Botan  2.6.0
Crypto and TLS for C++11
Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
Botan::EC_PublicKey Class Referenceabstract

#include <ecc_key.h>

Inheritance diagram for Botan::EC_PublicKey:
Botan::Public_Key Botan::EC_PrivateKey Botan::ECDH_PublicKey Botan::ECDSA_PublicKey Botan::ECGDSA_PublicKey Botan::ECKCDSA_PublicKey Botan::GOST_3410_PublicKey Botan::SM2_Encryption_PublicKey Botan::SM2_Signature_PublicKey

Public Member Functions

virtual std::string algo_name () const =0
 
AlgorithmIdentifier algorithm_identifier () const override
 
bool check_key (RandomNumberGenerator &rng, bool strong) const override
 
virtual std::unique_ptr< PK_Ops::Encryptioncreate_encryption_op (RandomNumberGenerator &rng, const std::string &params, const std::string &provider) const
 
virtual std::unique_ptr< PK_Ops::KEM_Encryptioncreate_kem_encryption_op (RandomNumberGenerator &rng, const std::string &params, const std::string &provider) const
 
virtual std::unique_ptr< PK_Ops::Verificationcreate_verification_op (const std::string &params, const std::string &provider) const
 
std::vector< uint8_t > DER_domain () const
 
const EC_Groupdomain () const
 
EC_Group_Encoding domain_format () const
 
 EC_PublicKey (const EC_Group &dom_par, const PointGFp &pub_point)
 
 EC_PublicKey (const AlgorithmIdentifier &alg_id, const std::vector< uint8_t > &key_bits)
 
 EC_PublicKey (const EC_PublicKey &other)=default
 
size_t estimated_strength () const override
 
std::string fingerprint_public (const std::string &alg="SHA-256") const
 
virtual OID get_oid () const
 
size_t key_length () const override
 
virtual size_t message_part_size () const
 
virtual size_t message_parts () const
 
EC_PublicKeyoperator= (const EC_PublicKey &other)=default
 
PointGFp::Compression_Type point_encoding () const
 
std::vector< uint8_t > public_key_bits () const override
 
const PointGFppublic_point () const
 
void set_parameter_encoding (EC_Group_Encoding enc)
 
void set_point_encoding (PointGFp::Compression_Type enc)
 
std::vector< uint8_t > subject_public_key () const
 
virtual ~EC_PublicKey ()=default
 

Protected Member Functions

 EC_PublicKey ()
 

Protected Attributes

EC_Group_Encoding m_domain_encoding
 
EC_Group m_domain_params
 
PointGFp::Compression_Type m_point_encoding = PointGFp::UNCOMPRESSED
 
PointGFp m_public_key
 

Detailed Description

This class represents abstract ECC public keys. When encoding a key via an encoder that can be accessed via the corresponding member functions, the key will decide upon its internally stored encoding information whether to encode itself with or without domain parameters, or using the domain parameter oid. Furthermore, a public key without domain parameters can be decoded. In that case, it cannot be used for verification until its domain parameters are set by calling the corresponding member function.

Definition at line 28 of file ecc_key.h.

Constructor & Destructor Documentation

◆ EC_PublicKey() [1/4]

Botan::EC_PublicKey::EC_PublicKey ( const EC_Group dom_par,
const PointGFp pub_point 
)

Create a public key.

Parameters
dom_parEC domain parameters
pub_pointpublic point on the curve

Definition at line 30 of file ecc_key.cpp.

References domain(), Botan::EC_DOMPAR_ENC_EXPLICIT, Botan::EC_DOMPAR_ENC_OID, Botan::OID::empty(), Botan::EC_Group::get_curve(), Botan::PointGFp::get_curve(), Botan::EC_Group::get_curve_oid(), m_domain_encoding, and public_point().

