### Individual Decrypt Example

Source: https://fhe.desilo.dev/latest/api/engine/individual_decrypt

Demonstrates how to use `individual_decrypt` to obtain a decrypted share. This is part of a multiparty computation setup.

```python
from desilofhe import Engine

engine = Engine(use_multiparty=True)
secret_key1 = engine.create_secret_key()
secret_key2 = engine.create_secret_key()
public_key_a = engine.create_public_key_a()
public_key_b1 = engine.create_public_key_b(secret_key1, public_key_a)
public_key_b2 = engine.create_public_key_b(secret_key2, public_key_a)

public_key = engine.create_multiparty_public_key(
    [public_key_b1, public_key_b2], public_key_a
)

message = [1, 2, 3]
ciphertext = engine.encrypt(message, public_key)
decrypted_share1 = engine.individual_decrypt(ciphertext, secret_key1)
```

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

### Get Bootstrap Key Serialized Size

Source: https://fhe.desilo.dev/latest/api/data-type/bootstrap_key/serialized_nbytes

Use this snippet to create a bootstrap key and retrieve its serialized size in bytes. Ensure the `desilofhe` library is installed and the engine is initialized with `use_bootstrap=True`.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
bootstrap_key = engine.create_bootstrap_key(secret_key)
serialized_nbytes = bootstrap_key.serialized_nbytes

```

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

### Install DESILO FHE (CPU Version) with pip

Source: https://fhe.desilo.dev/latest/install

Use this command to install the CPU-only version of the DESILO FHE library. Ensure your system meets the specified OS and Python version requirements.

```bash
pip install desilofhe

```

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

### Accessing nbytes

Source: https://fhe.desilo.dev/latest/api/data-type/small_bootstrap_key/nbytes

Demonstrates how to create a small bootstrap key and access its `nbytes` attribute to get its memory size.

```APIDOC
## Accessing nbytes

### Description
Retrieves the memory size of a small bootstrap key.

### Method
Attribute access

### Endpoint
N/A (Object attribute)

### Parameters
None

### Request Example
```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
small_bootstrap_key = engine.create_small_bootstrap_key(secret_key)
nbytes = small_bootstrap_key.nbytes
print(f"The small bootstrap key uses {nbytes} bytes.")
```

### Response
#### Success Response
- **nbytes** (int) - The memory size of the small bootstrap key in bytes.
```

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

### Get Small Bootstrap Key Size

Source: https://fhe.desilo.dev/latest/api/data-type/small_bootstrap_key/nbytes

Instantiate the engine, create a secret key, then a small bootstrap key, and finally access its `nbytes` attribute to get its memory size.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
small_bootstrap_key = engine.create_small_bootstrap_key(secret_key)
nbytes = small_bootstrap_key.nbytes

```

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

### Install DESILO FHE with CUDA 12.9 Support (poetry)

Source: https://fhe.desilo.dev/latest/install

Add the DESILO FHE library with CUDA 12.9 support to your project using poetry. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
poetry add desilofhe-cu129

```

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

### Install DESILO FHE with CUDA 12.1 Support (poetry)

Source: https://fhe.desilo.dev/latest/install

Add the DESILO FHE library with CUDA 12.1 support to your project using poetry. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
poetry add desilofhe-cu121

```

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

### Install DESILO FHE with CUDA 13.0 Support (poetry)

Source: https://fhe.desilo.dev/latest/install

Add the DESILO FHE library with CUDA 13.0 support to your project using poetry. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
poetry add desilofhe-cu130

```

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

### Install DESILO FHE with CUDA 12.8 Support (poetry)

Source: https://fhe.desilo.dev/latest/install

Add the DESILO FHE library with CUDA 12.8 support to your project using poetry. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
poetry add desilofhe-cu128

```

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

### Install DESILO FHE with CUDA 12.6 Support (poetry)

Source: https://fhe.desilo.dev/latest/install

Add the DESILO FHE library with CUDA 12.6 support to your project using poetry. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
poetry add desilofhe-cu126

```

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

### Install DESILO FHE with CUDA 12.4 Support (poetry)

Source: https://fhe.desilo.dev/latest/install

Add the DESILO FHE library with CUDA 12.4 support to your project using poetry. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
poetry add desilofhe-cu124

```

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

### Get Public Key Serialized Size

Source: https://fhe.desilo.dev/latest/api/data-type/public_key/serialized_nbytes

Demonstrates how to create a public key and retrieve its serialized size in bytes using the `serialized_nbytes` attribute.

```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
serialized_nbytes = public_key.serialized_nbytes


```

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

### Get Relinearization Key Level

Source: https://fhe.desilo.dev/latest/api/data-type/relinearization_key/level

Demonstrates how to create a relinearization key and access its maximum relinearization level.

```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
relinearization_key = engine.create_relinearization_key(secret_key)
level = relinearization_key.level

```

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

### Create Engine with Bootstrap Enabled

Source: https://fhe.desilo.dev/latest/create_engine

Enable bootstrapping for advanced users. This configuration uses `log_coeff_count=16` and `special_prime_count=4`. Bootstrapping is not available for `log_coeff_count` below 15 or at 17 and above due to key size limitations.

```python
from desilofhe import Engine

bootstrap_engine = Engine(use_bootstrap=True)
```

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

### Get PlainMatrix Level

Source: https://fhe.desilo.dev/latest/api/data-type/plain_matrix/level

This snippet demonstrates how to encode a message into a plain matrix and then retrieve its level. Ensure the desilofhe library and numpy are installed.

```python
import numpy as np

from desilofhe import Engine

engine = Engine(slot_count=64)

message = np.arange(64 * 64).reshape(64, 64)
plain_matrix = engine.encode_to_plain_matrix(message)
level = plain_matrix.level

