Botan::XMSS_PublicKey Class Reference

#include <xmss.h>

Inheritance diagram for Botan::XMSS_PublicKey:

Public Member Functions
virtual Signature_Format	_default_x509_signature_format () const
virtual std::optional< size_t >	_signature_element_size_for_DER_encoding () const
std::string	algo_name () const override
AlgorithmIdentifier	algorithm_identifier () const override
bool	check_key (RandomNumberGenerator &rng, bool strong) const override
virtual std::unique_ptr< PK_Ops::Encryption >	create_encryption_op (RandomNumberGenerator &rng, std::string_view params, std::string_view provider) const
virtual std::unique_ptr< PK_Ops::KEM_Encryption >	create_kem_encryption_op (std::string_view params, std::string_view provider) const
std::unique_ptr< PK_Ops::Verification >	create_verification_op (std::string_view params, std::string_view provider) const override
std::unique_ptr< PK_Ops::Verification >	create_x509_verification_op (const AlgorithmIdentifier &alg_id, std::string_view provider) const override
Signature_Format	default_x509_signature_format () const
size_t	estimated_strength () const override
std::string	fingerprint_public (std::string_view alg="SHA-256") const
std::unique_ptr< Private_Key >	generate_another (RandomNumberGenerator &rng) const final
virtual const BigInt &	get_int_field (std::string_view field) const
OID	get_oid () const
size_t	key_length () const override
size_t	message_part_size () const
size_t	message_parts () const
virtual OID	object_identifier () const
std::vector< uint8_t >	public_key_bits () const override
std::vector< uint8_t >	raw_public_key () const
std::vector< uint8_t >	raw_public_key_bits () const override
std::vector< uint8_t >	subject_public_key () const
bool	supports_operation (PublicKeyOperation op) const override
BOTAN_FUTURE_EXPLICIT	XMSS_PublicKey (std::span< const uint8_t > key_bits)
	XMSS_PublicKey (XMSS_Parameters::xmss_algorithm_t xmss_oid, RandomNumberGenerator &rng)
	XMSS_PublicKey (XMSS_Parameters::xmss_algorithm_t xmss_oid, secure_vector< uint8_t > root, secure_vector< uint8_t > public_seed)

Protected Member Functions
const secure_vector< uint8_t > &	public_seed () const
const secure_vector< uint8_t > &	root () const
void	set_root (secure_vector< uint8_t > root)
const XMSS_Parameters &	xmss_parameters () const

Friends
class	XMSS_Verification_Operation

Detailed Description

An XMSS: Extended Hash-Based Signature public key.

[1] XMSS: Extended Hash-Based Signatures, Request for Comments: 8391 Release: May 2018. https://datatracker.ietf.org/doc/rfc8391/

Definition at line 36 of file xmss.h.

Constructor & Destructor Documentation

XMSS_PublicKey() [1/3]

Botan::XMSS_PublicKey::XMSS_PublicKey	(	XMSS_Parameters::xmss_algorithm_t	xmss_oid,
		RandomNumberGenerator &	rng )

Creates a new XMSS public key for the chosen XMSS signature method. New public and prf seeds are generated using rng. The appropriate WOTS signature method will be automatically set based on the chosen XMSS signature method.

Parameters

xmss_oid	Identifier for the selected XMSS signature method.
Random Number Generators	A random number generator to use for key generation.

Definition at line 102 of file xmss_publickey.cpp.

                                                                                                   {
   const auto params = XMSS_Parameters::from_id(xmss_oid);
   m_public_key = std::make_shared<XMSS_PublicKey_Internal>(
      params, secure_vector<uint8_t>(params.element_size()), rng.random_vec(params.element_size()));
}

References Botan::XMSS_Parameters::from_id(), and Botan::RandomNumberGenerator::random_vec().

Referenced by Botan::XMSS_PrivateKey::XMSS_PrivateKey(), Botan::XMSS_PrivateKey::XMSS_PrivateKey(), and Botan::XMSS_PrivateKey::XMSS_PrivateKey().

XMSS_PublicKey() [2/3]

Botan::XMSS_PublicKey::XMSS_PublicKey

(

std::span< const uint8_t >

key_bits

)

Loads a public key.

Public key must be encoded as in RFC draft-vangeest-x509-hash-sigs-03.