31  :
32  m_domain_params(dom_par), m_public_key(pub_point)
33  {
34  if (!dom_par.get_curve_oid().empty())
36  else
38 
39 #if 0
40  if(domain().get_curve() != public_point().get_curve())
41  throw Invalid_Argument("EC_PublicKey: curve mismatch in constructor");
42 #endif
43  }
const PointGFp & public_point() const
Definition: ecc_key.h:57
PointGFp m_public_key
Definition: ecc_key.h:115
const CurveGFp & get_curve() const
Definition: ec_group.cpp:392
const EC_Group & domain() const
Definition: ecc_key.h:72
const CurveGFp & get_curve() const
Definition: point_gfp.h:262
EC_Group m_domain_params
Definition: ecc_key.h:114
EC_Group_Encoding m_domain_encoding
Definition: ecc_key.h:116

◆ EC_PublicKey() [2/4]

Botan::EC_PublicKey::EC_PublicKey ( const AlgorithmIdentifier alg_id,
const std::vector< uint8_t > &  key_bits 
)

Load a public key.

Parameters
alg_idthe X.509 algorithm identifier
key_bitsDER encoded public key bits

Definition at line 45 of file ecc_key.cpp.

References Botan::AlgorithmIdentifier::get_parameters().

46  :
47  m_domain_params{EC_Group(alg_id.get_parameters())},
48  m_public_key{domain().OS2ECP(key_bits)}
49  {
50  if (!domain().get_curve_oid().empty())
52  else
54  }
PointGFp m_public_key
Definition: ecc_key.h:115
const EC_Group & domain() const
Definition: ecc_key.h:72
PointGFp OS2ECP(const uint8_t bits[], size_t len) const
Definition: ec_group.cpp:477
EC_Group m_domain_params
Definition: ecc_key.h:114
EC_Group_Encoding m_domain_encoding
Definition: ecc_key.h:116

◆ EC_PublicKey() [3/4]

Botan::EC_PublicKey::EC_PublicKey ( const EC_PublicKey other)
default

◆ ~EC_PublicKey()

virtual Botan::EC_PublicKey::~EC_PublicKey ( )
virtualdefault

◆ EC_PublicKey() [4/4]

Botan::EC_PublicKey::EC_PublicKey ( )
inlineprotected

Definition at line 111 of file ecc_key.h.

Member Function Documentation

◆ algo_name()

virtual std::string Botan::Public_Key::algo_name ( ) const
pure virtualinherited

Get the name of the underlying public key scheme.

Returns
name of the public key scheme

Implemented in Botan::XMSS_WOTS_PublicKey, Botan::XMSS_PublicKey, Botan::TPM_PrivateKey, Botan::XMSS_WOTS_Addressed_PublicKey, Botan::ECDSA_PublicKey, Botan::ECDH_PublicKey, Botan::GOST_3410_PublicKey, Botan::ECGDSA_PublicKey, Botan::ECKCDSA_PublicKey, Botan::SM2_Signature_PublicKey, Botan::SM2_Encryption_PublicKey, Botan::RSA_PublicKey, Botan::McEliece_PublicKey, Botan::DH_PublicKey, Botan::DSA_PublicKey, Botan::Ed25519_PublicKey, Botan::ElGamal_PublicKey, and Botan::Curve25519_PublicKey.