```

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

### Create Engine with Custom Parameters

Source: https://fhe.desilo.dev/latest/create_engine

For advanced users, specify `log_coeff_count` (logarithm of polynomial size) and `special_prime_count` (key switching partition size) for custom configurations.

```python
from desilofhe import Engine

# Multiplication count  0 ~  2:
tiny_engine = Engine(log_coeff_count=13, special_prime_count=1)

# Multiplication count  3 ~  7:
small_engine = Engine(log_coeff_count=14, special_prime_count=1)

# Multiplication count  8 ~ 16:
medium_engine = Engine(log_coeff_count=15, special_prime_count=2)

# Multiplication count 17 ~ 34:
large_engine = Engine(log_coeff_count=16, special_prime_count=4)

# Multiplication count 35 ~ 72:
huge_engine = Engine(log_coeff_count=17, special_prime_count=6)
```

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

### Create Lossy Bootstrap Key with Different Configurations

Source: https://fhe.desilo.dev/latest/api/engine/lossy_bootstrap_key/create_lossy_bootstrap_key

Demonstrates creating a lossy bootstrap key with default settings, custom stage counts, and custom sizes. The `for_bootstrap` parameter must be set to `True` when initializing the `Engine` for bootstrapping operations.

```python
from desilofhe import Engine

engine = Engine(for_bootstrap=True)
secret_key = engine.create_secret_key()
lossy_bootstrap_key = engine.create_lossy_bootstrap_key(secret_key)

medium_lossy_bootstrap_key_with_5_stages = engine.create_lossy_bootstrap_key(
    secret_key, stage_count=5
)

large_lossy_bootstrap_key = engine.create_lossy_bootstrap_key(
    secret_key, size="large"
)

large_lossy_bootstrap_key_with_4_stages = engine.create_lossy_bootstrap_key(
    secret_key, stage_count=4, size="large"
)
```

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

### Create and Use Bootstrap Key

Source: https://fhe.desilo.dev/latest/bootstrap

Demonstrates the creation of a standard bootstrap key and its use in bootstrapping a ciphertext. Ensure the Engine is initialized with `use_bootstrap=True`.

```python
from desilofhe import Engine

engine = Engine(slot_count=1024, use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
bootstrap_key = engine.create_bootstrap_key(secret_key, stage_count=3)

message = [-1, 0, 1, 0] * 256
ciphertext = engine.encrypt(message, public_key, level=0)
bootstrapped = engine.bootstrap(
    ciphertext, relinearization_key, conjugation_key, bootstrap_key
)

```

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

### Install DESILO FHE with CUDA 13.0 Support (pip)

Source: https://fhe.desilo.dev/latest/install

Install the DESILO FHE library with CUDA 13.0 support using pip. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
pip install desilofhe-cu130

```

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

### Get PublicKey Level

Source: https://fhe.desilo.dev/latest/api/data-type/public_key/level

Demonstrates how to create a PublicKey and access its level attribute. The level indicates the maximum encryption level the key supports.

```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)

level = public_key.level

```

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

### Install DESILO FHE with CUDA 12.9 Support (pip)

Source: https://fhe.desilo.dev/latest/install

Install the DESILO FHE library with CUDA 12.9 support using pip. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
pip install desilofhe-cu129

```

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

### Create Default Engine

Source: https://fhe.desilo.dev/latest/api/engine/engine

Instantiate an Engine with default settings or specify mode, multiparty, bootstrap, thread count, and GPU device ID. Note that only one of bootstrap, bootstrap_to_14_levels, bootstrap_to_17_levels, or multiparty can be enabled.

```python
from desilofhe import Engine

engine1 = Engine()
engine2 = Engine(mode="parallel", use_multiparty=True, thread_count=256)
engine3 = Engine(mode="gpu", use_bootstrap=True, thread_count=512, device_id=1)
```

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

### Sign Bootstrap Example

Source: https://fhe.desilo.dev/latest/bootstrap

Performs a sign bootstrap operation and calculates the resulting average noise. This is useful for understanding the noise amplification or reduction characteristics of the bootstrapping process.

```python
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
lossy_bootstrap_key = engine.create_lossy_bootstrap_key(secret_key)

message = [-1, 1] * (engine.slot_count // 2)

ciphertext = engine.encrypt(message, secret_key)
bootstrapped = engine.sign_bootstrap(
    ciphertext, relinearization_key, conjugation_key, lossy_bootstrap_key
)
decrypted = engine.decrypt(bootstrapped, secret_key)

average_noise = np.mean(abs(message - decrypted))
print(f"Sign Bootstrap Average Noise :{average_noise}")
print(f"Sign Bootstrap Average Noise (Bits) :{np.log2(average_noise)}")
```

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

### Install DESILO FHE with CUDA 12.8 Support (pip)

Source: https://fhe.desilo.dev/latest/install

Install the DESILO FHE library with CUDA 12.8 support using pip. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
pip install desilofhe-cu128

```

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

### Install DESILO FHE with CUDA 12.6 Support (pip)

Source: https://fhe.desilo.dev/latest/install

Install the DESILO FHE library with CUDA 12.6 support using pip. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
pip install desilofhe-cu126

```

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

### Create a Basic Engine

Source: https://fhe.desilo.dev/latest/create_engine

Use this for the default engine creation. It supports a multiplicative depth of 7.

```python
from desilofhe import Engine

engine = Engine()
```

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

### Install DESILO FHE with CUDA 12.4 Support (pip)

Source: https://fhe.desilo.dev/latest/install

Install the DESILO FHE library with CUDA 12.4 support using pip. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
pip install desilofhe-cu124

```

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

### Check PublicKey Storage Location (GPU vs CPU)

Source: https://fhe.desilo.dev/latest/api/data-type/public_key/is_cuda

Demonstrates how to create public keys using both GPU and CPU engines and assert their respective storage locations using the `is_cuda` attribute. This helps in verifying that keys are correctly allocated to the intended hardware.

