pwd;
```

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

### deriveHkdfSha256

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/deriveHkdfSha256.html

Derives a key using the HKDF-SHA256 algorithm. This function takes the desired length of the output key, a salt, the input keying material, and an optional info context.

```APIDOC
## deriveHkdfSha256 Method

### Description
Derives a key using the HKDF-SHA256 algorithm. This function takes the desired length of the output key, a salt, the input keying material, and an optional info context.

### Signature
```dart
Uint8List deriveHkdfSha256(
  int L,
  Uint8List salt,
  Uint8List key,
  Uint8List info,
)
```

### Parameters
* **L** (int) - The desired length of the derived key in bytes.
* **salt** (Uint8List) - The salt to be used in the HKDF process.
* **key** (Uint8List) - The input keying material.
* **info** (Uint8List) - Optional context and application specific information.

### Returns
* **Uint8List** - The derived key.
```

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

### Declare blockSize Property

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters/blockSize.html

This snippet shows the declaration of the final blockSize property in Java. It is typically initialized during object construction.

```java
final int blockSize;

```

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

### computeTranscript

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/computeTranscript.html

Computes the transcript of the Spake2+ protocol exchange. This method takes various byte arrays representing protocol elements and constructs a transcript byte array.

```APIDOC
## computeTranscript

### Description
Computes the transcript of the Spake2+ protocol exchange. This method takes various byte arrays representing protocol elements and constructs a transcript byte array.

### Method Signature
`Uint8List computeTranscript(Uint8List context, Uint8List idProver, Uint8List idVerifier, Uint8List bytesX, Uint8List bytesY, Uint8List bytesZ, Uint8List bytesV, Uint8List w0Bytes)`

### Parameters
#### Path Parameters
- None

#### Query Parameters
- None

#### Request Body
- **context** (Uint8List) - The context of the protocol exchange.
- **idProver** (Uint8List) - The identifier for the prover.
- **idVerifier** (Uint8List) - The identifier for the verifier.
- **bytesX** (Uint8List) - The X component of the prover's public key.
- **bytesY** (Uint8List) - The Y component of the prover's public key.
- **bytesZ** (Uint8List) - The Z component of the verifier's public key.
- **bytesV** (Uint8List) - The V component used in the protocol.
- **w0Bytes** (Uint8List) - The W0 value used in the protocol.

### Request Example
```dart
// Example usage (assuming necessary setup and curve points are available)
// final transcript = computeTranscript(context, idProver, idVerifier, bytesX, bytesY, bytesZ, bytesV, w0Bytes);
```

### Response
#### Success Response
- Returns a `Uint8List` representing the computed transcript.

#### Response Example
```dart
// Example response (actual bytes will vary)
// Uint8List transcript = [0x01, 0x02, 0x03, ...];
```
```

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

### computeShareP

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/computeShareP.html

Computes a share using the Spake2+ protocol. This method is part of the cryptographic operations for secure password-based key exchange.

```APIDOC
## computeShareP

### Description
Computes a share in the Spake2+ protocol. This function is essential for the key exchange process, taking pre-computed values and generating a share.

### Method Signature
`Uint8List computeShareP(Uint8List w0bytes, Uint8List xBytes)`

### Parameters
#### Parameters
- **w0bytes** (Uint8List) - Required - A byte array representing the pre-computed value w0.
- **xBytes** (Uint8List) - Required - A byte array representing the user's secret value x.

### Returns
- **Uint8List** - A byte array representing the computed share (X).

### Example
```dart
// Assuming w0bytes and xBytes are already defined Uint8List variables
// final w0bytes = ...;
// final xBytes = ...;
// final shareP = computeShareP(w0bytes, xBytes);
```
```

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

### hmacSha256

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/hmacSha256.html

Computes the HMAC-SHA256 hash using the provided key and data.

```APIDOC
## hmacSha256

### Description
Computes the HMAC-SHA256 hash for a given key and data.

### Signature
Uint8List hmacSha256(Uint8List key, Uint8List data)

### Parameters
#### Arguments
1. **key** (Uint8List) - The secret key for HMAC computation.
2. **data** (Uint8List) - The data to be hashed.

### Returns
- **Uint8List** - The resulting HMAC-SHA256 hash (32 bytes).
```

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

### computeShareV

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/computeShareV.html

Computes a share value using the Spake2+ protocol. This method is part of the cryptographic operations for secure key agreement.

