# Botan

# Public Key Cryptography

Public key cryptography is a collection of techniques allowing for encryption, signatures, and key agreement.

## Key Objects

Public and private keys are represented by classes `Public_Key` and `Private_Key`. Both derive from `Asymmetric_Key`.

Currently there is an inheritance relationship between `Private_Key` and `Public_Key`, so that a private key can also be used as the corresponding public key. It is best to avoid relying on this, as this inheritance will be removed in a future major release.

class Asymmetric_Key
  std::string algo_name()

    Return a short string identifying the algorithm of this key, eg “RSA” or “ML-DSA”.

  size_t estimated_strength() const

    Return an estimate of the strength of this key, in terms of brute force key search. For example if this function returns 128, then it is is estimated to be roughly as difficult to crack as AES-128.

  OID object_identifier() const

    Return an object identifier which can be used to identify this type of key.

  bool supports_operation(PublicKeyOperation op) const

    Check if this key could be used for the queried operation type.

class Public_Key
  size_t key_length() const = 0;

    Return an integer value that most accurately captures for the security level of the key. For example for RSA this returns the length of the public modules, while for ECDSA keys it returns the size of the elliptic curve group.

  bool check_key(RandomNumberGenerator &rng, bool strong) const = 0;

    Check if the key seems to be valid. If strong is set to true then more expensive tests are performed.

  AlgorithmIdentifier algorithm_identifier() const = 0;

    Return an X.509 algorithm identifier that can be used to identify the key.

  std::vector<uint8_t> public_key_bits() const = 0;

    Returns a binary representation of the public key. Typically this is a BER encoded structure that includes metadata like the algorithm and parameter set used to generate the key.

    Note that pre-standard post-quantum algorithms of the NIST competition (e.g. Kyber, Dilithium, FrodoKEM, etc) do not have a standardized BER encoding, yet. For the time being, the raw public key bits are returned for these algorithms. That might change as the standards evolve.

  std::vector<uint8_t> raw_public_key_bits() const = 0;

    Returns a binary representation of the public key’s canonical structure. Typically, this does not include any metadata like an algorithm identifier or parameter set. Note that some schemes (e.g. RSA) do not know such “raw” canonical structure and therefore throw Not_Implemented. For key agreement algorithms, this is the canonical public value of the scheme.

    Decoding the resulting raw bytes typically requires knowledge of the algorithm and parameters used to generate the key.

  std::vector<uint8_t> subject_public_key() const;

    Return the X.509 `SubjectPublicKeyInfo` encoding of this key. See RFC 5280 for details.

  std::string fingerprint_public(const std::string &alg = "SHA-256") const;

    Return a hashed fingerprint of this public key.

class Private_Key
  std::unique_ptr<Public_Key> public_key() const

    Return an object containing the public key corresponding to this private key.

    Prefer this over the (deprecated) implicit conversion of a private key to a public key currently possible due to an inheritance relation.

  secure_vector<uint8_t> private_key_info() const

    Return the key encoded as a PKCS #8 PrivateKeyInfo structure. See RFC 5208 for details.

    Further functions relating to encoding and encrypting PKCS #8 private are detailed in Serializing Private Keys Using PKCS #8.

  secure_vector<uint8_t> private_key_bits() const

    Return the serialization of the private key, corresponding to the PrivateKey field of a PKCS #8 PrivateKeyInfo structure. See RFC 5208 for details.

  bool stateful_operation() const;

    Returns true if this keys operation is stateful, that is if updating the key is required after each private operation. Currently the only stateful schemes included are XMSS and LMS.

  std::optional<uint64_t> remaining_operations() const

    If this algorithm is stateful, returns the number of private operations remaining before this key is exhausted. Returns nullopt if the key is not stateful.

## Public Key Algorithms

Botan includes a number of public key algorithms, some of which are in common use, others only used in specialized or niche applications.

### RSA

Based on the difficulty of factoring. Usable for encryption, signatures, and key encapsulation.

### ECDSA

Fast signature scheme based on elliptic curves.

### ECDH, DH, X25519 and X448

Key agreement schemes. DH uses arithmetic over finite fields and is slower and with larger keys. ECDH, X25519 and X448 use elliptic curves instead.

### ML-DSA (FIPS 204)

Post-quantum secure signature scheme based on (structured) lattices. This algorithm is standardized in FIPS 204. Signing keys are always stored and expanded from the 32-byte private random seed (xi), loading the expanded key format specified in FIPS 204 is explicitly not supported.

Support for ML-DSA is implemented in the module `ml_dsa`

Additionally, support for the pre-standardized version “Dilithium” is retained for the time being. The implemented specification is commonly referred to as version 3.1 of the CRYSTALS-Dilithium submission to NIST’s third round of the PQC competition. This is not compatible to the “Initial Public Draft” version of FIPS 204 for which Botan does not offer an implementation.

Currently two flavors of Dilithium are implemented in separate Botan modules:

> - `dilithium`, that uses Keccak (SHAKE), and that saw some public usage by early adopters.

> - `dilithium_aes`, that uses AES instead of Keccak-based primitives. This mode is deprecated and will be removed in a future release.

### ML-KEM (FIPS 203)

Post-quantum key encapsulation scheme based on (structured) lattices. This algorithm is standardized in FIPS 203. New decapsulation keys are stored and expanded from the 64-byte private random seeds (`d || z`). Keys imported as seeds are always serialized as seeds, while keys imported in expanded format (as specified in FIPS 203) are serialized in expanded format. Exporting seeds as expanded keys is supported using ML-KEM private key-specific methods.

Support for ML-KEM is implemented in the module `ml_kem`.

Additionally, support for the pre-standardized version “Kyber” is retained for the time being. The implemented specification is commonly referred to as version 3.01 of the CRYSTALS-Kyber submission to NIST’s third round of the PQC competition. This is not compatible to the “Initial Public Draft” version of FIPS 203 for which Botan does not offer an implementation.

Currently two flavors of Kyber are implemented in separate Botan modules:

> - `kyber`, that uses Keccak (SHAKE and SHA-3), and that saw some public usage by early adopters.

> - `kyber_90s`, that uses AES/SHA-2 instead of Keccak-based primitives. This mode is deprecated and will be removed in a future release.

### Ed25519 and Ed448

Signature schemes based on a specific elliptic curve.

### XMSS

A post-quantum secure signature scheme whose security is based (only) on the security of a hash function. Unfortunately XMSS is stateful, meaning the private key changes with each signature, and only a certain pre-specified number of signatures can be created. If the same state is ever used to generate two signatures, then the whole scheme becomes insecure, and signatures can be forged.

> Warning

> Maintaining consistent state without replays is extremely difficult, especially when multiple machines are involved. Even a single error will compromise the entire signature scheme. XMSS should only be used in an environment carefully designed to maintain consistent state. Prefer the stateless SLH-DSA in new designs.

### HSS-LMS

A post-quantum secure hash-based signature scheme similar to XMSS. Contains support for multitrees. It is stateful, meaning the private key changes after each signature. If the same state is ever used to generate two signatures, then the whole scheme becomes insecure, and signatures can be forged.

> Warning

> Maintaining consistent state without replays is extremely difficult, especially when multiple machines are involved. Even a single error will compromise the entire signature scheme. HSS-LMS should only be used in an environment carefully designed to maintain consistent state. Prefer the stateless SLH-DSA in new designs.