```python
from desilofhe import Engine

gpu_engine = Engine(mode="gpu")
gpu_secret_key = gpu_engine.create_secret_key()
gpu_public_key = gpu_engine.create_public_key(gpu_secret_key)

assert gpu_public_key.is_cuda

cpu_engine = Engine(mode="cpu")
cpu_secret_key = cpu_engine.create_secret_key()
cpu_public_key = cpu_engine.create_public_key(cpu_secret_key)

assert not cpu_public_key.is_cuda
```

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

### Install DESILO FHE with CUDA 12.1 Support (pip)

Source: https://fhe.desilo.dev/latest/install

Install the DESILO FHE library with CUDA 12.1 support using pip. This version requires a compatible CUDA toolkit installed on your system. Not available for musllinux or macOS.

```bash
pip install desilofhe-cu121

```

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

### Check PublicKeyB CUDA Storage

Source: https://fhe.desilo.dev/latest/api/data-type/public_key_b/is_cuda

Demonstrates how to create PublicKeyB instances on both GPU and CPU and assert their respective `is_cuda` status. Use this to verify device placement.

```python
from desilofhe import Engine

gpu_engine = Engine(use_multiparty=True, mode="gpu")
gpu_secret_key = gpu_engine.create_secret_key()
gpu_public_key_a = gpu_engine.create_public_key_a()
gpu_public_key_b = gpu_engine.create_public_key_b(
    gpu_secret_key, gpu_public_key_a
)

assert gpu_public_key_b.is_cuda

cpu_engine = Engine(use_multiparty=True, mode="cpu")
cpu_secret_key = cpu_engine.create_secret_key()
cpu_public_key_a = cpu_engine.create_public_key_a()
cpu_public_key_b = cpu_engine.create_public_key_b(
    cpu_secret_key, cpu_public_key_a
)

assert not cpu_public_key_b.is_cuda

```

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

### Get Plaintext Length

Source: https://fhe.desilo.dev/latest/api/data-type/plaintext/__len__

Demonstrates how to get the length of a plaintext object after encoding. The length is calculated based on the engine's slot count.

```python
from desilofhe import Engine

engine = Engine()

message = [1] * 2 * engine.slot_count
plaintext = engine.encode(message)
length = len(plaintext)  # 2

```

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

### Create Engine with Bootstrap to 17 Levels

Source: https://fhe.desilo.dev/latest/create_engine

Enable bootstrapping that results in 17 levels remaining after the operation. This is for advanced users requiring a specific number of levels post-bootstrapping.

```python
from desilofhe import Engine

bootstrap_engine = Engine(use_bootstrap_to_17_levels=True)
```

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

### Get Public Key Size in Bytes

Source: https://fhe.desilo.dev/latest/api/data-type/public_key/nbytes

Demonstrates how to create a public key and retrieve its size in bytes using the `nbytes` attribute. This is useful for estimating memory usage.

```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
nbytes = public_key.nbytes


```

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

### Get Plaintext Serialized Bytes

Source: https://fhe.desilo.dev/latest/api/data-type/plaintext/serialized_nbytes

Use the `serialized_nbytes` attribute on a plaintext object to get its size in bytes after serialization. This is useful for understanding data size before transmission or storage.

```python
from desilofhe import Engine

engine = Engine()

message = [1, 2, 3]
plaintext = engine.encode(message)
serialized_nbytes = plaintext.serialized_nbytes


```

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

### Create Bootstrap Key with Default Settings

Source: https://fhe.desilo.dev/latest/api/engine/bootstrap_key/create_bootstrap_key

Creates a bootstrap key with default stage count (3) and size (medium). Requires an initialized Engine and a secret key.

```python
from desilofhe import Engine

engine = Engine(for_bootstrap=True)
secret_key = engine.create_secret_key()
bootstrap_key = engine.create_bootstrap_key(secret_key)
```

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

### Get Rotation Key Level

Source: https://fhe.desilo.dev/latest/api/data-type/rotation_key/level

This snippet demonstrates how to create an Engine, generate a secret key and a rotation key, and then access the `level` attribute to get the maximum rotation level.

```APIDOC
## Get Rotation Key Level

### Description
Retrieves the maximum level of a ciphertext that the rotation key can rotate.

### Method
Attribute Access

### Endpoint
N/A (Object Attribute)

### Parameters
None

### Request Example
```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
rotation_key = engine.create_rotation_key(secret_key)
level = rotation_key.level
print(level)
```

### Response
#### Success Response
- **level** (int) - The maximum rotation level.
```

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

### Sign Bootstrap with Small Key and Stage Count

Source: https://fhe.desilo.dev/latest/api/engine/sign_bootstrap

Illustrates bootstrapping sign values using the small bootstrap key, which is slower but more memory-efficient. This example also shows how to specify a custom stage count for bootstrapping. The ciphertext level must be at least the specified stage count.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
rotation_key = engine.create_rotation_key(secret_key)
small_bootstrap_key = engine.create_small_bootstrap_key(secret_key)

message = [-1, 1]
ciphertext_level_3 = engine.encrypt(message, public_key, level=3)
bootstrapped = engine.sign_bootstrap(
    ciphertext_level_3,
    relinearization_key,
    conjugation_key,
    rotation_key,
    small_bootstrap_key,
)

ciphertext_level_5 = engine.encrypt(message, public_key, level=5)
bootstrapped_stage_count_5 = engine.sign_bootstrap(
    ciphertext_level_5,
    relinearization_key,
    conjugation_key,
    rotation_key,
    small_bootstrap_key,
    stage_count=5,
)