```APIDOC
## computeShareV

### Description
Computes a share value in the Spake2+ protocol.

### Method Signature
`Uint8List computeShareV(Uint8List w0Bytes, Uint8List yBytes)`

### Parameters
#### Path Parameters
- **w0Bytes** (Uint8List) - Required - The first input byte array.
- **yBytes** (Uint8List) - Required - The second input byte array.

### Returns
- **Uint8List** - A byte array representing the computed share value.
```

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

### dkLen Property Declaration

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters/dkLen.html

Declares the dkLen property as a final integer.

```java
final int dkLen;

```

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

### digestSha256

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/digestSha256.html

Computes the SHA-256 digest of the provided transcript.

```APIDOC
## digestSha256

### Description
Computes the SHA-256 hash of the provided transcript.

### Signature
Uint8List digestSha256(Uint8List transcript)

### Parameters
#### Path Parameters
- **transcript** (Uint8List) - Required - The byte array representing the transcript to be hashed.
```

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

### HMAC-SHA256 Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/hmacSha256.html

This function computes the HMAC-SHA256 hash of the given data using the provided key. It utilizes the openssl library and frees allocated memory after computation.

```dart
Uint8List hmacSha256(Uint8List key, Uint8List data) {
  final hmac = _openssl.hmacSha256(key, data);
  final ret =
      Uint8List.fromList((hmac as ffi.Pointer<ffi.Uint8>).asTypedList(32));
  calloc.free(hmac);
  return ret;
}
```

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

### digestSha512

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/digestSha512.html

Computes the SHA-512 digest of the provided transcript.

```APIDOC
## digestSha512

### Description
Computes the SHA-512 digest of the provided transcript.

### Parameters
#### Path Parameters
- **transcript** (Uint8List) - Required - The input data to be hashed.

### Implementation
```dart
Uint8List digestSha512(Uint8List transcript) {
  return _digest(SN_sha512, transcript);
}
```
```

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

### convertToUncompressedECPoint

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/convertToUncompressedECPoint.html

Converts a given EC point data into its uncompressed representation. This method is useful for standardizing EC point formats.

```APIDOC
## convertToUncompressedECPoint

### Description
Converts an EC point from its byte representation to an uncompressed EC point format.

### Method Signature
```dart
Uint8List convertToUncompressedECPoint(Uint8List pointData)
```

### Parameters
#### Path Parameters
- **pointData** (Uint8List) - Required - The byte data representing the EC point.

### Returns
- **Uint8List** - The byte data of the EC point in uncompressed format.
```

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

### cmacAes128

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus-class.html

Computes the CMAC-AES128 for the given key and data.

```APIDOC
## cmacAes128

### Description
Computes the Cipher-based Message Authentication Code (CMAC) using AES-128 encryption.

### Parameters
- **key** (Uint8List) - The secret key for CMAC computation.
- **data** (Uint8List) - The data to authenticate.

### Returns
- **Uint8List** - The computed CMAC tag.
```

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

### Compute Spake2+ Transcript

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/computeTranscript.html

This function computes the transcript for the Spake2+ protocol. It takes various context and identity byte arrays, converts curve points to uncompressed format, and concatenates them with their lengths in little-endian byte format.

```dart
Uint8List computeTranscript(
  Uint8List context,
  Uint8List idProver,
  Uint8List idVerifier,
  Uint8List bytesX,
  Uint8List bytesY,
  Uint8List bytesZ,
  Uint8List bytesV,
  Uint8List w0Bytes,
) {
  final uncompressedM = convertToUncompressedECPoint(_curvePointM);
  final uncompressedN = convertToUncompressedECPoint(_curvePointN);
  return Uint8List.fromList([
    ...littleEndianBytes(context.length),
    ...context,
    ...littleEndianBytes(idProver.length),
    ...idProver,
    ...littleEndianBytes(idVerifier.length),
    ...idVerifier,
    ...littleEndianBytes(uncompressedM.length),
    ...uncompressedM,
    ...littleEndianBytes(uncompressedN.length),
    ...uncompressedN,
    ...littleEndianBytes(bytesX.length),
    ...bytesX,
    ...littleEndianBytes(bytesY.length),
    ...bytesY,
    ...littleEndianBytes(bytesZ.length),
    ...bytesZ,
    ...littleEndianBytes(bytesV.length),
    ...bytesV,
    ...littleEndianBytes(w0Bytes.length),
    ...w0Bytes,
  ]);
}
```

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

### Convert to Uncompressed EC Point

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/convertToUncompressedECPoint.html

Converts provided point data into an uncompressed elliptic curve point format. Ensure the input pointData is valid. This method utilizes OpenSSL for cryptographic operations.