### SLH-DSA (FIPS 205)

The Stateless Hash-Based Digital Signature Standard (SLH-DSA) is the FIPS 205 post-quantum secure signature scheme whose security is solely based on the security of a hash function. Unlike XMSS, it is a stateless signature scheme, meaning that the private key does not change with each signature. It has high security but very long signatures and high runtime.

Support for SLH-DSA is implemented in the modules `slh_dsa_sha2` and `slh_dsa_shake`.

Additionally, support for the pre-standardized version “SPHINCS+” is retained for the time being. The implemented specification is commonly referred to as version 3.1 of the SPHINCS+ submission to NIST’s third round of the PQC competition. This is not compatible with the “Initial Public Draft” version of FIPS 205 for which Botan does not offer an implementation. Also, Botan does not support the Haraka hash function.

Currently, two flavors of SPHINCS+ are implemented in separate Botan modules:

> - `sphincsplus_shake`, that uses Keccak (SHAKE) hash functions

> - `sphincsplus_sha2`, that uses SHA-256

### FrodoKEM

A post-quantum secure key encapsulation scheme based on (unstructured) lattices.

### McEliece

Deprecated since version 3.0.0.

Post-quantum secure key encapsulation scheme based on the hardness of certain decoding problems. Deprecated; use Classic McEliece

### Classic McEliece

Post-quantum secure, code-based key encapsulation scheme.

### ElGamal

Encryption scheme based on the discrete logarithm problem. Generally unused except in PGP.

### DSA

Deprecated since version 3.7.0.

Finite field based signature scheme. A NIST standard but now quite obsolete.

### ECGDSA, ECKCDSA, SM2, GOST-34.10

A set of signature schemes based on elliptic curves. All are national standards in their respective countries (Germany, South Korea, China, and Russia, resp), and are completely obscure and unused outside of that context.

GOST-34.10 support is deprecated.

## Creating New Private Keys

Creating a new private key requires two things: a source of random numbers (see Random Number Generators) and potentially some algorithm specific parameters.

### Generic Method

There is a generic method which can create keys of any algorithm type, defined in `pk_algs.h`

std::unique_ptr<Private_Key> create_private_key(std::string_view algo, RandomNumberGenerator &rng, std::string_view params)

  Examples of algorithm/parameter pairs that can be provided here:

  - “RSA” / “3072”

  - “ECDSA” / “secp256r1”

  - “Ed5519” / “”

  - “ML-KEM” / “ML-KEM-768”

  - “DH” / “modp/ietf/2048”

  If params is left empty then a suitable algorithm-specific default will be chosen. This default may change from release to release, but generally tries to reflect a conservative setting.

### Creating A New RSA Private Key

RSA_PrivateKey::RSA_PrivateKey(RandomNumberGenerator &rng, size_t bits)

  A constructor that creates a new random RSA private key with a modulus of length bits.

  RSA key generation is relatively slow, and can take an unpredictable amount of time. Generating a 2048 bit RSA key might take 5 to 10 seconds on a slow machine like a Raspberry Pi 2. Even on a fast desktop it might take up to half a second. In a GUI blocking for that long can be a problem. The usual approach is to perform key generation in a new thread, with a animated modal UI element so the user knows the application is still alive. If you wish to provide a progress estimate things get a bit complicated but some library users documented their approach in a blog post.

### Creating A New EC Private Key

For a few schemes, the curve and signature scheme come as a package, and there are no extra parameters:

Ed25519_PrivateKey::Ed25519_PrivateKey(RandomNumberGenerator &rng)

  Generate a new Ed25519 private key

Ed448_PrivateKey::Ed448_PrivateKey(RandomNumberGenerator &rng)

  Generate a new Ed448 private key

X25519_PrivateKey::X25519_PrivateKey(RandomNumberGenerator &rng)

  Generate a new X25519 private key

X448_PrivateKey::X448_PrivateKey(RandomNumberGenerator &rng)

  Generate a new X448 private key

Others require additionally specifying which curve to use. First create a relevant `EC_Group` using for example `EC_Group::from_name` or `EC_Group::from_OID`. Then pass it to the private key constructor. If the choice of group is not otherwise mandated by your application, use “secp256r1” (aka P-256) or “secp384r1” (aka P-384) as they are fastest, widely implemented, and considered secure.

ECDH_PrivateKey::ECDH_PrivateKey(RandomNumberGenerator &rng, const EC_Group &group)

  Generate a new ECDH private key

ECDSA_PrivateKey::ECDSA_PrivateKey(RandomNumberGenerator &rng, const EC_Group &group)

  Generate a new ECDSA private key

ECKCDSA_PrivateKey::ECKCDSA_PrivateKey(RandomNumberGenerator &rng, const EC_Group &group)

  Generate a new ECKCDSA private key

ECGDSA_PrivateKey::ECGDSA_PrivateKey(RandomNumberGenerator &rng, const EC_Group &group)

  Generate a new ECGDSA private key

GOST_3410_PrivateKey::GOST_3410_PrivateKey(RandomNumberGenerator &rng, const EC_Group &group)

  Generate a new GOST-34.10 private key

SM2_PrivateKey::SM2_PrivateKey(RandomNumberGenerator &rng, const EC_Group &group)

  Generate a new SM2 private key

### Creating A New Finite Field DL Private Key

Instead of elliptic curves, some older algorithms are based on the security of discrete logarithms in the group of integers modulo a prime. For security, these require much larger keys than elliptic curve schemes, and are typically much slower.

Warning

Avoid such algorithms in new code

DH_PrivateKey::DH_PrivateKey(RandomNumberGenerator &rng, const DL_Group &group)

  Create a new Diffie-Hellman private key. In most protocols that still support finite field DH, it is used with a set of pre-created and trusted groups. These were specified in RFC 3526 and are usually called the IETF MODP groups.

  The MODP groups are built into the library and can be accessed by name for example `DL_Group::from_name("modp/ietf/3072")`, where 3072 refers to the number of bits in the prime modulus.

DSA_PrivateKey::DSA_PrivateKey(RandomNumberGenerator &rng, const DL_Group &group)

  Create a new DSA private key. DSA requires groups of a special form. The best way to create such a group is to create a new `DL_Group` at random for each key, using the “DSA kosherizer” algorithm. See DL_Group for more information.

ElGamal_PrivateKey::ElGamal_PrivateKey(RandomNumberGenerator &rng, const DL_Group &group)

## Serializing Private Keys Using PKCS #8

The standard format for serializing a private key is PKCS #8, the operations for which are defined in `pkcs8.h`. It supports both unencrypted and encrypted storage.

secure_vector<uint8_t> PKCS8::BER_encode(const Private_Key &key, RandomNumberGenerator &rng, const std::string &password, const std::string &pbe_algo = "")

  Takes any private key object, serializes it, encrypts it using password, and returns a binary structure representing the private key.

  The final (optional) argument, pbe_algo, specifies a particular password based encryption (or PBE) algorithm. If you don’t specify a PBE, a sensible default will be used.

  The currently supported PBE is PBES2 from PKCS5. Format is as follows: `PBE-PKCS5v20(CIPHER,PBKDF)` or `PBES2(CIPHER,PBKDF)`.

  Cipher can be any block cipher using CBC or GCM modes, for example “AES-128/CBC” or “Camellia-256/GCM”. For best interop with other systems, use AES in CBC mode. The PBKDF can be either the name of a hash function (in which case PBKDF2 is used with that hash) or “Scrypt”, which causes the scrypt memory hard password hashing function to be used. Scrypt is supported since version 2.7.0.