```

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

### Get Merge Bootstrap Key Size

Source: https://fhe.desilo.dev/latest/api/data-type/merge_bootstrap_key/nbytes

Instantiate an Engine, create a secret key, then a merge bootstrap key, and finally access its `nbytes` attribute to get its size in memory.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
merge_bootstrap_key = engine.create_merge_bootstrap_key(secret_key)
nbytes = merge_bootstrap_key.nbytes


```

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

### Running Argmax on Encrypted Data

Source: https://fhe.desilo.dev/latest/advanced_examples

Demonstrates how to encrypt data, compute its argmax using the previously defined function, and decrypt the result. Requires setting up the engine and keys.

```python
from desilofhe import Engine
import math

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
rotation_key = engine.create_rotation_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
bootstrap_key = engine.create_bootstrap_key(secret_key, stage_count=3)

# data
data = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8]
n = len(data)

# encrypt
encrypted = engine.encrypt(data, secret_key)

# compute argmax
encrypted_argmax = argmax(
    encrypted,
    n,
    rotation_key,
    relinearization_key,
    conjugation_key,
    bootstrap_key,
)

# decrypt and print the result
decrypted = engine.decrypt(encrypted_argmax, secret_key)
print(decrypted[:16])  # [~0 ~0 ~0 ~0 ~0 ~0 ~0 ~1 ~0 ...]

```

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

### Check SmallBootstrapKey CUDA Storage

Source: https://fhe.desilo.dev/latest/api/data-type/small_bootstrap_key/is_cuda

Demonstrates how to create small bootstrap keys for both GPU and CPU modes and assert their respective CUDA storage status using `is_cuda`.

```python
from desilofhe import Engine

gpu_engine = Engine(use_bootstrap=True, mode="gpu")
gpu_secret_key = gpu_engine.create_secret_key()
gpu_small_bootstrap_key = gpu_engine.create_small_bootstrap_key(gpu_secret_key)

assert gpu_small_bootstrap_key.is_cuda

cpu_engine = Engine(use_bootstrap=True, mode="cpu")
cpu_secret_key = cpu_engine.create_secret_key()
cpu_small_bootstrap_key = cpu_engine.create_small_bootstrap_key(cpu_secret_key)

assert not cpu_small_bootstrap_key.is_cuda
```

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

### Get Serialized Size of Light Plaintext

Source: https://fhe.desilo.dev/latest/api/data-type/light_plaintext/serialized_nbytes

Use `serialized_nbytes` to get the size of a light plaintext object after encoding a message. This property returns an integer representing the size in bytes.

```python
from desilofhe import Engine

engine = Engine()

message = [1, 2, 3]
light_plaintext = engine.encode_to_light_plaintext(message)
serialized_nbytes = light_plaintext.serialized_nbytes


```

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

### Get Lossy Bootstrap Key Size

Source: https://fhe.desilo.dev/latest/api/data-type/lossy_bootstrap_key/nbytes

Instantiate the engine, create a secret key, then a lossy bootstrap key, and finally access its `nbytes` attribute to get its memory size.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
lossy_bootstrap_key = engine.create_lossy_bootstrap_key(secret_key)
nbytes = lossy_bootstrap_key.nbytes


```

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

### Get Decrypted Share Length

Source: https://fhe.desilo.dev/latest/api/data-type/decrypted_share/__len__

This snippet demonstrates how to obtain the length of a decrypted share. It requires setting up an engine, keys, encrypting a message, and then decrypting it to get the `DecryptedShare` object.

```python
from desilofhe import Engine

engine = Engine(use_multiparty=True)
secret_key_1 = engine.create_secret_key()
secret_key_2 = engine.create_secret_key()
public_key_a = engine.create_public_key_a()
public_key_b1 = engine.create_public_key_b(secret_key1, public_key_a)
public_key_b2 = engine.create_public_key_b(secret_key2, public_key_a)
public_key = engine.create_multiparty_public_key(
    [public_key_b1, public_key_b2], public_key_a
)

message = [1] * 2 * engine.slot_count
ciphertext = engine.encrypt(message, public_key)
decrypted_share = engine.individual_decrypt(ciphertext, secret_key_1)
length = len(decrypted_share)  # 2
```

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

### Create PublicKeyB with and without Level - Python

Source: https://fhe.desilo.dev/latest/api/engine/public_key_b/create_public_key_b

Demonstrates creating a PublicKeyB using the `create_public_key_b` function. Shows both a default creation and one with a specified multiplication level.

```python
from desilofhe import Engine

engine = Engine(use_multiparty=True)
secret_key = engine.create_secret_key()
public_key_a = engine.create_public_key_a()

public_key_b = engine.create_public_key_b(secret_key, public_key_a)

level_3_public_key_b = engine.create_public_key_b(
    secret_key, public_key_a, level=3
)