Parameters

key_bits

DER encoded public key bits

Definition at line 108 of file xmss_publickey.cpp.

                                                              {
   const auto raw_key = extract_raw_public_key(key_bits);
   const auto xmss_oid = deserialize_xmss_oid(raw_key);
   const auto params = XMSS_Parameters::from_id(xmss_oid);
   if(raw_key.size() < params.raw_public_key_size()) {
      throw Decoding_Error("Invalid XMSS public key size detected");
   }
 
   BufferSlicer s(raw_key);
   s.skip(4 /* algorithm ID -- already consumed by `deserialize_xmss_oid()` */);
 
   auto root = s.copy_as_secure_vector(params.element_size());
   auto public_seed = s.copy_as_secure_vector(params.element_size());
 
   m_public_key = std::make_shared<XMSS_PublicKey_Internal>(params, std::move(root), std::move(public_seed));
}

References Botan::BufferSlicer::copy_as_secure_vector(), Botan::XMSS_Parameters::from_id(), public_seed(), root(), and Botan::BufferSlicer::skip().

XMSS_PublicKey() [3/3]

Botan::XMSS_PublicKey::XMSS_PublicKey	(	XMSS_Parameters::xmss_algorithm_t	xmss_oid,
		secure_vector< uint8_t >	root,
		secure_vector< uint8_t >	public_seed )

Creates a new XMSS public key for a chosen XMSS signature method as well as pre-computed root node and public_seed values.

Parameters

xmss_oid	Identifier for the selected XMSS signature method.
root	Root node value.
public_seed	Public seed value.

Definition at line 125 of file xmss_publickey.cpp.

                                                                   {
   const auto params = XMSS_Parameters::from_id(xmss_oid);
   BOTAN_ARG_CHECK(root.size() == params.element_size(), "XMSS: unexpected byte length of root hash");
   BOTAN_ARG_CHECK(public_seed.size() == params.element_size(), "XMSS: unexpected byte length of public seed");
   m_public_key = std::make_shared<XMSS_PublicKey_Internal>(params, std::move(root), std::move(public_seed));
}

References BOTAN_ARG_CHECK, Botan::XMSS_Parameters::from_id(), public_seed(), and root().

Member Function Documentation

_default_x509_signature_format()

Signature_Format Botan::Asymmetric_Key::_default_x509_signature_format ( ) const

virtualinherited

Reimplemented in Botan::GOST_3410_PublicKey.

Definition at line 30 of file pk_keys.cpp.

                                                                      {
   if(_signature_element_size_for_DER_encoding()) {
      return Signature_Format::DerSequence;
   } else {
      return Signature_Format::Standard;
   }
}

References _signature_element_size_for_DER_encoding(), Botan::DerSequence, and Botan::Standard.

Referenced by Botan::X509_Object::choose_sig_format(), Botan::Public_Key::default_x509_signature_format(), and Botan::PK_Verifier::PK_Verifier().

_signature_element_size_for_DER_encoding()

virtual std::optional< size_t > Botan::Asymmetric_Key::_signature_element_size_for_DER_encoding ( ) const

inlinevirtualinherited

Certain signatures schemes such as ECDSA have more than one element, and certain unfortunate protocols decided the thing to do was not concatenate them as normally done, but instead DER encode each of the elements as independent values.

If this returns a value x then the signature is checked to be exactly 2*x bytes and split in half for DER encoding.

Reimplemented in Botan::DSA_PublicKey, Botan::ECDSA_PublicKey, Botan::ECGDSA_PublicKey, Botan::ECKCDSA_PublicKey, Botan::GOST_3410_PublicKey, and Botan::SM2_PublicKey.

Definition at line 144 of file pk_keys.h.

{ return {}; }

Referenced by _default_x509_signature_format(), Botan::Public_Key::message_part_size(), Botan::Public_Key::message_parts(), Botan::PK_Verifier::PK_Verifier(), and Botan::PK_Verifier::PK_Verifier().

algo_name()

std::string Botan::XMSS_PublicKey::algo_name ( ) const

inlineoverridevirtual

Get the name of the underlying public key scheme.

Returns

name of the public key scheme

Implements Botan::Asymmetric_Key.

Definition at line 71 of file xmss.h.