  Use PBE-PKCS5v20(AES-256/CBC,SHA-256) if you want to ensure the keys can be imported by different software packages. Use PBE-PKCS5v20(AES-256/GCM,Scrypt) for best security assuming you do not care about interop.

  For ciphers you can use anything which has an OID defined for CBC, GCM or SIV modes. Currently this includes AES, Camellia, Serpent, Twofish, and SM4. Most other libraries only support CBC mode for private key encryption. GCM has been supported in PBES2 since 2.0. SIV has been supported since 2.8.

std::string PKCS8::PEM_encode(const Private_Key &key, RandomNumberGenerator &rng, const std::string &pass, const std::string &pbe_algo = "")

  This formats the key in the same manner as `BER_encode`, but additionally encodes it into a text format with identifying headers. Using PEM encoding is highly recommended for many reasons, including compatibility with other software, for transmission over 8-bit unclean channels, because it can be identified by a human without special tools, and because it sometimes allows more sane behavior of tools that process the data.

Unencrypted serialization is also supported.

Warning

In most situations, using unencrypted private key storage is a bad idea, because anyone can come along and grab the private key without having to know any passwords or other secrets. Unless you have very particular security requirements, always use the versions that encrypt the key based on a passphrase, described above.

secure_vector<uint8_t> PKCS8::BER_encode(const Private_Key &key)

  Serializes the private key and returns the result.

std::string PKCS8::PEM_encode(const Private_Key &key)

  Serializes the private key, base64 encodes it, and returns the result.

Last but not least, there are some functions that will load (and decrypt, if necessary) a PKCS #8 private key:

std::unique_ptr<Private_Key> load_key(DataSource &source, std::function<std::string()> get_passphrase)

std::unique_ptr<Private_Key> load_key(DataSource &source, const std::string &pass)

std::unique_ptr<Private_Key> load_key(DataSource &source)

These functions will return an object allocated key object based on the data from whatever source it is using (assuming, of course, the source is in fact storing a representation of a private key, and the decryption was successful). The encoding used (PEM or BER) need not be specified; the format will be detected automatically. The `DataSource` is usually a `DataSource_Stream` to read from a file or `DataSource_Memory` for an in-memory buffer.

The versions taking a `std::string` attempt to decrypt using the password given (if the key is encrypted; if it is not, the passphase value will be ignored). If the passphrase does not decrypt the key, an exception will be thrown.

## Serializing Public Keys

To import and export public keys, use:

std::vector<uint8_t> X509::BER_encode(const Public_Key &key)

std::string X509::PEM_encode(const Public_Key &key)

std::unique_ptr<Public_Key> X509::load_key(DataSource &in)

std::unique_ptr<Public_Key> X509::load_key(const secure_vector<uint8_t> &buffer)

std::unique_ptr<Public_Key> X509::load_key(const std::string &filename)

  These functions operate in the same way as the ones described in Serializing Private Keys Using PKCS #8, except that no encryption option is available.

Note

In versions prior to 3.0, these functions returned a raw pointer instead of a `unique_ptr`.

## DL_Group

class DL_Group

  Represents parameters for finite field discrete logarithm algorithms

static DL_Group DL_Group::from_name(std::string_view name)

  The name here is a (Botan specific) identifier which maps to one of the standard discrete logarithm groups.

  For the groups from RFC 5208 (often called the MODP groups, the IETF groups, or the IPsec groups) use “modp/ietf/N” where N can be any of 1024, 1536, 2048, 3072, 4096, 6144, or 8192. This group type is used for Diffie-Hellman and ElGamal algorithms, but cannot be used with DSA.

  For the groups from RFC 7919 (often called the TLS FFDHE groups) use “ffdhe/ietf/N” where N is any of 2048, 3072, 4096, 6144, or 8192. These groups are typically only used in TLS, but can be used with Diffie-Hellman more generally. They cannot be used with DSA.

  For the groups from RFC 5054 (the SRP6 groups) use “modp/srp/N” where N can be any of 1024, 1536, 2048, 3072, 4096, 6144, or 8192. These groups should only be used with SRP6.

  Finally a small number of pre-created groups usable for DSA are available. These are “dsa/jce/1024”, “dsa/botan/2048”, and “dsa/botan/3072”. Support for these groups is deprecated and they will be removed in a future major release. Should DSA be required, create a new random group for each key.

You can generate a new random group using

DL_Group::DL_Group(RandomNumberGenerator &rng, PrimeType type, size_t pbits, size_t qbits = 0)

  The type can be

  - `Strong`: A group where (p-1)/2 is also prime. Best for Diffie-Hellman, but very slow to generate.

  - `Prime_Subgroup`: A group where (p-1) is divided by a large prime q, of size `qbits`. Faster to generate than `Strong`, suitable for Diffie-Hellman.

  - `DSA_Kosherizer`: Generate a group suitable for DSA using the algorithm specified in FIPS 186-3.

  If qbits is set to zero then a suitable value is chosen relative to the value of pbits and the type of group being created.

You can serialize a `DL_Group` using

std::vector<uint8_t> DL_Group::DER_Encode(Format format) const

or

std::string DL_Group::PEM_encode(Format format) const

where format is any of

- `ANSI_X9_42` (or `DH_PARAMETERS`) for modp groups

- `ANSI_X9_57` (or `DSA_PARAMETERS`) for DSA-style groups

- `PKCS_3` is an older format for modp groups; it should only be used for backwards compatibility.

You can reload a serialized group from BER or PEM formats using

DL_Group::DL_Group(std::span<const uint8_t> ber, DL_Group_Format format)

static DL_Group DL_Group::from_pem(std::string_view pem, DL_Group_Format format)

### Code Example: DL_Group

The example below creates a new 2048 bit `DL_Group`, prints the generated parameters and ANSI_X9_42 encodes the created group for further usage with DH.

    #include <botan/auto_rng.h>
    #include <botan/dl_group.h>
    #include <botan/rng.h>

    #include <iostream>

    int main() {
       Botan::AutoSeeded_RNG rng;
       auto group = std::make_unique<Botan::DL_Group>(rng, Botan::DL_Group::Strong, 2048);

       std::cout << "P = " << group->get_p().to_hex_string() << "\n"
                 << "Q = " << group->get_q().to_hex_string() << "\n"
                 << "G = " << group->get_g().to_hex_string() << "\n";

       std::cout << "\nPEM:\n" << group->PEM_encode(Botan::DL_Group_Format::ANSI_X9_42) << "\n";

       return 0;
    }

## Key Checking

Most public key algorithms have limitations or restrictions on their parameters. For example RSA requires an odd exponent, and algorithms based on the discrete logarithm problem need a generator > 1.

Each public key type has a function

bool Public_Key::check_key(RandomNumberGenerator &rng, bool strong)

  This function performs a number of algorithm-specific tests that the key seems to be mathematically valid and consistent, and returns true if all of the tests pass.

  It does not have anything to do with the validity of the key for any particular use, nor does it have anything to do with certificates that link a key (which, after all, is just some numbers) with a user or other entity. If strong is `true`, then it does “strong” checking, which includes expensive operations like primality checking.

As key checks are not automatically performed they must be called manually after loading keys from untrusted sources. If a key from an untrusted source is not checked, the implementation might be vulnerable to algorithm specific attacks.

The following example loads the Subject Public Key from the x509 certificate `cert.pem` and checks the loaded key. If the key check fails a respective error is thrown.

