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# Algorithm Details

This chapter describes details of algorithms in the crypto application.

The tables only documents the supported cryptos and key lengths. The user should
not draw any conclusion on security from the supplied tables.

## Ciphers

A [cipher](`t:crypto:cipher/0`) in the [new api](new_api.md#the-new-api) is
categorized as either [cipher_no_iv()](`t:crypto:cipher_no_iv/0`),
[cipher_iv()](`t:crypto:cipher_iv/0`) or
[cipher_aead()](`t:crypto:cipher_aead/0`). The letters IV are short for
_Initialization Vector_ and AEAD is an abbreviation of _Authenticated Encryption
with Associated Data_.

Due to irregular naming conventions, some cipher names in the old api are
substituted by new names in the new api. For a list of retired names, see
[Retired cipher names](new_api.md#retired-cipher-names).

To dynamically check availability, check that the name in the _Cipher and Mode_
column is present in the list returned by
[crypto:supports(ciphers)](`crypto:supports/1`).

### Ciphers without an IV - cipher_no_iv()

To be used with:

- [crypto_one_time/4](`crypto:crypto_one_time/4`)
- [crypto_init/3](`crypto:crypto_init/3`)

The ciphers are:

| **Cipher and Mode** | **Key length** **\[bytes]** | **Block size** **\[bytes]** |
| ------------------- | --------------------------- | --------------------------- |
| `aes_128_ecb`       | 16                          | 16                          |
| `aes_192_ecb`       | 24                          | 16                          |
| `aes_256_ecb`       | 32                          | 16                          |
| `blowfish_ecb`      | 16                          |  8                          |
| `des_ecb`           |  8                          |  8                          |
| `rc4`               | 16                          |  1                          |
| `sm4_ecb`           | 16                          | 16                          |

_Table: Ciphers without IV_

### Ciphers with an IV - cipher_iv()

To be used with:

- [crypto_one_time/5](`crypto:crypto_one_time/5`)
- [crypto_init/4](`crypto:crypto_init/4`)

The ciphers are:

| **Cipher and Mode** | **Key length** **\[bytes]** | **IV length** **\[bytes]** | **Block size** **\[bytes]** | **Limited to** **OpenSSL versions** |
| ------------------- | --------------------------- | -------------------------- | --------------------------- | ----------------------------------- |
| `aes_128_cbc`       | 16                          | 16                         | 16                          |                                     |
| `aes_192_cbc`       | 24                          | 16                         | 16                          |                                     |
| `aes_256_cbc`       | 32                          | 16                         | 16                          |                                     |
| `aes_128_cfb8`      | 16                          | 16                         |  1                          |                                     |
| `aes_192_cfb8`      | 24                          | 16                         |  1                          |                                     |
| `aes_256_cfb8`      | 32                          | 16                         |  1                          |                                     |
| `aes_128_cfb128`    | 16                          | 16                         |  1                          |                                     |
| `aes_192_cfb128`    | 24                          | 16                         |  1                          |                                     |
| `aes_256_cfb128`    | 32                          | 16                         |  1                          |                                     |
| `aes_128_ctr`       | 16                          | 16                         |  1                          |                                     |
| `aes_192_ctr`       | 24                          | 16                         |  1                          |                                     |
| `aes_256_ctr`       | 32                          | 16                         |  1                          |                                     |
| `aes_128_ofb`       | 16                          | 16                         |  1                          |                                     |
| `aes_192_ofb`       | 24                          | 16                         |  1                          |                                     |
| `aes_256_ofb`       | 32                          | 16                         |  1                          |                                     |
| `blowfish_cbc`      | 16                          |  8                         |  8                          |                                     |
| `blowfish_cfb64`    | 16                          |  8                         |  1                          |                                     |
| `blowfish_ofb64`    | 16                          |  8                         |  1                          |                                     |
| `chacha20`          | 32                          | 16                         |  1                          | ≥1.1.0d                             |
| `des_cbc`           |  8                          |  8                         |  8                          |                                     |
| `des_ede3_cbc`      | 24                          |  8                         |  8                          |                                     |
| `des_cfb`           |  8                          |  8                         |  1                          |                                     |
| `des_ede3_cfb`      | 24                          |  8                         |  1                          |                                     |
| `rc2_cbc`           | 16                          |  8                         |  8                          |                                     |
| `sm4_cbc`           | 16                          | 16                         | 16                          | ≥1.1.1                              |
| `sm4_cfb`           | 16                          | 16                         | 16                          | ≥1.1.1                              |
| `sm4_ofb`           | 16                          | 16                         | 16                          | ≥1.1.1                              |
| `sm4_ctr`           | 16                          | 16                         | 16                          | ≥1.1.1                              |

