# Module crypto

`:- use_module(library(crypto)).`

Predicates for cryptographic applications.

This library assumes that the Prolog flag `double_quotes`

is set to `chars`

. In Scryer Prolog, lists of characters are very efficiently represented, and strings have the advantage that the atom table remains unmodified.

Especially for cryptographic applications, it is an advantage that using strings leaves little trace of what was processed in the system.

#### hex_bytes(?Hex, ?Bytes) is det.

Relation between a hexadecimal sequence and a list of bytes. Hex is a string of hexadecimal numbers. Bytes is a list of *integers* between 0 and 255 that represent the sequence as a list of bytes. At least one of the arguments must be instantiated.

Example:

```
?- hex_bytes("501ACE", Bs).
Bs = [80,26,206].
```

#### crypto_n_random_bytes(+N, -Bytes) is det.

Bytes is unified with a list of N cryptographically secure pseudo-random bytes. Each byte is an integer between 0 and 255. If the internal pseudo-random number generator (PRNG) has not been seeded with enough entropy to ensure an unpredictable byte sequence, an exception is thrown.

One way to relate such a list of bytes to an *integer* is to use CLP(ℤ) constraints as follows:

```
:- use_module(library(clpz)).
:- use_module(library(lists)).
bytes_integer(Bs, N) :-
foldl(pow, Bs, 0-0, N-_).
pow(B, N0-I0, N-I) :-
B in 0..255,
N #= N0 + B*256^I0,
I #= I0 + 1.
```

With this definition, we can generate a random 256-bit integer *from* a list of 32 random *bytes*:

```
?- crypto_n_random_bytes(32, Bs),
bytes_integer(Bs, I).
Bs = [146,166,162,210,242,7,25,132,64,94|...],
I = 337420085690608915485...(56 digits omitted).
```

The above relation also works in the other direction, letting you translate an integer *to* a list of bytes. In addition, you can use `hex_bytes/2`

to convert bytes to *tokens* that can be easily exchanged in your applications.

```
?- crypto_n_random_bytes(12, Bs),
hex_bytes(Hex, Bs).
Bs = [34,25,50,72,58,63,50,172,32,46|...], Hex = "221932483a3f32ac202 ...".
```

#### crypto_data_hash(+Data, -Hash, +Options)

Where Data is a list of characters, and Hash is the computed hash as a list of hexadecimal characters.

Options is a list of:

`algorithm(+A)`

where`A`

is one of`ripemd160`

,`sha256`

,`sha384`

,`sha512`

,`sha512_256`

,`sha3_224`

,`sha3_256`

,`sha3_384`

,`sha3_512`

,`blake2s256`

,`blake2b512`

, or a variable. If`A`

is a variable, then it is unified with the default algorithm, which is an algorithm that is considered cryptographically secure at the time of this writing.`encoding(+Encoding)`

The default encoding is`utf8`

. The alternative is`octet`

, to use the character code of each character in Data as a byte value.`hmac(+Key)`

Compute a hash-based message authentication code (HMAC) using Key, a list of bytes. This option is currently supported for algorithms`sha256`

,`sha384`

and`sha512`

. If`Hash`

is instantiated, then it is compared with the computed HMAC in such a way that no information about the expected HMAC is revealed, using a comparison of strings that always takes the same time independent of whether and where the strings differ. This option can therefore also be used to safely*verify*a given HMAC.

Example:

```
?- crypto_data_hash("abc", Hs, [algorithm(sha256)]).
Hs = "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad".
```

#### crypto_data_hkdf(+Data, +Length, -Bytes, +Options) is det.

Concentrate possibly dispersed entropy of Data and then expand it to the desired length. Data is a list of characters.

Bytes is unified with a list of bytes of length Length, and is suitable as input keying material and initialization vectors to symmetric encryption algorithms.

Admissible options are:

`algorithm(+Algorithm)`

One of`sha256`

,`sha384`

or`sha512`

. If you specify a variable, then it is unified with the algorithm that was used, which is a cryptographically secure algorithm by default.`info(+Info)`

Optional context and application specific information, specified as a list of characters. The default is`[]`

.`salt(+List)`

Optionally, a list of bytes that are used as salt. The default is all zeroes.`encoding(+Encoding)`

The default encoding is`utf8`

. The alternative is`octet`

, to use the character code of each character in Data as a byte value.

The `info/1`

option can be used to generate multiple keys from a single master key, using for example values such as "key" and "iv", or the name of a file that is to be encrypted.

See `crypto_n_random_bytes/2`

to obtain a suitable salt.

#### crypto_password_hash(+Password, ?Hash) is semidet.

If Hash is instantiated, the predicate succeeds *iff* the hash matches the given password. Otherwise, the call is equivalent to `crypto_password_hash(Password, Hash, [])`

and computes a password-based hash using the default options.