    #include <botan/auto_rng.h>
    #include <botan/pk_keys.h>
    #include <botan/rng.h>
    #include <botan/x509cert.h>
    #include <iostream>

    int main() {
       const Botan::X509_Certificate cert("cert.pem");
       Botan::AutoSeeded_RNG rng;
       auto key = cert.subject_public_key();
       if(!key->check_key(rng, false)) {
          std::cerr << "Loaded key is invalid";
          return 1;
       }

       return 0;
    }

## Public Key Encryption/Decryption

Safe public key encryption requires the use of a padding scheme which hides the underlying mathematical properties of the algorithm. Additionally, they will add randomness, so encrypting the same plaintext twice produces two different ciphertexts.

The primary interface for encryption is

class PK_Encryptor
  std::vector<uint8_t> encrypt(const uint8_t in[], size_t length, RandomNumberGenerator &rng) const
  std::vector<uint8_t> encrypt(std::span<const uint8_t> in, RandomNumberGenerator &rng) const

    These encrypt a message, returning the ciphertext.

  size_t maximum_input_size() const

    Returns the maximum size of the message that can be processed, in bytes. If you call `PK_Encryptor::encrypt` with a value larger than this the operation will fail with an exception.

  size_t ciphertext_length(size_t ctext_len) const

    Return an upper bound on the returned size of a ciphertext, if this particular key/padding scheme is used to encrypt a message of the provided length.

`PK_Encryptor` is only an interface - to actually encrypt you have to create an implementation, of which there are currently three available in the library, `PK_Encryptor_EME`, `DLIES_Encryptor` and `ECIES_Encryptor`. DLIES is a hybrid encryption scheme (from IEEE 1363) that uses Diffie-Hellman key agreement technique in combination with a KDF, a MAC and a symmetric encryption algorithm to perform message encryption. ECIES is similar to DLIES, but uses ECDH for the key agreement. Normally, public key encryption is done using algorithms which support it directly, such as RSA or ElGamal; these use the EME class:

class PK_Encryptor_EME
  PK_Encryptor_EME(const Public_Key &key, std::string padding)

    With key being the key you want to encrypt messages to. The padding method to use is specified in padding.

    If you are not sure what padding to use, use “OAEP(SHA-256)”. If you need compatibility with protocols using the PKCS #1 v1.5 standard, you can also use “PKCS1v15”.

    For SM2 encryption, the padding string specifies which hash function to use; normally this would be “SM3”.

class DLIES_Encryptor

  Deprecated since version 2.13.0: DLIES should no longer be used

  Available in the header `dlies.h`

  DLIES_Encryptor(const DH_PrivateKey &own_priv_key, RandomNumberGenerator &rng, std::unique_ptr<KDF> kdf, std::unique_ptr<MessageAuthenticationCode> mac, size_t mac_key_len = 20)

    Where kdf is a key derivation function (see Key Derivation Functions (KDF)) and mac is a MessageAuthenticationCode. The encryption is performed by XORing the message with a stream of bytes provided by the KDF.

  DLIES_Encryptor(const DH_PrivateKey &own_priv_key, RandomNumberGenerator &rng, std::unique_ptr<KDF> kdf, std::unique_ptr<Cipher_Mode> cipher, size_t cipher_key_len, std::unique_ptr<MessageAuthenticationCode> mac, size_t mac_key_len = 20)

    Instead of XORing the message with KDF output, a cipher mode can be used

class ECIES_Encryptor

  Available in the header `ecies.h`.

  Warning

  ECIES is standardized by various organizations (including IEEE and ISO) but unfortunately has dozens of different options which greatly hinder interoperability. ECDH key exchange with a static receiver key is much simpler, and provides similar security properties.

  Parameters for encryption and decryption are set by the `ECIES_System_Params` class which stores the EC domain parameters, the KDF (see Key Derivation Functions (KDF)), the cipher (see Cipher Modes) and the MAC.

  ECIES_Encryptor(const PK_Key_Agreement_Key &private_key, const ECIES_System_Params &ecies_params, RandomNumberGenerator &rng)

    Where private_key is the key to use for the key agreement. The system parameters are specified in ecies_params and the RNG to use is passed in rng.

  ECIES_Encryptor(RandomNumberGenerator &rng, const ECIES_System_Params &ecies_params)

    Creates an ephemeral private key which is used for the key agreement.

class PK_Decryptor

  Interface for public key decryption.

  secure_vector<uint8_t> decrypt(std::span<const uint8_t> in) const

    Decrypts a message, throwing an exception in the case of failure.

    Warning

    If using PKCS1v1.5 encryption padding this function is not safe since it exposes via a side channel if the decryption succeeded or not. This side channel is sufficient for an attacker to decrypt arbitrary messages and forge arbitrary signatures. Use `PK_Decryptor::decrypt_or_random` to avoid this situation.

  secure_vector<uint8_t> decrypt_or_random(const uint8_t in[], size_t length, size_t expected_pt_len, RandomNumberGenerator &rng) const

    Similar to decrypt except that if the decryption fails, or if the decrypted key is not of the expected length, then it returns a random string of the expected length. This hides the PKCS1v1.5 oracle.

  secure_vector<uint8_t> decrypt_or_random(const uint8_t in[], size_t length, size_t expected_pt_len, RandomNumberGenerator &rng, const uint8_t required_content_bytes[], const uint8_t required_content_offsets[], size_t required_contents) const

    Similar to decrypt except that if the decryption fails, or if the decrypted key is not of the expected length, then it returns a random string of the expected length. This hides the PKCS1v1.5 oracle.

    This variant of the function is used if there are specific bytes within the message which must take on a certain value, rather than the encrypted “message” just being a random key, which is the more typical usage. If any of the required values are incorrect, then again a randomly generated key is returned to hide the PKCS1v1.5 oracle.

Botan implements the following encryption algorithms:

1. RSA. Requires a padding scheme as parameter.

2. DLIES (deprecated)

3. ECIES

4. SM2. Takes an optional `HashFunction` as parameter which defaults to SM3.

5. ElGamal. Requires a padding scheme as parameter.

### Code Example: RSA Encryption

The following code sample reads a PKCS #8 keypair from the passed location and subsequently encrypts a fixed plaintext with the included public key, using OAEP with SHA-256. For the sake of completeness, the ciphertext is then decrypted using the private key.

    #include <botan/auto_rng.h>
    #include <botan/hex.h>
    #include <botan/pk_keys.h>
    #include <botan/pkcs8.h>
    #include <botan/pubkey.h>
    #include <botan/rng.h>

    #include <iostream>

    int main(int argc, char* argv[]) {
       if(argc != 2) {
          return 1;
       }
       const std::string_view plaintext(
          "Your great-grandfather gave this watch to your granddad for good luck. "
          "Unfortunately, Dane's luck wasn't as good as his old man's.");
       const Botan::secure_vector<uint8_t> pt(plaintext.data(), plaintext.data() + plaintext.length());
       Botan::AutoSeeded_RNG rng;

       // load keypair
       Botan::DataSource_Stream in(argv[1]);
       auto kp = Botan::PKCS8::load_key(in);

       // encrypt with pk
       const Botan::PK_Encryptor_EME enc(*kp, rng, "OAEP(SHA-256)");
       const auto ct = enc.encrypt(pt, rng);

       // decrypt with sk
       const Botan::PK_Decryptor_EME dec(*kp, rng, "OAEP(SHA-256)");
       const auto pt2 = dec.decrypt(ct);

       std::cout << "\nenc: " << Botan::hex_encode(ct) << "\ndec: " << Botan::hex_encode(pt2);

       return 0;
    }

### Available encryption padding schemes

Note

Padding schemes in the context of encryption are sometimes also called Encoding Method for Encryption (EME).