```

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

### Verify GPU vs CPU Storage for Merge Bootstrap Key

Source: https://fhe.desilo.dev/latest/api/data-type/merge_bootstrap_key/is_cuda

Instantiate engines for both GPU and CPU modes, create secret keys, and then create merge bootstrap keys. Assert that `is_cuda` is true for the GPU key and false for the CPU key to confirm correct storage.

```python
from desilofhe import Engine

gpu_engine = Engine(use_bootstrap=True, mode="gpu")
gpu_secret_key = gpu_engine.create_secret_key()
gpu_merge_bootstrap_key = gpu_engine.create_merge_bootstrap_key(gpu_secret_key)

assert gpu_merge_bootstrap_key.is_cuda

cpu_engine = Engine(use_bootstrap=True, mode="cpu")
cpu_secret_key = cpu_engine.create_secret_key()
cpu_merge_bootstrap_key = cpu_engine.create_merge_bootstrap_key(cpu_secret_key)

assert not cpu_merge_bootstrap_key.is_cuda
```

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

### Lossy Bootstrap with Lossy Bootstrap Key

Source: https://fhe.desilo.dev/latest/api/engine/lossy_bootstrap

Use this method for faster bootstrapping when memory is not a constraint. The engine must be initialized with `use_bootstrap=True`. The ciphertext level must be at least the stage count of the lossy bootstrap key.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
lossy_bootstrap_key = engine.create_lossy_bootstrap_key(
    secret_key, stage_count=3
)

message = [-1, 0, 1]
ciphertext = engine.encrypt(message, public_key, level=3)
bootstrapped = engine.lossy_bootstrap(
    ciphertext, relinearization_key, conjugation_key, lossy_bootstrap_key
)

```

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

### Get DecryptedShare Serialized Size

Source: https://fhe.desilo.dev/latest/api/data-type/decrypted_share/serialized_nbytes

Access the `serialized_nbytes` attribute of a `DecryptedShare` object to get its size in bytes. This requires setting up the FHE engine, keys, and encrypting/decrypting a message to obtain a `DecryptedShare` object.

```python
from desilofhe import Engine

engine = Engine(use_multiparty=True)
secret_key_1 = engine.create_secret_key()
secret_key_2 = engine.create_secret_key()
public_key_a = engine.create_public_key_a()
public_key_b1 = engine.create_public_key_b(secret_key1, public_key_a)
public_key_b2 = engine.create_public_key_b(secret_key2, public_key_a)
public_key = engine.create_multiparty_public_key(
    [public_key_b1, public_key_b2], public_key_a
)

message = [1] * 2 * engine.slot_count
ciphertext = engine.encrypt(message, public_key)
decrypted_share = engine.individual_decrypt(ciphertext, secret_key_1)
serialized_nbytes = decrypted_share.serialized_nbytes

```

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

### Get Conjugation Key Size

Source: https://fhe.desilo.dev/latest/api/data-type/conjugation_key/nbytes

Demonstrates how to create a conjugation key and retrieve its size in bytes using the .nbytes attribute. Requires the desilofhe library.

```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
conjugation_key = engine.create_conjugation_key(secret_key)
nbytes = conjugation_key.nbytes


```

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

### Create Conjugation Key with and without Level

Source: https://fhe.desilo.dev/latest/api/engine/conjugation_key/create_conjugation_key

Demonstrates creating a default conjugation key and one with a specified multiplication level. Requires an initialized Engine and a secret key.

```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
conjugation_key = engine.create_conjugation_key(secret_key)

level_3_conjugation_key = engine.create_conjugation_key(secret_key, level=3)

```

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

### Create and Use Small Bootstrap Key

Source: https://fhe.desilo.dev/latest/bootstrap

Illustrates the creation and usage of a small bootstrap key, which is more efficient for bootstrapping operations. This variant requires a rotation key as well.

```python
from desilofhe import Engine

engine = Engine(slot_count=1024, use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
rotation_key = engine.create_rotation_key(secret_key)
small_bootstrap_key = engine.create_small_bootstrap_key(secret_key)

message = [-1, 0, 1, 0] * 256
ciphertext = engine.encrypt(message, public_key, level=0)
bootstrapped = engine.bootstrap(
    ciphertext,
    relinearization_key,
    conjugation_key,
    rotation_key,
    small_bootstrap_key,
    stage_count=1,
)

```

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

### Merge Bootstrap with Merge Bootstrap Key

Source: https://fhe.desilo.dev/latest/api/engine/merge_bootstrap

Use this snippet when faster bootstrapping is preferred and memory is not a constraint. Ensure the engine is initialized for bootstrapping.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
merge_bootstrap_key = engine.create_merge_bootstrap_key(
    secret_key, stage_count=3
)

message1 = [-1, 0, 1]
message2 = [1, 0, -1]
ciphertext1 = engine.encrypt(message1, public_key, level=0)
ciphertext2 = engine.encrypt(message2, public_key, level=0)
bootstrapped1, bootstrapped2 = engine.merge_bootstrap(
    ciphertext1,
    ciphertext2,
    relinearization_key,
    conjugation_key,
    merge_bootstrap_key,
)

```

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

### Create Merge Bootstrap Key with Default Settings

Source: https://fhe.desilo.dev/latest/api/engine/merge_bootstrap_key/create_merge_bootstrap_key

Creates a merge bootstrap key using default settings for stage count and size. Requires a secret key.

```python
from desilofhe import Engine

engine = Engine(for_bootstrap=True)
secret_key = engine.create_secret_key()
merge_bootstrap_key = engine.create_merge_bootstrap_key(secret_key)
```

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

### Create PublicKeyA with Engine

Source: https://fhe.desilo.dev/latest/api/engine/public_key_a/create_public_key_a