{ return "XMSS"; }

Referenced by Botan::XMSS_PrivateKey::create_signature_op(), create_verification_op(), and create_x509_verification_op().

algorithm_identifier()

AlgorithmIdentifier Botan::XMSS_PublicKey::algorithm_identifier ( ) const

inlineoverridevirtual

Returns

X.509 AlgorithmIdentifier for this key

Implements Botan::Public_Key.

Definition at line 73 of file xmss.h.

                                                                {
         return AlgorithmIdentifier(object_identifier(), AlgorithmIdentifier::USE_EMPTY_PARAM);
      }

References Botan::Asymmetric_Key::object_identifier(), and Botan::AlgorithmIdentifier::USE_EMPTY_PARAM.

Referenced by create_x509_verification_op().

check_key()

bool Botan::XMSS_PublicKey::check_key ( RandomNumberGenerator & rng, bool strong ) const

overridevirtual

Implements Botan::Asymmetric_Key.

Definition at line 158 of file xmss_publickey.cpp.

                                                                     {
   // The public key consists of (OID, root hash, public seed). The OID is
   // validated and the byte lengths of root and public_seed are verified
   // against the parameter set during deserialization. These are opaque
   // hash outputs with no further structural invariants to check.
   return true;
}

create_encryption_op()

std::unique_ptr< PK_Ops::Encryption > Botan::Public_Key::create_encryption_op ( RandomNumberGenerator & rng, std::string_view params, std::string_view provider ) const

virtualinherited

This is an internal library function exposed on key types. In almost all cases applications should use wrappers in pubkey.h

Return an encryption operation for this key/params or throw

Parameters

Random Number Generators	a random number generator. The PK_Op may maintain a reference to the RNG and use it many times. The rng must outlive any operations which reference it.
params	additional parameters
provider	the provider to use

Reimplemented in Botan::ElGamal_PublicKey, Botan::RSA_PublicKey, Botan::SM2_PublicKey, and Botan::TPM2::RSA_PublicKey.

Definition at line 105 of file pk_keys.cpp.

                                                                                             {
   throw Lookup_Error(fmt("{} does not support encryption", algo_name()));
}

References Botan::Asymmetric_Key::algo_name(), and Botan::fmt().

Referenced by Botan::PK_Encryptor_EME::PK_Encryptor_EME().

create_kem_encryption_op()

std::unique_ptr< PK_Ops::KEM_Encryption > Botan::Public_Key::create_kem_encryption_op ( std::string_view params, std::string_view provider ) const

virtualinherited

This is an internal library function exposed on key types. In almost all cases applications should use wrappers in pubkey.h

Return a KEM encryption operation for this key/params or throw

Parameters

params	additional parameters
provider	the provider to use

Reimplemented in Botan::Classic_McEliece_PublicKey, Botan::FrodoKEM_PublicKey, Botan::KEX_to_KEM_Adapter_PublicKey, Botan::Kyber_PublicKey, Botan::McEliece_PublicKey, Botan::RSA_PublicKey, and Botan::TLS::Hybrid_KEM_PublicKey.

Definition at line 111 of file pk_keys.cpp.

                                                                                                     {
   throw Lookup_Error(fmt("{} does not support KEM encryption", algo_name()));
}

References Botan::Asymmetric_Key::algo_name(), and Botan::fmt().

Referenced by Botan::PK_KEM_Encryptor::PK_KEM_Encryptor().

create_verification_op()

std::unique_ptr< PK_Ops::Verification > Botan::XMSS_PublicKey::create_verification_op ( std::string_view params, std::string_view provider ) const

overridevirtual

This is an internal library function exposed on key types. In all cases applications should use wrappers in pubkey.h

Return a verification operation for this key/params or throw

Parameters

params	additional parameters
provider	the provider to use

Reimplemented from Botan::Public_Key.

Definition at line 166 of file xmss_publickey.cpp.

                                                                                                            {
   if(provider == "base" || provider.empty()) {
      return std::make_unique<XMSS_Verification_Operation>(*this);
   }
   throw Provider_Not_Found(algo_name(), provider);
}

References algo_name().

create_x509_verification_op()

std::unique_ptr< PK_Ops::Verification > Botan::XMSS_PublicKey::create_x509_verification_op ( const AlgorithmIdentifier & signature_algorithm, std::string_view provider ) const

overridevirtual

This is an internal library function exposed on key types. In all cases applications should use wrappers in pubkey.h

Return a verification operation for this combination of key and signature algorithm or throw.