Referenced by Botan::PKCS8::BER_encode(), botan_pubkey_sm2_compute_za(), Botan::TLS::Policy::check_peer_key_acceptable(), Botan::TLS::Handshake_State::choose_sig_format(), Botan::TLS::Client_Key_Exchange::Client_Key_Exchange(), Botan::EMSA1::config_for_x509(), Botan::PSSR::config_for_x509(), Botan::EMSA_PKCS1v15::config_for_x509(), Botan::Private_Key::create_decryption_op(), Botan::Public_Key::create_encryption_op(), Botan::Private_Key::create_kem_decryption_op(), Botan::Public_Key::create_kem_encryption_op(), Botan::Private_Key::create_key_agreement_op(), Botan::Private_Key::create_signature_op(), Botan::Public_Key::create_verification_op(), Botan::Public_Key::get_oid(), Botan::TLS::Handshake_State::parse_sig_format(), Botan::PK_Decryptor_EME::PK_Decryptor_EME(), Botan::PK_Encryptor_EME::PK_Encryptor_EME(), Botan::PK_KEM_Decryptor::PK_KEM_Decryptor(), Botan::PK_KEM_Encryptor::PK_KEM_Encryptor(), Botan::PK_Key_Agreement::PK_Key_Agreement(), Botan::PK_Signer::PK_Signer(), Botan::PK_Verifier::PK_Verifier(), Botan::verify_cert_constraints_valid_for_key_type(), and Botan::X509_Object::verify_signature().

◆ algorithm_identifier()

AlgorithmIdentifier Botan::EC_PublicKey::algorithm_identifier ( ) const
overridevirtual
Returns
X.509 AlgorithmIdentifier for this key

Implements Botan::Public_Key.

Reimplemented in Botan::GOST_3410_PublicKey.

Definition at line 64 of file ecc_key.cpp.

References DER_domain(), and Botan::Public_Key::get_oid().

Referenced by Botan::GOST_3410_PrivateKey::pkcs8_algorithm_identifier().

65  {
66  return AlgorithmIdentifier(get_oid(), DER_domain());
67  }
virtual OID get_oid() const
Definition: pk_keys.cpp:51
std::vector< uint8_t > DER_domain() const
Definition: ecc_key.h:90

◆ check_key()

bool Botan::EC_PublicKey::check_key ( RandomNumberGenerator rng,
bool  strong 
) const
overridevirtual

Test the key values for consistency.

Parameters
rngrng to use
strongwhether to perform strong and lengthy version of the test
Returns
true if the test is passed

Implements Botan::Public_Key.

Reimplemented in Botan::ECDSA_PrivateKey, Botan::ECGDSA_PrivateKey, Botan::ECKCDSA_PrivateKey, Botan::SM2_Signature_PrivateKey, and Botan::SM2_Encryption_PrivateKey.

Definition at line 56 of file ecc_key.cpp.

References m_domain_params, public_point(), Botan::EC_Group::verify_group(), and Botan::EC_Group::verify_public_element().

58  {
59  return m_domain_params.verify_group(rng) &&
61  }
const PointGFp & public_point() const
Definition: ecc_key.h:57
bool verify_public_element(const PointGFp &y) const
Definition: ec_group.cpp:598
EC_Group m_domain_params
Definition: ecc_key.h:114
bool verify_group(RandomNumberGenerator &rng, bool strong=false) const
Definition: ec_group.cpp:621

◆ create_encryption_op()

std::unique_ptr< PK_Ops::Encryption > Botan::Public_Key::create_encryption_op ( RandomNumberGenerator rng,
const std::string &  params,
const std::string &  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
rnga 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.
paramsadditional parameters
providerthe provider to use

Reimplemented in Botan::RSA_PublicKey, Botan::SM2_Encryption_PublicKey, and Botan::ElGamal_PublicKey.

Definition at line 92 of file pk_keys.cpp.

References Botan::Public_Key::algo_name().

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

95  {
96  throw Lookup_Error(algo_name() + " does not support encryption");
97  }
virtual std::string algo_name() const =0

◆ create_kem_encryption_op()

std::unique_ptr< PK_Ops::KEM_Encryption > Botan::Public_Key::create_kem_encryption_op ( RandomNumberGenerator rng,
const std::string &  params,
const std::string &  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
rnga 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.
paramsadditional parameters
providerthe provider to use

Reimplemented in Botan::RSA_PublicKey, and Botan::McEliece_PublicKey.

Definition at line 100 of file pk_keys.cpp.

References Botan::Public_Key::algo_name().