#### crypto_password_hash(+Password, -Hash, +Options) is det.

Derive Hash based on Password. This predicate is similar to `crypto_data_hash/3`

in that it derives a hash from given data. However, it is tailored for the specific use case of *passwords*. One essential distinction is that for this use case, the derivation of a hash should be *as slow as possible* to counteract brute-force attacks over possible passwords.

Another important distinction is that equal passwords must yield, with very high probability, *different* hashes. For this reason, cryptographically strong random numbers are automatically added to the password before a hash is derived.

Hash is unified with a string that contains the computed hash and all parameters that were used, except for the password. Instead of storing passwords, store these hashes. Later, you can verify the validity of a password with `crypto_password_hash/2`

, comparing the then entered password to the stored hash. If you need to export this atom, you should treat it as opaque ASCII data with up to 255 bytes of length. The maximal length may increase in the future.

Admissible options are:

`algorithm(+Algorithm)`

The algorithm to use. Currently, the only available algorithm is`'pbkdf2-sha512'`

, which is therefore also the default.`cost(+C)`

C is an integer, denoting the binary logarithm of the number of*iterations*used for the derivation of the hash. This means that the number of iterations is set to 2^C. Currently, the default is 17, and thus more than one hundred*thousand*iterations. You should set this option as high as your server and users can tolerate. The default is subject to change and will likely increase in the future or adapt to new algorithms.`salt(+Salt)`

Use the given list of bytes as salt. By default, cryptographically secure random numbers are generated for this purpose. The default is intended to be secure, and constitutes the typical use case of this predicate.

Currently, PBKDF2 with SHA-512 is used as the hash derivation function, using 128 bits of salt. All default parameters, including the algorithm, are subject to change, and other algorithms will also become available in the future. Since computed hashes store all parameters that were used during their derivation, such changes will not affect the operation of existing deployments. Note though that new hashes will then be computed with the new default parameters.

See `crypto_data_hkdf/4`

for generating keys from Hash.

#### crypto_data_encrypt(+PlainText, +Algorithm, +Key, +IV, -CipherText, +Options).

Encrypt the given PlainText, using the symmetric algorithm Algorithm, key Key, and initialization vector (or nonce) IV, to give CipherText.

PlainText must be a list of characters, Key and IV must be lists of bytes, and CipherText is created as a list of characters.

Keys and IVs can be chosen at random (using for example `crypto_n_random_bytes/2`

) or derived from input keying material (IKM) using for example `crypto_data_hkdf/4`

. This input is often a shared secret, such as a negotiated point on an elliptic curve, or the hash that was computed from a password via `crypto_password_hash/3`

with a freshly generated and specified *salt*.

Reusing the same combination of Key and IV typically leaks at least *some* information about the plaintext. For example, identical plaintexts will then correspond to identical ciphertexts. For some algorithms, reusing an IV with the same Key has disastrous results and can cause the loss of all properties that are otherwise guaranteed. Especially in such cases, an IV is also called a *nonce* (number used once).

It is safe to store and transfer the used initialization vector (or nonce) in plain text, but the key *must be kept secret*.

Currently, the only supported algorithm is 'chacha20-poly1305', a powerful and efficient *authenticated* encryption scheme, providing secrecy and at the same time reliable protection against undetected *modifications* of the encrypted data. This is a very good choice for virtually all use cases. It is a stream cipher and can encrypt data of any length up to 256 GB. Further, the encrypted data has exactly the same length as the original, and no padding is used.

Options:

`encoding(+Encoding)`

Encoding to use for PlainText. The default is`utf8`

. The alternative is`octet`

, to use the character code of each character in PlainText as a byte value.`tag(-List)`

For authenticated encryption schemes, List is unified with a list of*bytes*holding the tag. This tag must be provided for decryption.`aad(+Data)`

Data is additional authenticated data (AAD), a list of characters. It is authenticated in that it influences the tag, but it is not encrypted. The`encoding/1`

option also specifies the encoding of Data.

Here is an example encryption and decryption, using the ChaCha20 stream cipher with the Poly1305 authenticator. This cipher uses a 256-bit key and a 96-bit nonce, i.e., 32 and 12 *bytes*, respectively:

```
?- Algorithm = 'chacha20-poly1305',
crypto_n_random_bytes(32, Key),
crypto_n_random_bytes(12, IV),
crypto_data_encrypt("this text is to be encrypted", Algorithm,
Key, IV, CipherText, [tag(Tag)]),
crypto_data_decrypt(CipherText, Algorithm,
Key, IV, RecoveredText, [tag(Tag)]).
```

Yielding:

```
Algorithm = 'chacha20-poly1305',
Key = [113,247,153,134,177,220,13,193,50,150|...],
IV = [135,20,149,153,63,35,68,114,247,171|...],
CipherText = "\x94\0Ej\x94\®Â\x95\óÑÆXÃn¾ð©b\x1c\ ...",
RecoveredText = "this text is to be ...",
Tag = [152,117,152,17,162,75,150,206,144,40|...]
```

In this example, we use `crypto_n_random_bytes/2`

to generate a key and nonce from cryptographically secure random numbers. For repeated applications, you must ensure that a nonce is only used *once* together with the same key. Note that for *authenticated* encryption schemes, the *tag* that was computed during encryption is necessary for decryption. It is safe to store and transfer the tag in plain text.