Instantiate a PublicKeyA object using the Engine. Use the `use_multiparty=True` flag when initializing the Engine for multiparty computation. The `create_public_key_a` method can be called without arguments for a default key, or with a `level` argument to generate a key with a reduced size for a specific number of multiplication levels.

```python
from desilofhe import Engine

engine = Engine(use_multiparty=True)
public_key_a = engine.create_public_key_a()

level_3_public_key_a = engine.create_public_key_a(level=3)

```

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

### Subtraction between two ciphertexts

Source: https://fhe.desilo.dev/latest/api/engine/subtract

Example demonstrating subtraction between two ciphertexts.

```APIDOC
## Subtraction between two ciphertexts

### Description
Subtracts one ciphertext from another.

### Code Example
```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)

message1 = [1, 2, 3]
ciphertext1 = engine.encrypt(message1, public_key)

message2 = [4, 5, 6]
ciphertext2 = engine.encrypt(message2, public_key)

subtracted = engine.subtract(ciphertext1, ciphertext2)
```
```

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

### Create Engine with Bootstrap to 14 Levels

Source: https://fhe.desilo.dev/latest/create_engine

Enable bootstrapping that results in 14 levels remaining after the operation. This differs from the standard bootstrap option which leaves 10 levels but supports more bootstrapping operation varieties.

```python
from desilofhe import Engine

bootstrap_engine = Engine(use_bootstrap_to_14_levels=True)
```

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

### RotationKey.nbytes

Source: https://fhe.desilo.dev/latest/api/data-type/rotation_key/nbytes

Access the `nbytes` attribute to get the memory size of the rotation key.

```APIDOC
## RotationKey.nbytes

### Description
Shows the memory size of a rotation key.

### Output
- **nbytes** (int) - The memory size of the rotation key in bytes.
```

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

### RelinearizationKey.nbytes

Source: https://fhe.desilo.dev/latest/api/data-type/relinearization_key/nbytes

Access the `nbytes` attribute to get the memory size of a relinearization key.

```APIDOC
## RelinearizationKey.nbytes

### Description
Shows the memory size of a relinearization key.

### Method
Attribute Access

### Endpoint
N/A

### Parameters
None

### Request Example
```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
relinearization_key = engine.create_relinearization_key(secret_key)
nbytes = relinearization_key.nbytes
print(nbytes)
```

### Response
#### Success Response (int)
- **nbytes** (int) - The memory size of the relinearization key in bytes.
```

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

### Bootstrap Ciphertext with Small Bootstrap Key

Source: https://fhe.desilo.dev/latest/api/engine/bootstrap

Initializes the engine for bootstrapping, creates necessary keys, encrypts a message, and then bootstraps the ciphertext using the small bootstrap key. This method uses less memory but is slower. The stage_count parameter can be adjusted.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
rotation_key = engine.create_rotation_key(secret_key)
small_bootstrap_key = engine.create_small_bootstrap_key(secret_key)

message = [-1, 0, 1]
ciphertext = engine.encrypt(message, public_key, level=0)
bootstrapped = engine.bootstrap(
    ciphertext,
    relinearization_key,
    conjugation_key,
    rotation_key,
    small_bootstrap_key,
)

bootstrapped_stage_count_5 = engine.bootstrap(
    ciphertext,
    relinearization_key,
    conjugation_key,
    rotation_key,
    small_bootstrap_key,
    stage_count=5,
)

```

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

### Sum along the 1-axis

Source: https://fhe.desilo.dev/latest/api/engine/sum

Example demonstrating how to sum a ciphertext along the 1-axis.

```APIDOC
## Sum along the 1-axis

### Description
This example shows how to compute the sum of a ciphertext specifically along the 1-axis.

### Code Example
```python
from desilofhe import Engine

engine = Engine(slot_count=4)
secret_key = engine.create_secret_key()
rotation_key = engine.create_rotation_key(secret_key)

message_4 = [1, 2, 3, 4]
ciphertext_4 = engine.encrypt(message_4, secret_key)

# contents of ciphertext_4:
# [[1, 2, 3, 4]]

sum_of_ciphertext_4 = engine.sum(ciphertext_4, rotation_key, axis=1)

# contents of sum_of_ciphertext_4:
# [[10, 10, 10, 10]]

message_8 = [1, 2, 3, 4, 5, 6, 7, 8]
ciphertext_8 = engine.encrypt(message_8, secret_key)

# contents of ciphertext_8:
# [[1, 2, 3, 4],
#  [5, 6, 7, 8]]

sum_of_ciphertext_8 = engine.sum(ciphertext_8, rotation_key, axis=1)

# contents of sum_of_ciphertext_8:
# [[10, 10, 10, 10],
#  [26, 26, 26, 26]]
```
```

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

### Create Bootstrap Key with Custom Stage Count

Source: https://fhe.desilo.dev/latest/api/engine/bootstrap_key/create_bootstrap_key

Creates a bootstrap key with a specified stage count. This example uses 5 stages, which affects bootstrapping speed and result level.