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

103  {
104  throw Lookup_Error(algo_name() + " does not support KEM encryption");
105  }
virtual std::string algo_name() const =0

◆ create_verification_op()

std::unique_ptr< PK_Ops::Verification > Botan::Public_Key::create_verification_op ( const std::string &  params,
const std::string &  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 verification operation for this key/params or throw

Parameters
paramsadditional parameters
providerthe provider to use

Reimplemented in Botan::XMSS_PublicKey, Botan::RSA_PublicKey, Botan::XMSS_WOTS_Addressed_PublicKey, Botan::GOST_3410_PublicKey, Botan::Ed25519_PublicKey, Botan::ECDSA_PublicKey, Botan::ECGDSA_PublicKey, Botan::ECKCDSA_PublicKey, Botan::SM2_Signature_PublicKey, and Botan::DSA_PublicKey.

Definition at line 108 of file pk_keys.cpp.

References Botan::Public_Key::algo_name().

Referenced by Botan::XMSS_WOTS_Addressed_PublicKey::create_verification_op(), and Botan::PK_Verifier::PK_Verifier().

110  {
111  throw Lookup_Error(algo_name() + " does not support verification");
112  }
virtual std::string algo_name() const =0

◆ DER_domain()

std::vector<uint8_t> Botan::EC_PublicKey::DER_domain ( ) const
inline

Return the DER encoding of this keys domain in whatever format is preset for this particular key

Definition at line 90 of file ecc_key.h.

Referenced by algorithm_identifier().

91  { return domain().DER_encode(domain_format()); }
const EC_Group & domain() const
Definition: ecc_key.h:72
EC_Group_Encoding domain_format() const
Definition: ecc_key.h:97
std::vector< uint8_t > DER_encode(EC_Group_Encoding form) const
Definition: ec_group.cpp:533

◆ domain()

const EC_Group& Botan::EC_PublicKey::domain ( ) const
inline

Get the domain parameters of this key.

Exceptions
Invalid_Stateis thrown if the domain parameters of this point are not set
Returns
the domain parameters of this key

Definition at line 72 of file ecc_key.h.

Referenced by Botan::GOST_3410_PublicKey::algorithm_identifier(), botan_pubkey_sm2_compute_za(), Botan::EC_PrivateKey::EC_PrivateKey(), EC_PublicKey(), Botan::GOST_3410_PublicKey::GOST_3410_PublicKey(), key_length(), and Botan::SM2_Signature_PrivateKey::SM2_Signature_PrivateKey().

72 { return m_domain_params; }
EC_Group m_domain_params
Definition: ecc_key.h:114

◆ domain_format()

EC_Group_Encoding Botan::EC_PublicKey::domain_format ( ) const
inline

Get the domain parameter encoding to be used when encoding this key.

Returns
the encoding to use

Definition at line 97 of file ecc_key.h.

98  { return m_domain_encoding; }
EC_Group_Encoding m_domain_encoding
Definition: ecc_key.h:116

◆ estimated_strength()

size_t Botan::EC_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::Public_Key.

Definition at line 25 of file ecc_key.cpp.

References Botan::ecp_work_factor(), and key_length().

26  {
27  return ecp_work_factor(key_length());
28  }
size_t ecp_work_factor(size_t bits)
Definition: workfactor.cpp:14
size_t key_length() const override
Definition: ecc_key.cpp:20

◆ fingerprint_public()

std::string Botan::Public_Key::fingerprint_public ( const std::string &  alg = "SHA-256") const
inherited
Returns
Hash of the subject public key

Definition at line 78 of file pk_keys.cpp.

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

79  {
81  }
AlgorithmIdentifier hash_algo
Definition: x509_obj.cpp:23
std::string create_hex_fingerprint(const uint8_t bits[], size_t bits_len, const std::string &hash_name)
Definition: pk_keys.cpp:17
std::vector< uint8_t > subject_public_key() const
Definition: pk_keys.cpp:38

◆ get_oid()

OID Botan::Public_Key::get_oid ( ) const
virtualinherited

Get the OID of the underlying public key scheme.