#### OAEP

OAEP (called EME1 in IEEE 1363 and in earlier versions of the library) as specified in PKCS#1 v2.0 (RFC 2437) or PKCS#1 v2.1 (RFC 3447).

- Name: `OAEP`,

- Deprecated aliases: `EME-OAEP`, `EME1`

- Parameters specification:

  - `(<HashFunction>)`

  - `(<HashFunction>,MGF1)`

  - `(<HashFunction>,MGF1(<HashFunction>))`

  - `(<HashFunction>,MGF1(<HashFunction>),<optional label>)`

- The only Mask generation function available is MGF1, which is also the default.

- By default the same hash function will be used for the label and MGF1.

- By default the OAEP label is the empty string

- Examples: `OAEP(SHA-256)`, `OAEP(SHA-256,MGF1)`, `OAEP(SHA-256,MGF1(SHA-512))`, `OAEP(SHA-512,MGF1(SHA-512),TCPA)`

#### PKCS #1 v1.5 Type 2 (encryption)

PKCS #1 v1.5 Type 2 (encryption) padding.

Name: `PKCS1v15` Deprecated alias: `EME-PKCS1-v1_5`

Warning

PKCS v1.5 encryption padding is prone to oracle attacks (the Bleichenbacher attack, and the many variations thereof). Avoid it if at all possible. If you must use it, use `PK_Decryptor::decrypt_or_random` function which can hide the decryption failures.

#### Raw EME

Does not change the input during padding. Unpadding will strip leading zero bytes.

Warning

This is extremely unsafe and only necessary in specialized situations. Don’t use this unless you know what you are doing.

Name: `Raw`

## Public Key Signature Schemes

Signature generation is performed using

class PK_Signer
  PK_Signer(const Private_Key &key, const std::string &padding, Signature_Format format = Signature_Format::Standard)

    Constructs a new signer object for the private key key using the hash/padding specified in padding. The key must support signature operations. In the current version of the library, this includes RSA, ECDSA, ML-DSA, ECKCDSA, ECGDSA, SM2, and others.

    Note

    Botan both supports non-deterministic and deterministic (as per RFC 6979) DSA and ECDSA signatures. Either type of signature can be verified by any other (EC)DSA library, regardless of which mode it prefers. If the `rfc6979` module is enabled at build time, deterministic DSA and ECDSA signatures will be created.

    The proper value of padding depends on the algorithm. For many signature schemes including ECDSA and DSA, simply naming a hash function like “SHA-256” is all that is required.

    For RSA, more complicated padding is required. The two most common schemes for RSA signature padding are PSS and PKCS1v1.5, so you must specify both the padding mechanism as well as a hash, for example “PSS(SHA-256)” or “PKCS1v15(SHA-256)”.

    Certain newer signature schemes, especially post-quantum based ones, hardcode the hash function associated with their signatures, and no configuration is possible. In this case padding should be left blank, or may possibly be used to identify some algorithm-specific option. For instance ML-DSA may be parameterized with “Randomized” or “Deterministic” to choose if the generated signature is randomized or not. If left blank, a default is chosen.

    Another available option, usable in certain specialized scenarios, is using padding scheme “Raw”, where the provided input is treated as if it was already hashed, and directly signed with no other processing.

    The format defaults to `Standard` which is either the usual, or the only, available formatting method, depending on the algorithm. For certain signature schemes including ECDSA, DSA, ECGDSA and ECKCDSA you can also use `DerSequence`, which will format the signature as an ASN.1 SEQUENCE value. This formatting is used in protocols such as TLS and Bitcoin.

  void update(const uint8_t *in, size_t length)
  void update(std::span<const uint8_t> in)
  void update(uint8_t in)

    These add more data to be included in the signature computation. Typically, the input will be provided directly to a hash function.

  std::vector<uint8_t> signature(RandomNumberGenerator &rng)

    Creates the signature and returns it. The rng may or may not be used, depending on the scheme.

  std::vector<uint8_t> sign_message(const uint8_t *in, size_t length, RandomNumberGenerator &rng)
  std::vector<uint8_t> sign_message(std::span<const uint8_t> in, RandomNumberGenerator &rng)

    These functions are equivalent to calling `PK_Signer::update` and then `PK_Signer::signature`. Any data previously provided using `update` will also be included in the signature.

  size_t signature_length() const

    Return an upper bound on the length of the signatures returned by this object.

  AlgorithmIdentifier algorithm_identifier() const

    Return an algorithm identifier appropriate to identify signatures generated by this object in an X.509 structure.

  std::string hash_function() const

    Return the hash function which is being used

Signatures are verified using

class PK_Verifier
  PK_Verifier(const Public_Key &pub_key, const std::string &padding, Signature_Format format = Signature_Format::Standard)

    Construct a new verifier for signatures associated with public key pub_key. The padding and format should be the same as that used by the signer.

  void update(const uint8_t *in, size_t length)
  void update(std::span<const uint8_t> in)
  void update(uint8_t in)

    Add further message data that is purportedly associated with the signature that will be checked.

  bool check_signature(const uint8_t *sig, size_t length)
  bool check_signature(std::span<const uint8_t> sig)

    Check to see if sig is a valid signature for the message data that was written in. Return true if so. This function clears the internal message state, so after this call you can call `PK_Verifier::update` to start verifying another message.

  bool verify_message(const uint8_t *msg, size_t msg_length, const uint8_t *sig, size_t sig_length)
  bool verify_message(std::span<const uint8_t> msg, std::span<const uint8_t> sig)

    These are equivalent to calling `PK_Verifier::update` on msg and then calling `PK_Verifier::check_signature` on sig. Any data previously provided to `PK_Verifier::update` will also be included.

Botan implements the following signature algorithms:

1. RSA. Requires a padding scheme as parameter.

2. DSA. Requires a hash function as parameter.

3. ECDSA. Requires a hash function as parameter.

4. ECGDSA. Requires a hash function as parameter.

5. ECKDSA. Requires a hash function as parameter, not supporting `Raw`.

6. GOST 34.10-2001. Requires a hash function as parameter.

7. Ed25519 and Ed448. See Ed25519 and Ed448 Variants for parameters.

8. SM2. Takes one of the following as parameter:

   - `<user ID>` (uses `SM3`)

   - `<user ID>,<HashFunction>`

9. ML-DSA (Dilithium). Takes the optional parameter `Deterministic` (default) or `Randomized`.

10. SLH-DSA. Takes the optional parameter `Deterministic` (default) or `Randomized`.

11. XMSS. Takes no parameter.

12. HSS-LMS. Takes no parameter.

### Code Example: ECDSA Signature

The following sample program below demonstrates the generation of a new ECDSA keypair over the curve secp512r1 and a ECDSA signature using SHA-256. Subsequently the computed signature is validated.

    #include <botan/auto_rng.h>
    #include <botan/ec_group.h>
    #include <botan/ecdsa.h>
    #include <botan/hex.h>
    #include <botan/pubkey.h>

    #include <iostream>

    int main() {
       Botan::AutoSeeded_RNG rng;
       // Generate ECDSA keypair
       const auto group = Botan::EC_Group::from_name("secp521r1");
       const Botan::ECDSA_PrivateKey key(rng, group);

       const std::string message("This is a tasty burger!");

       // sign data
       Botan::PK_Signer signer(key, rng, "SHA-256");
       signer.update(message);
       std::vector<uint8_t> signature = signer.signature(rng);
       std::cout << "Signature:\n" << Botan::hex_encode(signature);

       // now verify the signature
       Botan::PK_Verifier verifier(key, "SHA-256");
       verifier.update(message);
       std::cout << "\nis " << (verifier.check_signature(signature) ? "valid" : "invalid");
       return 0;
    }

### RSA signature padding schemes

These signature padding mechanisms are specific to RSA; no other public key algorithms included in Botan make use of then. For historical reasons, many different padding schemes have been defined for RSA over the years. The most common are PSS and the (now obsolete) PKCS1v15.