```dart
Uint8List convertToUncompressedECPoint(Uint8List pointData) {
  return _context((group, ctx, _) {
    final cp = _openssl.EC_POINT_new(group);
    final buf = pointData.toPointer();
    _openssl.EC_POINT_oct2point(group, cp, buf, pointData.length, ctx);

    final len = 65;
    final ptr = calloc<ffi.UnsignedChar>(len);
    _openssl.EC_POINT_point2oct(
      group,
      cp,
      point_conversion_form_t.POINT_CONVERSION_UNCOMPRESSED,
      ptr,
      len,
      ctx,
    );
    final ret = Uint8List.fromList(ptr.cast<ffi.Uint8>().asTypedList(len));
    _openssl.EC_POINT_free(cp);
    calloc.free(buf);
    calloc.free(ptr);
    return ret;
  });
}
```

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

### randomValidScalar

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus-class.html

Generates a cryptographically secure random scalar.

```APIDOC
## randomValidScalar

### Description
Generates a cryptographically secure random scalar value suitable for use in elliptic curve cryptography.

### Returns
- **Uint8List** - A random scalar as a byte array.
```

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

### randomValidScalar Method

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/randomValidScalar.html

Generates a cryptographically secure random scalar value of 32 bytes.

```APIDOC
## randomValidScalar()

### Description
Generates a cryptographically secure random scalar value. This method is used internally for generating random numbers within a specific range, typically for cryptographic protocols.

### Signature
`Uint8List randomValidScalar()`

### Returns
- `Uint8List`: A 32-byte array representing the random scalar value.
```

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

### cmacAes128 Function

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/cmacAes128.html

The cmacAes128 function computes the CMAC for the given data using a provided key. It utilizes an underlying OpenSSL implementation and returns the resulting 16-byte CMAC tag.

```APIDOC
## cmacAes128 Function Signature

### Description
Computes the Cipher-based Message Authentication Code (CMAC) using AES-128.

### Parameters
- **key** (Uint8List) - The secret key for AES-128 encryption.
- **data** (Uint8List) - The data for which to compute the CMAC.

### Returns
- **Uint8List** - A 16-byte array representing the CMAC tag.

### Implementation Example
```dart
Uint8List cmacAes128(Uint8List key, Uint8List data) {
  final cmac = _openssl.cmacAes128(key, data);
  final ret = Uint8List.fromList((cmac as ffi.Pointer<ffi.Uint8>).asTypedList(16));
  calloc.free(cmac);
  return ret;
}
```
```

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

### CMAC AES128 Implementation

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/cmacAes128.html

This function computes the CMAC for given key and data using AES128. It utilizes an internal OpenSSL binding and frees allocated memory after use.

```dart
Uint8List cmacAes128(Uint8List key, Uint8List data) {
  final cmac = _openssl.cmacAes128(key, data);
  final ret =
      Uint8List.fromList((cmac as ffi.Pointer<ffi.Uint8>).asTypedList(16));
  calloc.free(cmac);
  return ret;
}
```

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

### Generate Random Scalar - Dart

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/Spake2plus/randomValidScalar.html

Generates a cryptographically secure random scalar of 32 bytes. This method is used internally for cryptographic operations requiring random values within a specific order.

```dart
Uint8List randomValidScalar() {
  return _context((group, ctx, order) {
    final p = _openssl.BN_new();
    _openssl.BN_rand_range(p, order);
    final ret = _openssl.bn2bytes(group, p, 32, ctx);
    _openssl.BN_free(p);
    return ret;
  });
}
```

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

### Declare Salt Property in Dart

Source: https://pub.dev/documentation/spake2plus/latest/spake2plus/ScryptParameters/salt.html

This snippet shows the declaration of the final String salt property in Dart. It is typically used to store a unique salt value for cryptographic operations.

```dart
final String salt;
```

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