Parameters

signature_algorithm	is the X.509 algorithm identifier encoding the padding scheme and hash hash function used in the signature if applicable.
provider	the provider to use

Reimplemented from Botan::Public_Key.

Definition at line 174 of file xmss_publickey.cpp.

                                                                                                                 {
   if(provider == "base" || provider.empty()) {
      if(alg_id != this->algorithm_identifier()) {
         throw Decoding_Error("Unexpected AlgorithmIdentifier for XMSS X509 signature");
      }
      return std::make_unique<XMSS_Verification_Operation>(*this);
   }
   throw Provider_Not_Found(algo_name(), provider);
}

References algo_name(), and algorithm_identifier().

default_x509_signature_format()

Signature_Format Botan::Public_Key::default_x509_signature_format ( ) const

inlineinherited

Definition at line 237 of file pk_keys.h.

                                                                                                           {
         return _default_x509_signature_format();
      }

References Botan::Asymmetric_Key::_default_x509_signature_format(), and default_x509_signature_format().

Referenced by default_x509_signature_format().

estimated_strength()

size_t Botan::XMSS_PublicKey::estimated_strength ( ) const

overridevirtual

Return the estimated strength of the underlying key against the best currently known attack. Note that this ignores anything but pure attacks against the key itself and do not take into account padding schemes, usage mistakes, etc which might reduce the strength. However it does suffice to provide an upper bound.

Returns

estimated strength in bits

Implements Botan::Asymmetric_Key.

Definition at line 150 of file xmss_publickey.cpp.

                                                {
   return xmss_parameters().estimated_strength();
}

References Botan::XMSS_Parameters::estimated_strength(), and xmss_parameters().

fingerprint_public()

std::string Botan::Public_Key::fingerprint_public ( std::string_view alg = "SHA-256" ) const

inherited

Returns

Hash of the subject public key

Definition at line 94 of file pk_keys.cpp.

                                                                       {
   return create_hex_fingerprint(subject_public_key(), hash_algo);
}

References Botan::create_hex_fingerprint(), and subject_public_key().

Referenced by public_key_bits().

generate_another()

std::unique_ptr< Private_Key > Botan::XMSS_PublicKey::generate_another ( RandomNumberGenerator & rng ) const

finalvirtual

Generate another (cryptographically independent) key pair using the same algorithm parameters as this key. This is most useful for algorithms that support PublicKeyOperation::KeyAgreement to generate a fitting ephemeral key pair. For other key types it might throw Not_Implemented.

Implements Botan::Asymmetric_Key.

Definition at line 199 of file xmss_publickey.cpp.

                                                                                            {
   // Note: Given only an XMSS public key we cannot know which WOTS key
   //       derivation method was used to build the XMSS tree. Hence, we have to
   //       use the default here.
   return std::make_unique<XMSS_PrivateKey>(xmss_parameters().oid(), rng);
}

References xmss_parameters().

get_int_field()

const BigInt & Botan::Asymmetric_Key::get_int_field ( std::string_view field ) const

virtualinherited

Access an algorithm specific field

If the field is not known for this algorithm, an Invalid_Argument is thrown. The interpretation of the result requires knowledge of which algorithm is involved. For instance for RSA "p" represents one of the secret primes, while for DSA "p" is the public prime.

Some algorithms may not implement this method at all.

This is primarily used to implement the FFI botan_pubkey_get_field and botan_privkey_get_field functions.

TODO(Botan4) Change this to return by value

Reimplemented in Botan::DH_PrivateKey, Botan::DH_PublicKey, Botan::DSA_PrivateKey, Botan::DSA_PublicKey, Botan::EC_PrivateKey, Botan::EC_PublicKey, Botan::ElGamal_PrivateKey, Botan::ElGamal_PublicKey, Botan::RSA_PrivateKey, and Botan::RSA_PublicKey.

Definition at line 18 of file pk_keys.cpp.

                                                                      {
   throw Unknown_PK_Field_Name(algo_name(), field);
}

References algo_name().

Referenced by estimated_strength(), Botan::EC_PublicKey::get_int_field(), and Botan::RSA_PublicKey::get_int_field().

get_oid()

OID Botan::Public_Key::get_oid ( ) const

inlineinherited

Deprecated version of object_identifier

Definition at line 168 of file pk_keys.h.