Note

Padding schemes in the context of signatures are sometimes also called Encoding methods for signatures with appendix (EMSA).

#### PKCS #1 v1.5 Type 1 (signature)

PKCS #1 v1.5 Type 1 (signature) padding, aka EMSA3 in IEEE 1363.

Note

While not as actively unsafe as PKCS1v15 encryption padding is, PKCS1 signature padding is considered quite obsolete.

- Name: `PKCS1v15`

- Deprecated aliases: `EMSA_PKCS1`, `EMSA-PKCS1-v1_5`, `EMSA3`

- Parameters specification:

  - `(<HashFunction>)`

  - `(Raw,<optional HashFunction>)`

- The raw variant encodes a precomputed hash, optionally with the digest ID of the given hash.

- Examples: `PKCS1v15(SHA-256)`, `PKCS1v15(Raw)`, `PKCS1v15(Raw,MD5)`,

#### Probabilistic signature scheme (PSS)

Called EMSA4 in IEEE 1363.

- Name: `PSS`

- Deprecated aliases: `EMSA-PSS`, `PSSR`, `PSS-MGF1`, `EMSA4`

- Parameters specification:

  - `(<HashFunction>)`

  - `(<HashFunction>,MGF1,<optional salt size>)`

- Examples: `PSS(SHA-256)`, `PSS(SHA-256,MGF1,32)`,

There also exists a raw version, which accepts a pre-hashed buffer instead of the message. Don’t use this unless you know what you are doing.

- Name: `PSS_Raw`

- Deprecated alias: `PSSR_Raw`

- Parameters specification:

  - `(<HashFunction>)`

  - `(<HashFunction>,MGF1,<optional salt size>)`

#### ISO-9796-2

The ISO-9796-2 padding schemes are used for signatures in the EMV contactless payment card system. There is likely no reason to use it in other contexts.

ISO-9796-2 - Digital signature scheme 2 (probabilistic).

- Name: `ISO_9796_DS2`

- Parameters specification:

  - `(<HashFunction>)`

  - `(<HashFunction>,<exp|imp>,<optional salt size>)`

- Defaults to the explicit mode.

- Examples: `ISO_9796_DS2(RIPEMD-160)`, `ISO_9796_DS2(RIPEMD-160,imp)`

ISO-9796-2 - Digital signature scheme 3 (deterministic), i.e. DS2 without a salt.

- Name: `ISO_9796_DS3`

- Parameters specification:

  - `(<HashFunction>)`

  - `(<HashFunction>,<exp|imp>`

- Defaults to the explicit mode.

- Examples: `ISO_9796_DS3(RIPEMD-160)`, `ISO_9796_DS3(RIPEMD-160,imp)`,

#### X9.31

Padding scheme from ANSI X9.31. Called EMSA2 in IEEE 1363.

Deprecated since version 3.7.0: X9.31 signatures are obsolete, and support for it is deprecated

- Name: `X9.31`

- Deprecated aliases: `EMSA2`, `EMSA_X931`

- Parameters specification: `(<HashFunction>)`

- Example: `X9.31(SHA-256)`

#### Raw

Sign inputs directly with no hashing or padding

Warning

This exists as an escape hatch allowing an application to define some protocol-specific padding scheme, and using it in a naive way is completely insecure. Don’t use this unless you know what you are doing.

- Name: `Raw`

- Parameters specification: `(<optional HashFunction>)`

- Examples: `Raw`, `Raw(SHA-256)`

### Signature with Hash

For many signature schemes including ECDSA and DSA, simply naming a hash function like `SHA-256` is all that is required.

Note

Previous versions of Botan required using a hash specifier like `EMSA1(SHA-256)` when generating or verifying ECDSA/DSA signatures, with the specified hash. The `EMSA1` was a reference to a now obsolete IEEE standard.

Parameters specification:

- `<HashFunction>`

- `EMSA1(<HashFunction>)` [deprecated]

There also exists a raw mode, which accepts a pre-hashed buffer instead of the message.

Warning

This is used for situations where somehow the hash is computed by another module and then signed. Many ways of doing this are insecure. Don’t use this unless you know what you are doing.

Parameters specification:

- `Raw`

- `Raw(<HashFunction>)`

### Ed25519 and Ed448 Variants

Warning

Ed25519 and Ed448 have different verification criteria, depending on the implementation. This can be problematic in systems which rely on consensus - see It’s 255:19AM. Do you know what your validation criteria are? for details.

Most signature schemes in Botan follow a hash-then-sign paradigm. That is, the entire message is digested to a fixed length representative using a collision resistant hash function, and then the digest is signed. Ed25519 and Ed448 instead sign the message directly. This is beneficial, in that the design should remain secure even in the (extremely unlikely) event that a collision attack on SHA-512 is found. However it means the entire message must be buffered in memory, which can be a problem for many applications which might need to sign large inputs. To use this variety of Ed25519/Ed448, use a padding name of “Pure”.

This is the default mode if no padding name is given.

Parameter specification: `Pure` / `Identity`

Ed25519ph (or Ed448) (pre-hashed) instead hashes the message with SHA-512 (or SHAKE256(512)) and then signs the digest plus a special prefix specified in RFC 8032. To use it, specify padding name “Ed25519ph” (or “Ed448ph”).

Parameter specification: `Ed25519ph`

Another variant of pre-hashing is used by GnuPG. There the message is digested with any hash function, then the digest is signed. To use it, specify any valid hash function. Even if SHA-512 is used, this variant is not compatible with Ed25519ph.

Parameter specification: `<HashFunction>`

For best interop with other systems, prefer “Ed25519ph”.

## Key Agreement

Key agreement is a scheme where two parties exchange public keys, after which it is possible for them to derive a secret key which is known only to the two of them.

There are different approaches possible for key agreement. In many protocols, both parties generate a new key, exchange public keys, and derive a secret, after which they throw away their private keys, using them only the once. However this requires the parties to both be online and able to communicate with each other.

In other protocols, one of the parties publishes their public key online in some way, and then it is possible for someone to send encrypted messages to that recipient by generating a new keypair, performing key exchange with the published public key, and then sending both the message along with their ephemeral public key. Then the recipient uses the provided public key along with their private key to complete the key exchange, recover the shared secret, and decrypt the message.

Typically the raw output of the key agreement function is not uniformly distributed, and may not be of an appropriate length to use as a key. To resolve these problems, key agreement will use a Key Derivation Functions (KDF) on the shared secret to produce an output of the desired length.

1. ECDH over GF(p) Weierstrass curves

2. ECDH over x25519 or x448

3. DH over prime fields

class PK_Key_Agreement
  PK_Key_Agreement(const Private_Key &key, RandomNumberGenerator &rng, const std::string &kdf, const std::string &provider = "")

    Set up to perform key derivation using the given private key and specified KDF.