```python
medium_bootstrap_key_with_5_stages = engine.create_bootstrap_key(
    secret_key, stage_count=5
)
```

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

### Bootstrap Ciphertext with Bootstrap Key

Source: https://fhe.desilo.dev/latest/api/engine/bootstrap

Initializes the engine for bootstrapping, creates necessary keys, encrypts a message, and then bootstraps the ciphertext using the bootstrap key. This method is faster but uses more memory.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
bootstrap_key = engine.create_bootstrap_key(secret_key, stage_count=3)

message = [-1, 0, 1]
ciphertext = engine.encrypt(message, public_key, level=0)
bootstrapped = engine.bootstrap(
    ciphertext, relinearization_key, conjugation_key, bootstrap_key
)

```

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

### Sum along the 0-axis

Source: https://fhe.desilo.dev/latest/api/engine/sum

Example demonstrating how to sum a ciphertext along the 0-axis.

```APIDOC
## Sum along the 0-axis

### Description
This example shows how to compute the sum of a ciphertext specifically along the 0-axis.

### Code Example
```python
from desilofhe import Engine

engine = Engine(slot_count=4)
secret_key = engine.create_secret_key()
rotation_key = engine.create_rotation_key(secret_key)

message_4 = [1, 2, 3, 4]
ciphertext_4 = engine.encrypt(message_4, secret_key)

# contents of ciphertext_4:
# [[1, 2, 3, 4]]

sum_of_ciphertext_4 = engine.sum(ciphertext_4, rotation_key, axis=0)

# contents of sum_of_ciphertext_4:
# [[1, 2, 3, 4]]

message_8 = [1, 2, 3, 4, 5, 6, 7, 8]
ciphertext_8 = engine.encrypt(message_8, secret_key)

# contents of ciphertext_8:
# [[1, 2, 3, 4],
#  [5, 6, 7, 8]]

sum_of_ciphertext_8 = engine.sum(ciphertext_8, rotation_key, axis=0)

# contents of sum_of_ciphertext_8:
# [[6, 8, 10, 12]]
```
```

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

### Create Rotation Key with GLEngine

Source: https://fhe.desilo.dev/latest/api/gl-engine/create_rotation_key

Demonstrates creating a secret key and then a default rotation key. Use this for standard 3D rotations.

```python
from desilofhe import GLEngine

engine = GLEngine()
secret_key = engine.create_secret_key()
rotation_key = engine.create_rotation_key(secret_key)


```

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

### LightPlainMatrix.serialized_nbytes

Source: https://fhe.desilo.dev/latest/api/data-type/light_plain_matrix/serialized_nbytes

Access the serialized_nbytes attribute to get the size of the serialized light plain matrix.

```APIDOC
## LightPlainMatrix.serialized_nbytes

### Description
Shows the size of a light plain matrix when serialized.

### Output
- `serialized_nbytes` (int): The size of the serialized matrix in bytes.

### Example
```python
import numpy as np

from desilofhe import Engine

engine = Engine(slot_count=64)

message = np.arange(64 * 64).reshape(64, 64)
light_plain_matrix = engine.encode_to_light_plain_matrix(message)
serialized_nbytes = light_plain_matrix.serialized_nbytes

print(f"Serialized size: {serialized_nbytes} bytes")
```
```

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

### Subtraction of a plaintext from a ciphertext in-place

Source: https://fhe.desilo.dev/latest/api/engine/subtract

Example demonstrating in-place subtraction of a plaintext from a ciphertext.

```APIDOC
## Subtraction of a plaintext from a ciphertext in-place

### Description
Performs subtraction in-place, modifying the ciphertext with the result of subtracting a plaintext from it.

### Code Example
```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)

message1 = [1, 2, 3]
plaintext1 = engine.encode(message1)
ciphertext1 = engine.encrypt(plaintext1, public_key)

message2 = [4, 5, 6]
plaintext2 = engine.encode(message2)

engine.subtract(ciphertext1, plaintext2, out=ciphertext1)

decrypted = engine.decrypt(ciphertext1, secret_key)  # [-3, -3, -3]
```
```

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

### Lossy Bootstrap with Small Bootstrap Key

Source: https://fhe.desilo.dev/latest/api/engine/lossy_bootstrap

Use this method when memory is a constraint, as it uses less memory than the lossy bootstrap key but is slower. The engine must be initialized with `use_bootstrap=True`. The ciphertext level must be at least the specified stage count.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
rotation_key = engine.create_rotation_key(secret_key)
small_bootstrap_key = engine.create_small_bootstrap_key(secret_key)

message = [-1, 0, 1]
ciphertext_level_3 = engine.encrypt(message, public_key, level=3)
bootstrapped = engine.lossy_bootstrap(
    ciphertext_level_3,
    relinearization_key,
    conjugation_key,
    rotation_key,
    small_bootstrap_key,
)

ciphertext_level_5 = engine.encrypt(message, public_key, level=5)
bootstrapped_stage_count_5 = engine.lossy_bootstrap(
    ciphertext_level_5,
    relinearization_key,
    conjugation_key,
    rotation_key,
    small_bootstrap_key,
    stage_count=5,
)

```

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

### Create Individual Fixed Rotation Keys

Source: https://fhe.desilo.dev/latest/api/engine/fixed_rotation_key/create_individual_fixed_rotation_key

Demonstrates the creation of individual fixed rotation keys with and without specifying a multiplication level. Ensure you have initialized the Engine and created the necessary secret and public keys beforehand.

```python
from desilofhe import Engine

engine = Engine()
secret_key1 = engine.create_secret_key()
secret_key2 = engine.create_secret_key()
public_key_a = engine.create_public_key_a()
public_key_b1 = engine.create_public_key_b(secret_key1, public_key_a)
public_key_b2 = engine.create_public_key_b(secret_key2, public_key_a)

public_key = engine.create_multiparty_public_key(
    [public_key_b1, public_key_b2], public_key_a
)

fixed_rotation_key1 = engine.create_individual_fixed_rotation_key(
    secret_key1, public_key, delta=1
)

level_3_fixed_rotation_key1 = engine.create_individual_fixed_rotation_key(
    secret_key1, public_key, delta=1, level=3
)

```

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

### Subtraction in-place between two ciphertexts

Source: https://fhe.desilo.dev/latest/api/engine/subtract

Example demonstrating in-place subtraction between two ciphertexts.