_Table: Ciphers with IV_

### Ciphers with AEAD - cipher_aead()

To be used with:

- [crypto_one_time_aead/6](`crypto:crypto_one_time_aead/6`)
- [crypto_one_time_aead/7](`crypto:crypto_one_time_aead/7`)

The ciphers are:

| **Cipher and Mode** | **Key length** **\[bytes]** | **IV length** **\[bytes]** | **AAD length** **\[bytes]** | **Tag length** **\[bytes]** | **Block size** **\[bytes]** | **Limited to** **OpenSSL versions** |
| ------------------- | --------------------------- | -------------------------- | --------------------------- | --------------------------- | --------------------------- | ----------------------------------- |
| `aes_128_ccm`       | 16                          | 7-13                       | any                         | even 4-16 default: 12       | any                         | ≥1.0.1                              |
| `aes_192_ccm`       | 24                          | 7-13                       | any                         | even 4-16 default: 12       | any                         | ≥1.0.1                              |
| `aes_256_ccm`       | 32                          | 7-13                       | any                         | even 4-16 default: 12       | any                         | ≥1.0.1                              |
| `aes_128_gcm`       | 16                          | ≥1                         | any                         | 1-16 default: 16            | any                         | ≥1.0.1                              |
| `aes_192_gcm`       | 24                          | ≥1                         | any                         | 1-16 default: 16            | any                         | ≥1.0.1                              |
| `aes_256_gcm`       | 32                          | ≥1                         | any                         | 1-16 default: 16            | any                         | ≥1.0.1                              |
| `chacha20_poly1305` | 32                          | 1-16                       | any                         | 16                          | any                         | ≥1.1.0                              |
| `sm4_gcm`           | 16                          | 12                         | any                         | 16                          | any                         | ≥3.1.0                              |
| `sm4_ccm`           | 16                          | 12                         | any                         | 16                          | any                         | ≥3.1.0                              |

_Table: AEAD ciphers_

## Message Authentication Codes (MACs)

To be used in [mac/4](`crypto:mac/4`) and
[related functions](new_api.md#macs-message-authentication-codes).

### CMAC

CMAC with the following ciphers are available with OpenSSL 1.0.1 or later if not
disabled by configuration.

To dynamically check availability, check that the name `cmac` is present in the
list returned by [crypto:supports(macs)](`crypto:supports/1`). Also check that
the name in the _Cipher and Mode_ column is present in the list returned by
[crypto:supports(ciphers)](`crypto:supports/1`).

| **Cipher and Mode** | **Key length** **\[bytes]** | **Max Mac Length** **(= default length)** **\[bytes]** |
| ------------------- | --------------------------- | ------------------------------------------------------ |
| `aes_128_cbc`       | 16                          | 16                                                     |
| `aes_192_cbc`       | 24                          | 16                                                     |
| `aes_256_cbc`       | 32                          | 16                                                     |
| `aes_128_ecb`       | 16                          | 16                                                     |
| `aes_192_ecb`       | 24                          | 16                                                     |
| `aes_256_ecb`       | 32                          | 16                                                     |
| `blowfish_cbc`      | 16                          |  8                                                     |
| `blowfish_ecb`      | 16                          |  8                                                     |
| `des_cbc`           |  8                          |  8                                                     |
| `des_ecb`           |  8                          |  8                                                     |
| `des_ede3_cbc`      | 24                          |  8                                                     |
| `rc2_cbc`           | 16                          |  8                                                     |

_Table: CMAC cipher key lengths_

### HMAC

Available in all OpenSSL compatible with Erlang CRYPTO if not disabled by
configuration.