{ return this->object_identifier(); }

References get_oid(), and Botan::Asymmetric_Key::object_identifier().

Referenced by get_oid().

key_length()

size_t Botan::XMSS_PublicKey::key_length ( ) const

overridevirtual

Return an integer value best approximating the length of the primary security parameter. For example for RSA this will be the size of the modulus, for ECDSA the size of the ECC group, and for McEliece the size of the code will be returned.

Implements Botan::Public_Key.

Definition at line 154 of file xmss_publickey.cpp.

                                        {
   return xmss_parameters().estimated_strength();
}

References Botan::XMSS_Parameters::estimated_strength(), and xmss_parameters().

message_part_size()

size_t Botan::Public_Key::message_part_size ( ) const

inlineinherited

Returns how large each of the message parts referred to by message_parts() is

This function is public but applications should have few reasons to ever call this.

Returns

size of the message parts in bits

Definition at line 228 of file pk_keys.h.

                                                                                     {
         return _signature_element_size_for_DER_encoding().value_or(0);
      }

References Botan::Asymmetric_Key::_signature_element_size_for_DER_encoding(), and message_part_size().

Referenced by message_part_size().

message_parts()

size_t Botan::Public_Key::message_parts ( ) const

inlineinherited

Returns more than 1 if the output of this algorithm (ciphertext, signature) should be treated as more than one value. This is used for algorithms like DSA and ECDSA, where the (r,s) output pair can be encoded as either a plain binary list or a TLV tagged DER encoding depending on the protocol.

This function is public but applications should have few reasons to ever call this.

Returns

number of message parts

Definition at line 215 of file pk_keys.h.

                                                                                 {
         return _signature_element_size_for_DER_encoding() ? 2 : 1;
      }

References Botan::Asymmetric_Key::_signature_element_size_for_DER_encoding(), and message_parts().

Referenced by message_parts().

object_identifier()

OID Botan::Asymmetric_Key::object_identifier ( ) const

virtualinherited

Get the OID of the underlying public key scheme.

Returns

OID of the public key scheme

Reimplemented in Botan::Classic_McEliece_PublicKey, Botan::Dilithium_PublicKey, Botan::FrodoKEM_PublicKey, Botan::HSS_LMS_PublicKey, Botan::Kyber_PublicKey, and Botan::SphincsPlus_PublicKey.

Definition at line 22 of file pk_keys.cpp.

                                            {
   try {
      return OID::from_string(algo_name());
   } catch(Lookup_Error&) {
      throw Lookup_Error(fmt("Public key algorithm {} has no defined OIDs", algo_name()));
   }
}

References algo_name(), Botan::fmt(), and Botan::OID::from_string().

Referenced by Botan::DH_PublicKey::algorithm_identifier(), Botan::DSA_PublicKey::algorithm_identifier(), Botan::EC_PublicKey::algorithm_identifier(), Botan::Ed25519_PublicKey::algorithm_identifier(), Botan::Ed448_PublicKey::algorithm_identifier(), Botan::ElGamal_PublicKey::algorithm_identifier(), Botan::GOST_3410_PublicKey::algorithm_identifier(), Botan::McEliece_PublicKey::algorithm_identifier(), Botan::RSA_PublicKey::algorithm_identifier(), Botan::TPM_PrivateKey::algorithm_identifier(), Botan::X25519_PublicKey::algorithm_identifier(), Botan::X448_PublicKey::algorithm_identifier(), Botan::XMSS_PublicKey::algorithm_identifier(), estimated_strength(), and Botan::Public_Key::get_oid().

public_key_bits()

std::vector< uint8_t > Botan::XMSS_PublicKey::public_key_bits ( ) const

overridevirtual

Returns the encoded public key as defined in RFC draft-vangeest-x509-hash-sigs-03.

Returns

encoded public key bits

Implements Botan::Public_Key.

Definition at line 189 of file xmss_publickey.cpp.

                                                         {
   std::vector<uint8_t> output;
   DER_Encoder(output).encode(raw_public_key_bits(), ASN1_Type::OctetString);
   return output;
}

References Botan::DER_Encoder::encode(), Botan::OctetString, and raw_public_key_bits().

public_seed()

const secure_vector< uint8_t > & Botan::XMSS_PublicKey::public_seed ( ) const

protected

Definition at line 134 of file xmss_publickey.cpp.