  SymmetricKey derive_key(size_t key_len, const uint8_t peer_key[], size_t peer_key_len, const uint8_t salt[], size_t salt_len) const
  SymmetricKey derive_key(size_t key_len, std::span<const uint8_t> peer_key, const uint8_t salt[], size_t salt_len) const
  SymmetricKey derive_key(size_t key_len, const uint8_t peer_key[], size_t peer_key_len, const std::string &salt = "") const
  SymmetricKey derive_key(size_t key_len, std::span<const uint8_t> peer_key, const std::string &salt = "") const

    Return a shared secret key.

    The peer_key parameter must be the public key associated with the other party.

    The shared key will be of length key_len. If the KDF cannot accommodate outputs of this size (only likely for very large values, or if using KDF1), an exception will be thrown. If a KDF is not in use (“Raw” KDF), key_len is ignored and this function will always return directly what the agreement scheme output, of length equal to `agreed_value_size`.

    The salt will be hashed along with the shared secret by the KDF; this can be useful to bind the shared secret to a specific usage. If a KDF is not being used (“Raw” KDF) then any non-empty salt will be rejected.

### Code Example: ECDH Key Agreement

The code below performs an unauthenticated ECDH key agreement using the secp521r1 elliptic curve and applies the key derivation function KDF2(SHA-256) with 256 bit output length to the computed shared secret.

    #include <botan/auto_rng.h>
    #include <botan/ec_group.h>
    #include <botan/ecdh.h>
    #include <botan/hex.h>
    #include <botan/pubkey.h>

    #include <iostream>

    int main() {
       Botan::AutoSeeded_RNG rng;

       // ec domain and KDF
       const auto domain = Botan::EC_Group::from_name("secp521r1");
       const std::string kdf = "KDF2(SHA-256)";

       // the two parties generate ECDH keys
       const Botan::ECDH_PrivateKey key_a(rng, domain);
       const Botan::ECDH_PrivateKey key_b(rng, domain);

       // now they exchange their public values
       const auto key_apub = key_a.public_value();
       const auto key_bpub = key_b.public_value();

       // Construct key agreements and agree on a shared secret
       const Botan::PK_Key_Agreement ka_a(key_a, rng, kdf);
       const auto sA = ka_a.derive_key(32, key_bpub).bits_of();

       const Botan::PK_Key_Agreement ka_b(key_b, rng, kdf);
       const auto sB = ka_b.derive_key(32, key_apub).bits_of();

       if(sA != sB) {
          return 1;
       }

       std::cout << "agreed key:\n" << Botan::hex_encode(sA);
       return 0;
    }

## Key Encapsulation

Key encapsulation (KEM) is a variation on public key encryption which is commonly used by post-quantum secure schemes. Instead of choosing a random secret and encrypting it, as in typical public key encryption, a KEM encryption takes no inputs and produces two values, the shared secret and the encapsulated key. The decryption operation takes in the encapsulated key and returns the shared secret.

class PK_KEM_Encryptor
  PK_KEM_Encryptor(const Public_Key &key, const std::string &kdf = "", const std::string &provider = "")

    Create a KEM encryptor

  size_t shared_key_length(size_t desired_shared_key_len) const

    Size in bytes of the shared key being produced by this PK_KEM_Encryptor.

  size_t encapsulated_key_length() const

    Size in bytes of the encapsulated key being produced by this PK_KEM_Encryptor.

  KEM_Encapsulation encrypt(RandomNumberGenerator &rng, size_t desired_shared_key_len = 32, std::span<const uint8_t> salt = {})

    Perform a key encapsulation operation with the result being returned as a convenient struct.

  void encrypt(std::span<uint8_t> out_encapsulated_key, std::span<uint8_t> out_shared_key, RandomNumberGenerator &rng, size_t desired_shared_key_len = 32, std::span<const uint8_t> salt = {})

    Perform a key encapsulation operation by passing in out-buffers of the correct output length. Use encapsulated_key_length() and shared_key_length() to pre-allocate the output buffers.

  void encrypt(secure_vector<uint8_t> &out_encapsulated_key, secure_vector<uint8_t> &out_shared_key, size_t desired_shared_key_len, RandomNumberGenerator &rng, std::span<const uint8_t> salt)

    Perform a key encapsulation operation by passing in out-vectors that will be re-allocated to the correct output size.

class KEM_Encapsulation
  std::vector<uint8_t> encapsulated_shared_key() const
  secure_vector<uint8_t> shared_key() const

class PK_KEM_Decryptor
  PK_KEM_Decryptor(const Public_Key &key, const std::string &kdf = "", const std::string &provider = "")

    Create a KEM decryptor

  size_t encapsulated_key_length() const

    Size in bytes of the encapsulated key expected by this PK_KEM_Decryptor.

  size_t shared_key_length(size_t desired_shared_key_len) const

    Size in bytes of the shared key being produced by this PK_KEM_Encryptor.

  secure_vector<uint8> decrypt(std::span<const uint8> encapsulated_key, size_t desired_shared_key_len, std::span<const uint8_t> salt)

    Perform a key decapsulation operation

  void decrypt(std::span<uint8_t> out_shared_key, std::span<const uint8_t> encap_key, size_t desired_shared_key_len = 32, std::span<const uint8_t> salt = {})

    Perform a key decapsulation operation by passing in a pre-allocated out-buffer. Use shared_key_length() to determine the byte-length required.

Botan implements the following KEM schemes:

1. RSA

2. ML-KEM (formerly known as Kyber)

3. FrodoKEM

4. Classic McEliece

5. HyMES McEliece (deprecated)

### Code Example: ML-KEM

The code below demonstrates key encapsulation using ML-KEM (FIPS 203), formerly known as Kyber.

    #include <botan/ml_kem.h>
    #include <botan/pubkey.h>
    #include <botan/system_rng.h>

    #include <iostream>

    int main() {
       const size_t shared_key_len = 32;
       const std::string_view kdf = "HKDF(SHA-512)";

       Botan::System_RNG rng;

       const auto salt = rng.random_array<16>();

       const Botan::ML_KEM_PrivateKey priv_key(rng, Botan::ML_KEM_Mode::ML_KEM_768);
       auto pub_key = priv_key.public_key();

       Botan::PK_KEM_Encryptor enc(*pub_key, kdf);

       const auto kem_result = enc.encrypt(rng, shared_key_len, salt);

       Botan::PK_KEM_Decryptor dec(priv_key, rng, kdf);

       auto dec_shared_key = dec.decrypt(kem_result.encapsulated_shared_key(), shared_key_len, salt);

       if(dec_shared_key != kem_result.shared_key()) {
          std::cerr << "Shared keys differ\n";
          return 1;
       }

       return 0;
    }

## HyMES McEliece cryptosystem

McEliece is a cryptographic scheme based on error correcting codes which is thought to be resistant to quantum computers. First proposed in 1978, it is fast and patent-free. Variants have been proposed and broken, but with suitable parameters the original scheme remains secure. However the public keys are quite large, which has hindered deployment in the past.

The implementation of McEliece in Botan was contributed by cryptosource GmbH. It is based on the implementation HyMES, with the kind permission of Nicolas Sendrier and INRIA to release a C++ adaption of their original C code under the Botan license. It was then modified by Falko Strenzke to add side channel and fault attack countermeasures. You can read more about the implementation at http://www.cryptosource.de/docs/mceliece_in_botan.pdf

Encryption in the McEliece scheme consists of choosing a message block of size n, encoding it in the error correcting code which is the public key, then adding t bit errors. The code is created such that knowing only the public key, decoding t errors is intractable, but with the additional knowledge of the secret structure of the code a fast decoding technique exists.