Returns
OID of the public key scheme

Reimplemented in Botan::XMSS_WOTS_Addressed_PublicKey.

Definition at line 51 of file pk_keys.cpp.

References Botan::Public_Key::algo_name(), and Botan::OIDS::lookup().

Referenced by Botan::DL_Scheme_PublicKey::algorithm_identifier(), Botan::Curve25519_PublicKey::algorithm_identifier(), Botan::Ed25519_PublicKey::algorithm_identifier(), Botan::McEliece_PublicKey::algorithm_identifier(), Botan::RSA_PublicKey::algorithm_identifier(), Botan::GOST_3410_PublicKey::algorithm_identifier(), algorithm_identifier(), Botan::TPM_PrivateKey::algorithm_identifier(), and Botan::XMSS_WOTS_Addressed_PublicKey::get_oid().

52  {
53  try {
54  return OIDS::lookup(algo_name());
55  }
56  catch(Lookup_Error&)
57  {
58  throw Lookup_Error("PK algo " + algo_name() + " has no defined OIDs");
59  }
60  }
virtual std::string algo_name() const =0
std::string lookup(const OID &oid)
Definition: oids.cpp:113

◆ key_length()

size_t Botan::EC_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 20 of file ecc_key.cpp.

References domain(), and Botan::EC_Group::get_p_bits().

Referenced by estimated_strength().

21  {
22  return domain().get_p_bits();
23  }
size_t get_p_bits() const
Definition: ec_group.cpp:402
const EC_Group & domain() const
Definition: ecc_key.h:72

◆ message_part_size()

virtual size_t Botan::Public_Key::message_part_size ( ) const
inlinevirtualinherited

Returns how large each of the message parts refered 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

Reimplemented in Botan::GOST_3410_PublicKey, Botan::ECDSA_PublicKey, Botan::ECGDSA_PublicKey, Botan::ECKCDSA_PublicKey, Botan::SM2_Signature_PublicKey, and Botan::DSA_PublicKey.

Definition at line 118 of file pk_keys.h.

Referenced by Botan::PK_Signer::PK_Signer(), and Botan::PK_Verifier::PK_Verifier().

118 { return 0; }

◆ message_parts()

virtual size_t Botan::Public_Key::message_parts ( ) const
inlinevirtualinherited

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

Reimplemented in Botan::GOST_3410_PublicKey, Botan::ECDSA_PublicKey, Botan::ECGDSA_PublicKey, Botan::ECKCDSA_PublicKey, Botan::SM2_Signature_PublicKey, and Botan::DSA_PublicKey.

Definition at line 107 of file pk_keys.h.

Referenced by Botan::X509_Object::choose_sig_format(), Botan::PK_Signer::PK_Signer(), Botan::PK_Verifier::PK_Verifier(), and Botan::X509_Object::verify_signature().

107 { return 1; }

◆ operator=()

EC_PublicKey& Botan::EC_PublicKey::operator= ( const EC_PublicKey other)
default

◆ point_encoding()

PointGFp::Compression_Type Botan::EC_PublicKey::point_encoding ( ) const
inline

Get the point encoding method to be used when encoding this key.

Returns
the encoding to use

Definition at line 104 of file ecc_key.h.

Referenced by public_key_bits().

105  { return m_point_encoding; }
PointGFp::Compression_Type m_point_encoding
Definition: ecc_key.h:117

◆ public_key_bits()

std::vector< uint8_t > Botan::EC_PublicKey::public_key_bits ( ) const
overridevirtual
Returns
BER encoded public key bits

Implements Botan::Public_Key.

Reimplemented in Botan::GOST_3410_PublicKey.

Definition at line 69 of file ecc_key.cpp.

References Botan::PointGFp::encode(), point_encoding(), and public_point().

