# Serialisation¶

This library does not enforce any particular serialisation scheme.

Every `EncryptedNumber`

instance has a `public_key`

attribute, and serialising each
`EncryptedNumber`

independently would be heinously inefficient when sending
a large list of instances. It is up to you to serialise in a way that is efficient for your use
case.

## Basic JSON Serialisation¶

This basic serialisation method is an example of serialising a vector of encrypted numbers.
Note that if you are only using the python-paillier library **g** will always be **n + 1**,
so these is no need to serialise it as part of the public key.

To send a list of values encrypted against one public key, the following is one way to serialise:

```
>>> import json
>>> enc_with_one_pub_key = {}
>>> enc_with_one_pub_key['public_key'] = {'n': public_key.n}
>>> enc_with_one_pub_key['values'] = [
... (str(x.ciphertext()), x.exponent) for x in encrypted_number_list
... ]
>>> serialised = json.dumps(enc_with_one_pub_key)
```

Deserialisation of the above scheme might look as follows:

```
>>> received_dict = json.loads(serialised)
>>> pk = received_dict['public_key']
>>> public_key_rec = paillier.PaillierPublicKey(n=int(pk['n']))
>>> enc_nums_rec = [
... paillier.EncryptedNumber(public_key_rec, int(x[0]), int(x[1]))
... for x in received_dict['values']
... ]
```

If both parties already know public_key, then you might instead send a hash of the public key.

## JWK Serialisation¶

This serialisation scheme is used by the Command Line Utility, and is based on the JSON Web Key (JWK) format. This serialisation scheme should be used to increase compatibility between libraries.

All cryptographic integers are represented as Base64UrlEncoded numbers.
Note the existence of `base64_to_int()`

and `int_to_base64()`

.

### “kty” (Key Type) Parameter¶

We define the family for all Paillier keys as “DAJ” for Damgard Jurik.

### “alg” (Algorithm) Parameter¶

We identify the algorithm for our Paillier keys as: “PAI-GN1”

### “key_ops” (Key Operations) Parameter¶

Values will be “encrypt” and “decrypt” for public and private keys respectively. We decided not to add homomorphic properties to the key operations.

### “kid” (Key Identifier)¶

The **kid** may be set to any ascii string. Useful for storing key names,
generation tools, times etc.

### Public Key¶

In addition to the “kty”, “kid”, “key_ops” and “alg” attributes, a public key will have:

**n**The public key’s modulus - Base64 url encoded

Example of a 256 bit public key:

```
python -m phe.command_line genpkey --keysize 256 - | python -m phe.command_line extract - -
{
"kty": "DAJ",
"kid": "Example Paillier public key",
"key_ops": [ "encrypt" ],
"n": "m0lOEwDHVA_VieL2k3BKMjf_HIgagfhNIZy1YhgZF5M",
"alg": "PAI-GN1"
}
```

### Private Key¶

Note

The serialised private key includes the public key.

In addition to the “kty”, “kid”, “key_ops” and “alg” attributes, a private key will have:

**mu**and**lambda**- The private key’s secrets. See Paillier’s paper for details.**pub**- The Public Key serialised as described above.

Example of a 256 bit private key:

```
python -m phe.command_line genpkey --keysize 256 -
{
"mu": "Dzq1_tz2qDX_-S4shia9Rw34Z9ix9b-fhPi3In76NaI",
"kty": "DAJ",
"key_ops": [ "decrypt" ],
"kid": "Paillier private key generated by pheutil on 2016-05-24 14:18:25",
"lambda": "haFTvA70KcI5XXReJUlQWRQdYHxaUS8baGQGug9dewA",
"pub": {
"alg": "PAI-GN1",
"n": "haFTvA70KcI5XXReJUlQWoZus12aSJJ5EXAvu93xR7k",
"kty": "DAJ",
"key_ops": [ "encrypt" ],
"kid": "Paillier public key generated by pheutil on 2016-05-24 14:18:25"
}
}
```

Warning

“kty” and “alg” values should be registered in the
IANA “JSON Web Key Types” registry
established by JWA. We have not registered **DAJ** or **PAI-GN1** - however we intend to begin that
conversation.