                                                                {
   return m_public_key->public_seed();
}

Referenced by Botan::XMSS_PrivateKey::public_key(), Botan::XMSS_PrivateKey::XMSS_PrivateKey(), XMSS_PublicKey(), XMSS_PublicKey(), and XMSS_Verification_Operation.

raw_public_key()

std::vector< uint8_t > Botan::XMSS_PublicKey::raw_public_key

(

)

const

Definition at line 195 of file xmss_publickey.cpp.

                                                        {
   return raw_public_key_bits();
}

References raw_public_key_bits().

Referenced by Botan::XMSS_PrivateKey::raw_private_key().

raw_public_key_bits()

std::vector< uint8_t > Botan::XMSS_PublicKey::raw_public_key_bits ( ) const

overridevirtual

Generates a byte sequence representing the XMSS public key, as defined in [1] (p. 23, "XMSS Public Key")

Returns

4-byte OID, followed by n-byte root node, followed by public seed.

Implements Botan::Public_Key.

Definition at line 185 of file xmss_publickey.cpp.

                                                             {
   return m_public_key->raw_public_key_bits();
}

Referenced by public_key_bits(), and raw_public_key().

root()

const secure_vector< uint8_t > & Botan::XMSS_PublicKey::root ( ) const

protected

Definition at line 138 of file xmss_publickey.cpp.

                                                         {
   return m_public_key->root();
}

Referenced by Botan::XMSS_PrivateKey::public_key(), set_root(), Botan::XMSS_PrivateKey::XMSS_PrivateKey(), XMSS_PublicKey(), XMSS_PublicKey(), and XMSS_Verification_Operation.

set_root()

void Botan::XMSS_PublicKey::set_root ( secure_vector< uint8_t > root )

protected

Definition at line 146 of file xmss_publickey.cpp.

                                                         {
   m_public_key->set_root(std::move(root));
}

References root().

Referenced by Botan::XMSS_PrivateKey::XMSS_PrivateKey(), and XMSS_Verification_Operation.

subject_public_key()

std::vector< uint8_t > Botan::Public_Key::subject_public_key ( ) const

inherited

Returns

X.509 subject key encoding for this key object

Definition at line 63 of file pk_keys.cpp.

                                                        {
   std::vector<uint8_t> output;
 
   DER_Encoder(output)
      .start_sequence()
      .encode(algorithm_identifier())
      .encode(public_key_bits(), ASN1_Type::BitString)
      .end_cons();
 
   return output;
}

References algorithm_identifier(), Botan::BitString, Botan::DER_Encoder::encode(), Botan::DER_Encoder::end_cons(), public_key_bits(), and Botan::DER_Encoder::start_sequence().

Referenced by Botan::X509::BER_encode(), Botan::PKCS10_Request::create(), fingerprint_public(), Botan::X509::PEM_encode(), and public_key_bits().

supports_operation()

bool Botan::XMSS_PublicKey::supports_operation ( PublicKeyOperation op ) const

inlineoverridevirtual

Return true if this key could be used for the specified type of operation.

Implements Botan::Asymmetric_Key.

Definition at line 104 of file xmss.h.

{ return (op == PublicKeyOperation::Signature); }

References Botan::Signature, and supports_operation().

Referenced by supports_operation().

xmss_parameters()

const XMSS_Parameters & Botan::XMSS_PublicKey::xmss_parameters ( ) const

protected

Definition at line 142 of file xmss_publickey.cpp.

                                                             {
   return m_public_key->xmss_parameters();
}

Referenced by estimated_strength(), generate_another(), key_length(), Botan::XMSS_PrivateKey::public_key(), Botan::XMSS_PrivateKey::XMSS_PrivateKey(), Botan::XMSS_PrivateKey::XMSS_PrivateKey(), Botan::XMSS_PrivateKey::XMSS_PrivateKey(), and XMSS_Verification_Operation.

Friends And Related Symbol Documentation

XMSS_Verification_Operation

friend class XMSS_Verification_Operation

friend

Definition at line 113 of file xmss.h.

References public_seed(), root(), set_root(), xmss_parameters(), and XMSS_Verification_Operation.

Referenced by XMSS_Verification_Operation.

---

The documentation for this class was generated from the following files:

• src/lib/pubkey/xmss/xmss.h
• src/lib/pubkey/xmss/xmss_publickey.cpp