See also `crypto_data_decrypt/6`

, and `hex_bytes/2`

for conversion between bytes and hex encoding.

#### crypto_data_decrypt(+CipherText, +Algorithm, +Key, +IV, -PlainText, +Options).

Decrypt the given CipherText, using the symmetric algorithm Algorithm, key Key, and initialization vector IV, to give PlainText. CipherText must be a list of characters, and Key and IV must be lists of bytes. PlainText is created as a list of characters.

Currently, the only supported algorithm is 'chacha20-poly1305', a very secure, fast and versatile authenticated encryption method.

Options is a list of:

`encoding(+Encoding)`

Encoding to use for PlainText. The default is`utf8`

. The alternative is`octet`

, to obtain a list of characters where each character code corresponds to a decrypted octet of CipherText.`tag(+Tag)`

For authenticated encryption schemes, the tag must be specified as a list of bytes exactly as they were generated upon encryption.`aad(+Data)`

Any additional authenticated data (AAD) must be specified. The`encoding/1`

option also specifies the encoding of Data.

#### ed25519_seed_keypair(+Seed, -Pair)

Use Seed to deterministically generate an Ed25519 key pair Pair, a list of characters. Seed must be a list of 32 bytes. It can be chosen at random (using for example `crypto_n_random_bytes/2`

) or derived from input keying material (IKM) using for example `crypto_data_hkdf/4`

. The pair contains the private key and must be kept absolutely secret. Pair can be used for signing. Its public key can be obtained with `ed25519_keypair_public_key/2`

.

#### ed25519_new_keypair(-Pair)

Yields a new Ed25519 key pair Pair, a list of characters. The pair contains the private key and must be kept absolutely secret. Pair can be used for signing. Its public key can be obtained with `ed25519_keypair_public_key/2`

.

#### ed25519_keypair_public_key(+Pair, -PublicKey)

PublicKey is the public key of the given key pair. The public key can be used for signature verification, and can be shared freely. The public key is represented as a list of characters.

#### ed25519_sign(+Key, +Data, -Signature, +Options)

Key and Data must be lists of characters. Key is a key pair in PKCS#8 v2 format as generated by `ed25519_new_keypair/1`

. Sign Data with Key, yielding Signature as a list of hexadecimal characters.

#### ed25519_verify(+Key, +Data, +Signature, +Options)

Key and Data must be lists of characters. Key is a public key. Succeeds if Data was signed with the private key corresponding to Key, where Signature is a list of hexadecimal characters as generated by `ed25519_sign/4`

. Fails otherwise.

Currently, the only option for signing and verifying is:

`encoding(+Encoding)`

The default encoding of Data is`utf8`

. The alternative is`octet`

, to use the character code of each character in Data as a byte value.

#### curve25519_generator(-Gs)

Points on Curve25519 are represented as lists of characters that denote the u-coordinate of the Montgomery curve. Gs is the generator point of Curve25519.

#### curve25519_scalar_mult(+Scalar, +Ps, -Rs)

Scalar must be an integer between 0 and 2^256-1, or a list of 32 bytes, and Ps must be a point on the curve. Computes the point *Rs = Scalar*Ps as* mandated by X25519.

Alice and Bob can use this to establish a shared secret as follows, where Gs is the generator point of Curve25519:

Alice creates a random integer

*a*and sends*As = a*Gs*to Bob.Bob creates a random integer

*b*and sends*Bs = b*Gs*to Alice.Alice computes

*Rs = a*Bs*.Bob computes

*Rs = b*As*.Alice and Bob use

`crypto_data_hkdf/4`

on Rs with suitable (same) parameters to obtain lists of bytes that can be used as keys and initialization vectors for symmetric encryption.

If *a* and *b* are kept secret, this method is considered very secure.

#### crypto_curve_generator(+Curve, -G)

Yields the generator point G of Curve.

#### crypto_curve_order(+Curve, -Order)

Yields the order of Curve.

#### crypto_curve_scalar_mult(+Curve, +Scalar, +Point, -Result)

Computes the point *Result = Scalar*Point*. Scalar must be an integer, and Point must be a point on Curve. This operation can be used to negotiate a shared secret over a public channel. Consider using `curve25519_scalar_mult/3`

instead for more desirable security properties.

#### crypto_name_curve(+Name, -Curve)

Yields a representation of the elliptic curve with name Name. Currently, the only supported name is `secp256k1`

, a Koblitz curve regarded as secure.