```APIDOC
## Subtraction in-place between two ciphertexts

### Description
Performs subtraction in-place, modifying the first ciphertext with the result of subtracting the second ciphertext from it.

### Code Example
```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)

message1 = [1, 2, 3]
ciphertext1 = engine.encrypt(message1, public_key)

message2 = [4, 5, 6]
ciphertext2 = engine.encrypt(message2, public_key)

engine.subtract(ciphertext1, ciphertext2, out=ciphertext1)

decrypted = engine.decrypt(ciphertext1, secret_key)  # [-3, -3, -3]
```
```

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

### Subtraction of a plaintext from a ciphertext

Source: https://fhe.desilo.dev/latest/api/engine/subtract

Example demonstrating subtraction of a plaintext from a ciphertext, and vice versa.

```APIDOC
## Subtraction of a plaintext from a ciphertext

### Description
Subtracts a plaintext from a ciphertext, or a ciphertext from a plaintext.

### Code Example
```python
from desilofhe import Engine

engine = Engine()
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)

message1 = [1, 2, 3]
plaintext1 = engine.encode(message1)
ciphertext1 = engine.encrypt(plaintext1, public_key)

message2 = [4, 5, 6]
plaintext2 = engine.encode(message2)
# ciphertext2 = engine.encrypt(plaintext2, public_key) # This line is not used in the example but is present in the source

subtracted1 = engine.subtract(ciphertext1, plaintext2)
subtracted2 = engine.subtract(plaintext1, ciphertext2)
```
```

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

### Execute ModRaise with Bootstrap Key

Source: https://fhe.desilo.dev/latest/api/engine/mod_raise

Use this snippet to execute the ModRaise function with a full bootstrap key. Ensure the engine is initialized with use_bootstrap=True and that a bootstrap key is generated.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
bootstrap_key = engine.create_bootstrap_key(secret_key, stage_count=3)

message = [-1, 0, 1]
ciphertext = engine.encrypt(message, public_key, level=0)
mod_raised = engine.mod_raise(ciphertext, bootstrap_key)

```

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

### Bootstrap to 14 Levels with Small Bootstrap Key

Source: https://fhe.desilo.dev/latest/bootstrap

Initializes the FHE engine for bootstrapping to 14 levels and generates necessary keys, including a small bootstrap key. This is useful when a smaller key size is preferred for bootstrapping.

```python
from desilofhe import Engine

engine = Engine(use_bootstrap_to_14_levels=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
rotation_key = engine.create_rotation_key(secret_key)
small_bootstrap_key = engine.create_small_bootstrap_key(secret_key)

message = [-1, 0, 1]
ciphertext = engine.encrypt(message, public_key, level=0)
bootstrapped = engine.bootstrap(
    ciphertext,
    relinearization_key,
    conjugation_key,
    rotation_key,
    small_bootstrap_key,
)


```

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

### Sum along all axes

Source: https://fhe.desilo.dev/latest/api/engine/sum

Example demonstrating how to sum all elements of a ciphertext when no axis is specified.

```APIDOC
## Sum along all axes

### Description
This example shows how to compute the sum of all elements in a ciphertext by omitting the `axis` parameter.

### Code Example
```python
from desilofhe import Engine

engine = Engine(slot_count=4)
secret_key = engine.create_secret_key()
rotation_key = engine.create_rotation_key(secret_key)

message_4 = [1, 2, 3, 4]
ciphertext_4 = engine.encrypt(message_4, secret_key)

# contents of ciphertext_4:
# [[1, 2, 3, 4]]

sum_of_ciphertext_4 = engine.sum(ciphertext_4, rotation_key)

# contents of sum_of_ciphertext_4:
# [[10, 10, 10, 10]]

message_8 = [1, 2, 3, 4, 5, 6, 7, 8]
ciphertext_8 = engine.encrypt(message_8, secret_key)

# contents of ciphertext_8:
# [[1, 2, 3, 4],
#  [5, 6, 7, 8]]

sum_of_ciphertext_8 = engine.sum(ciphertext_8, rotation_key)

# contents of sum_of_ciphertext_8:
# [[36, 36, 36, 36]]
```
```

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

### LightPlainMatrix.level

Source: https://fhe.desilo.dev/latest/api/data-type/light_plain_matrix/level

Accessing the level property of a LightPlainMatrix object to get the maximum possible number of multiplications.

```APIDOC
## LightPlainMatrix.level

### Description
Shows the maximum possible number of multiplications for a light plain matrix.

### Output
- **level** (int) - The maximum possible number of multiplications.
```

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

### Get Matrix Multiplication Key Size

Source: https://fhe.desilo.dev/latest/api/data-type/matrix_multiplication_key/nbytes

Demonstrates how to create a matrix multiplication key and retrieve its size in bytes using the `.nbytes` attribute. Requires the `desilofhe` library.

```python
from desilofhe import Engine

engine = Engine(slot_count=64)
secret_key = engine.create_secret_key()
matrix_multiplication_key = engine.create_matrix_multiplication_key(secret_key)
nbytes = matrix_multiplication_key.nbytes


```

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

### Get ConjugationKey Size

Source: https://fhe.desilo.dev/latest/api/data-type/conjugation_key/nbytes

The `nbytes` attribute of a `ConjugationKey` object returns its size in bytes as an integer.

```APIDOC
## ConjugationKey.nbytes

### Description
Shows the size of a conjugation key in bytes.

### Method
Attribute Access

### Endpoint
N/A (Object Attribute)

### Parameters
None

### Response
#### Success Response
- **nbytes** (int) - The size of the conjugation key in bytes.
```