To dynamically check availability, check that the name `hmac` is present in the
list returned by [crypto:supports(macs)](`crypto:supports/1`) and that the hash
name is present in the list returned by
[crypto:supports(hashs)](`crypto:supports/1`).

| **Hash**    | **Max Mac Length** **(= default length)** **\[bytes]** |
| ----------- | ------------------------------------------------------ |
| `sha`       | 20                                                     |
| `sha224`    | 28                                                     |
| `sha256`    | 32                                                     |
| `sha384`    | 48                                                     |
| `sha512`    | 64                                                     |
| `sha512_224`| 28                                                     |
| `sha512_256`| 32                                                     |
| `sha3_224`  | 28                                                     |
| `sha3_256`  | 32                                                     |
| `sha3_384`  | 48                                                     |
| `sha3_512`  | 64                                                     |
| `shake128`  | 64                                                     |
| `shake256`  | 64                                                     |
| `blake2b`   | 64                                                     |
| `blake2s`   | 32                                                     |
| `md4`       | 16                                                     |
| `md5`       | 16                                                     |
| `ripemd160` | 20                                                     |

_Table: HMAC output sizes_

### POLY1305

POLY1305 is available with OpenSSL 1.1.1 or later if not disabled by
configuration.

To dynamically check availability, check that the name `poly1305` is present in
the list returned by [crypto:supports(macs)](`crypto:supports/1`).

The poly1305 mac wants an 32 bytes key and produces a 16 byte MAC by default.

### SIPHASH

SipHash is available with OpenSSL 3.0 or later if not disabled by configuration.

To dynamically check availability, check that the name `siphash` is present in
the list returned by [crypto:supports(macs)](`crypto:supports/1`).

SipHash wants a 16 bytes key. It is configured through the `SubType` argument of
[`crypto:mac/4`](`crypto:mac/4`), [`crypto:macN/5`](`crypto:macN/5`) and
[`crypto:mac_init/3`](`crypto:mac_init/3`), which for `siphash` is a
[`t:crypto:siphash_options/0`](`t:crypto:siphash_options/0`) map with any of the
optional keys:

| Key | Meaning | Values | Default |
|------------|--------------------------------|-----------|---------|
| `size` | output size in bytes | `8` or `16` | `16` |
| `c_rounds` | SipHash compression rounds | `1`..`16` | `2` |
| `d_rounds` | SipHash finalization rounds | `1`..`16` | `4` |

The defaults correspond to SipHash-2-4 with a 16 byte output, matching the
cryptolib defaults. The round counts are capped at `16` (well above the
strongest standard variant, SipHash-4-8) so that a single call cannot
monopolise a scheduler. Omitting the `SubType` (for example
[`crypto:mac/3`](`crypto:mac/3`)) or passing `undefined` or `#{}` selects those
defaults; any subset of the keys overrides individual parameters, so for example
`#{size => 8}` selects the classic 64-bit SipHash-2-4 and `#{c_rounds => 1,
d_rounds => 3}` selects SipHash-1-3.

Note that the 8 and 16 byte outputs are _not_ truncations of one another; they
differ in finalization, so the output size must be chosen explicitly through the
`size` option.

## Hash

To dynamically check availability, check that the wanted name in the _Names_
column is present in the list returned by
[crypto:supports(hashs)](`crypto:supports/1`).

| **Type** | **Names**                                                  | **Limited to** **OpenSSL versions** |
| -------- | ---------------------------------------------------------- | ----------------------------------- |
| SHA1     | sha                                                        |                                     |
| SHA2     | sha224, sha256, sha384, sha512, sha512_224, sha512_256     |                                     |
| SHA3     | sha3_224, sha3_256, sha3_384, sha3_512, shake128, shake256 | ≥1.1.1                              |
| SM3      | sm3                                                        | ≥1.1.1                              |
| MD4      | md4                                                        |                                     |
| MD5      | md5                                                        |                                     |
| RIPEMD   | ripemd160                                                  |                                     |

## Key Derivation Functions

To be used in [kdf/4](`crypto:kdf/4`), which documents the full set of options
accepted by each function.