The McEliece implementation in HyMES, and also in Botan, uses an optimization to reduce the public key size, by converting the public key into a systemic code. This means a portion of the public key is a identity matrix, and can be excluded from the published public key. However it also means that in McEliece the plaintext is represented directly in the ciphertext, with only a small number of bit errors. Thus it is absolutely essential to only use McEliece with a CCA2 secure scheme.

For a given security level (SL) a McEliece key would use parameters n and t, and have the corresponding key sizes listed:

SL | n | t | public key KB | private key KB
--- | --- | --- | --- | ---
80 | 1632 | 33 | 59 | 140
107 | 2280 | 45 | 128 | 300
128 | 2960 | 57 | 195 | 459
147 | 3408 | 67 | 265 | 622
191 | 4624 | 95 | 516 | 1234
256 | 6624 | 115 | 942 | 2184

You can check the speed of McEliece with the suggested parameters above using `botan speed McEliece`

## Classic McEliece KEM

Classic McEliece is an IND-CCA2 secure key encapsulation algorithm based on the McEliece cryptosystem introduced in 1978. It is a code-based scheme that relies on conservative security assumptions and is considered secure against quantum computers. It is an alternative to lattice-based schemes.

Other advantages of Classic McEliece are the small ciphertext size and the fast encapsulation. Key generation and decapsulation are slower than in lattice-based schemes. The main disadvantage of Classic McEliece is the large public key size, ranging from 0.26 MB to 1.36 MB, depending on the instance. Due to its large key size, Classic McEliece is recommended for applications where the public key is stored for a long time, and memory is not a critical resource. Usage with ephemeral keys is not recommended.

Botan’s implementation covers the parameter sets of the NIST round 4 specification and the Classic McEliece ISO draft specification. These are the following:

Set without f/pc | Set with f | Set with pc | Set with pcf | Public Key Size
--- | --- | --- | --- | ---
mceliece348864 | mceliece348864f |  |  | 0.26 MB
mceliece460896 | mceliece460896f |  |  | 0.52 MB
mceliece6688128 | mceliece6688128f | mceliece6688128pc | mceliece6688128pcf | 1.04 MB
mceliece6960119 | mceliece6960119f | mceliece6960119pc | mceliece6960119pcf | 1.05 MB
mceliece8192128 | mceliece8192128f | mceliece8192128pc | mceliece8192128pcf | 1.36 MB

The instances with the suffix ‘f’ use a faster key generation algorithm that is more consistent in runtime. The instances with the suffix ‘pc’ use plaintext confirmation, which is only specified in the ISO document. The instances mceliece348864(f) and mceliece460896(f) are only defined in the NIST round 4 submission.

## eXtended Merkle Signature Scheme (XMSS)

Botan implements the single tree version of the eXtended Merkle Signature Scheme (XMSS) using Winternitz One Time Signatures+ (WOTS+). The implementation is based on RFC 8391 “XMSS: eXtended Merkle Signature Scheme”.

Warning

XMSS is stateful, meaning the private key updates after each signature creation. Applications are responsible for updating their persistent secret with the new output of `Private_Key::private_key_bits()` after each signature creation. If the same private key is ever used to generate two different signatures, then the scheme becomes insecure. For this reason, it can be challenging to use XMSS securely.

XMSS uses the Botan interfaces for public key cryptography. The following algorithms are implemented:

1. XMSS-SHA2_10_256

2. XMSS-SHA2_16_256

3. XMSS-SHA2_20_256

4. XMSS-SHA2_10_512

5. XMSS-SHA2_16_512

6. XMSS-SHA2_20_512

7. XMSS-SHAKE_10_256

8. XMSS-SHAKE_16_256

9. XMSS-SHAKE_20_256

10. XMSS-SHAKE_10_512

11. XMSS-SHAKE_16_512

12. XMSS-SHAKE_20_512

13. XMSS-SHA2_10_192

14. XMSS-SHA2_16_192

15. XMSS-SHA2_20_192

16. XMSS-SHAKE256_10_256

17. XMSS-SHAKE256_16_256

18. XMSS-SHAKE256_20_256

19. XMSS-SHAKE256_10_192

20. XMSS-SHAKE256_16_192

21. XMSS-SHAKE256_20_192

The algorithm name contains the hash function name, tree height and digest width defined by the corresponding parameter set. Choosing XMSS-SHA2_10_256 for instance will use the SHA2-256 hash function to generate a tree of height ten.

### Code Example: XMSS

The following code snippet shows a minimum example on how to create an XMSS public/private key pair and how to use these keys to create and verify a signature:

    #include <botan/auto_rng.h>
    #include <botan/pubkey.h>
    #include <botan/secmem.h>
    #include <botan/xmss.h>

    #include <iostream>
    #include <vector>

    int main() {
       // Create a random number generator used for key generation.
       Botan::AutoSeeded_RNG rng;

       // create a new public/private key pair using SHA2 256 as hash
       // function and a tree height of 10.
       const Botan::XMSS_PrivateKey private_key(Botan::XMSS_Parameters::xmss_algorithm_t::XMSS_SHA2_10_256, rng);
       const Botan::XMSS_PublicKey& public_key(private_key);

       // create Public Key Signer using the private key.
       Botan::PK_Signer signer(private_key, rng, "");

       // create and sign a message using the Public Key Signer.
       Botan::secure_vector<uint8_t> msg{0x01, 0x02, 0x03, 0x04};
       auto sig = signer.sign_message(msg, rng);

       // create Public Key Verifier using the public key
       Botan::PK_Verifier verifier(public_key, "");

       // verify the signature for the previously generated message.
       if(verifier.verify_message(msg, sig)) {
          std::cout << "Success.\n";
          return 0;
       } else {
          std::cout << "Error.\n";
          return 1;
       }
    }

## Hierarchical Signature System with Leighton-Micali Hash-Based Signatures (HSS-LMS)

HSS-LMS is a stateful hash-based signature scheme which is defined in RFC 8554 “Leighton-Micali Hash-Based Signatures”.

It is a multitree scheme, which is highly configurable. Multitree means, it consists of multiple layers of Merkle trees, which can be defined individually. Moreover, the used hash function and the Winternitz Parameter of the underlying one-time signature can be chosen for each tree layer. For a sensible selection of parameters refer to RFC 8554 Section 6.4..

Warning

HSS-LMS is stateful, meaning the private key updates after each signature creation. Applications are responsible for updating their persistent secret with the new output of `Private_Key::private_key_bits()` after each signature creation. If the same private key is ever used to generate two different signatures, then the scheme becomes insecure. For this reason, it can be challenging to use HSS-LMS securely.

HSS-LMS uses the Botan interfaces for public key cryptography. The `params` argument of the HSS-LMS private key is used to define the parameter set. The syntax of this argument must be the following:

`HSS-LMS(<hash>,HW(<h>,<w>),HW(<h>,<w>),...)`

e.g. `HSS-LMS(SHA-256,HW(5,1),HW(5,1))` to use SHA-256 in a two-layer HSS instance with LMS tree height 5 and Winternitz parameter 1. This results in a private key that can be used to create up to 2^(5+5)=1024 signatures.

The following parameters are allowed (which are specified in RFC 8554 and and draft-fluhrer-lms-more-parm-sets-11):

- hash: `SHA-256`, `Truncated(SHA-256,192)`, `SHAKE-256(256)`, `SHAKE-256(192)`

- h: `5`, `10`, `15`, `20`, `25`

- w: `1`, `2`, `4`, `8`