To dynamically check availability, check that the wanted name in the _KDF_
column is present in the list returned by
[crypto:supports(kdfs)](`crypto:supports/1`).

| **KDF**                          | **Standard**    | **Required options**                          | **Limited to** **OpenSSL versions** |
| -------------------------------- | --------------- | --------------------------------------------- | ----------------------------------- |
| `argon2id`, `argon2i`, `argon2d` | RFC 9106        | `salt`, `memory`, `iterations`, `parallelism` | ≥3.2                                |
| `hkdf`                           | RFC 5869        | `digest`                                      | ≥3.0                                |
| `pbkdf2`                         | RFC 8018        | `digest`, `salt`, `iterations`                | ≥3.0                                |
| `scrypt`                         | RFC 7914        | `salt`, `n`, `r`, `p`                         | ≥3.0                                |
| `sskdf`                          | NIST SP 800-56C | `digest`                                      | ≥3.0                                |

_Table: Key derivation functions_

## Public Key Cryptography

### RSA

RSA is available with all OpenSSL versions compatible with Erlang CRYPTO if not
disabled by configuration. To dynamically check availability, check that the
atom `rsa` is present in the list returned by
[crypto:supports(public_keys)](`crypto:supports/1`).

> #### Warning {: .warning }
>
> The RSA options are experimental.
>
> The exact set of options and there syntax _may_ be changed without prior
> notice.

| Option                                 | sign/verify | public encrypt      | private encrypt     |
| -------------------------------------- | ----------- | ------------------- | ------------------- |
|                                        |             | **private decrypt** | **public decrypt**  |
| \{rsa_padding,rsa_x931_padding\}       | x           |                     | x                   |
|                                        |             |                     |                     |
| \{rsa_padding,rsa_pkcs1_padding\}      | x           | x                   | x                   |
|                                        |             |                     |                     |
| \{rsa_padding,rsa_pkcs1_pss_padding\}  | x (2)       |                     |                     |
| \{rsa_pss_saltlen, -2..\}              | x (2)       |                     |                     |
| \{rsa_mgf1_md, atom()\}                | x (2)       |                     |                     |
|                                        |             |                     |                     |
| \{rsa_padding,rsa_pkcs1_oaep_padding\} |             | x (2)               |                     |
| \{rsa_mgf1_md, atom()\}                |             | x (2)               |                     |
| \{rsa_oaep_label, binary()\}\}         |             | x (3)               |                     |
| \{rsa_oaep_md, atom()\}                |             | x (3)               |                     |
|                                        |             |                     |                     |
| \{rsa_padding,rsa_no_padding\}         | x (1)       |                     |                     |

Notes:

1. OpenSSL ≤ 1.0.0
1. OpenSSL ≥ 1.0.1
1. OpenSSL ≥ 1.1.0

### DSS

DSS is available with OpenSSL versions compatible with Erlang CRYPTO if not
disabled by configuration. To dynamically check availability, check that the
atom `dss` is present in the list returned by
[crypto:supports(public_keys)](`crypto:supports/1`).

### ECDSA

ECDSA is available with OpenSSL 0.9.8o or later if not disabled by
configuration. To dynamically check availability, check that the atom `ecdsa` is
present in the list returned by
[crypto:supports(public_keys)](`crypto:supports/1`). If the atom `ec_gf2m` also
is present, the characteristic two field curves are available.

The actual supported named curves could be checked by examining the list
returned by [crypto:supports(curves)](`crypto:supports/1`).

### EdDSA

EdDSA is available with OpenSSL 1.1.1 or later if not disabled by configuration.
To dynamically check availability, check that the atom `eddsa` is present in the
list returned by [crypto:supports(public_keys)](`crypto:supports/1`).

Support for the curves ed25519 and ed448 is implemented. The actual supported
named curves could be checked by examining the list with the list returned by
[crypto:supports(curves)](`crypto:supports/1`).

### Diffie-Hellman

Diffie-Hellman computations are available with OpenSSL versions compatible with
Erlang CRYPTO if not disabled by configuration. To dynamically check
availability, check that the atom `dh` is present in the list returned by
[crypto:supports(public_keys)](`crypto:supports/1`).

### Elliptic Curve Diffie-Hellman

Elliptic Curve Diffie-Hellman is available with OpenSSL 0.9.8o or later if not
disabled by configuration. To dynamically check availability, check that the
atom `ecdh` is present in the list returned by
[crypto:supports(public_keys)](`crypto:supports/1`).

The Edward curves `x25519` and `x448` are supported with OpenSSL 1.1.1 or later
if not disabled by configuration.

The actual supported named curves could be checked by examining the list
returned by [crypto:supports(curves)](`crypto:supports/1`).