Referenced by Botan::EC_PrivateKey::EC_PrivateKey().

70  {
72  }
std::vector< uint8_t > encode(PointGFp::Compression_Type format) const
Definition: point_gfp.cpp:587
const PointGFp & public_point() const
Definition: ecc_key.h:57
PointGFp::Compression_Type point_encoding() const
Definition: ecc_key.h:104

◆ public_point()

const PointGFp& Botan::EC_PublicKey::public_point ( ) const
inline

◆ set_parameter_encoding()

void Botan::EC_PublicKey::set_parameter_encoding ( EC_Group_Encoding  enc)

Set the domain parameter encoding to be used when encoding this key.

Parameters
encthe encoding to use

Definition at line 84 of file ecc_key.cpp.

References Botan::EC_DOMPAR_ENC_EXPLICIT, Botan::EC_DOMPAR_ENC_IMPLICITCA, Botan::EC_DOMPAR_ENC_OID, Botan::OID::empty(), Botan::EC_Group::get_curve_oid(), m_domain_encoding, and m_domain_params.

85  {
86  if(form != EC_DOMPAR_ENC_EXPLICIT &&
87  form != EC_DOMPAR_ENC_IMPLICITCA &&
88  form != EC_DOMPAR_ENC_OID)
89  throw Invalid_Argument("Invalid encoding form for EC-key object specified");
90 
92  throw Invalid_Argument("Invalid encoding form OID specified for "
93  "EC-key object whose corresponding domain "
94  "parameters are without oid");
95 
96  m_domain_encoding = form;
97  }
const OID & get_curve_oid() const
Definition: ec_group.cpp:472
bool empty() const
Definition: asn1_oid.h:30
EC_Group m_domain_params
Definition: ecc_key.h:114
EC_Group_Encoding m_domain_encoding
Definition: ecc_key.h:116

◆ set_point_encoding()

void Botan::EC_PublicKey::set_point_encoding ( PointGFp::Compression_Type  enc)

Set the point encoding method to be used when encoding this key.

Parameters
encthe encoding to use

Definition at line 74 of file ecc_key.cpp.

References Botan::PointGFp::COMPRESSED, Botan::PointGFp::HYBRID, m_point_encoding, and Botan::PointGFp::UNCOMPRESSED.

75  {
76  if(enc != PointGFp::COMPRESSED &&
77  enc != PointGFp::UNCOMPRESSED &&
78  enc != PointGFp::HYBRID)
79  throw Invalid_Argument("Invalid point encoding for EC_PublicKey");
80 
81  m_point_encoding = enc;
82  }
PointGFp::Compression_Type m_point_encoding
Definition: ecc_key.h:117

◆ 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 38 of file pk_keys.cpp.

References Botan::Public_Key::algorithm_identifier(), Botan::BIT_STRING, Botan::DER_Encoder::encode(), Botan::DER_Encoder::end_cons(), Botan::DER_Encoder::get_contents_unlocked(), Botan::Public_Key::public_key_bits(), Botan::SEQUENCE, and Botan::DER_Encoder::start_cons().

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

39  {
40  return DER_Encoder()
41  .start_cons(SEQUENCE)
42  .encode(algorithm_identifier())
43  .encode(public_key_bits(), BIT_STRING)
44  .end_cons()
45  .get_contents_unlocked();
46  }
virtual std::vector< uint8_t > public_key_bits() const =0
virtual AlgorithmIdentifier algorithm_identifier() const =0

Member Data Documentation

◆ m_domain_encoding

EC_Group_Encoding Botan::EC_PublicKey::m_domain_encoding
protected

◆ m_domain_params

EC_Group Botan::EC_PublicKey::m_domain_params
protected

◆ m_point_encoding

PointGFp::Compression_Type Botan::EC_PublicKey::m_point_encoding = PointGFp::UNCOMPRESSED
protected

Definition at line 117 of file ecc_key.h.

Referenced by set_point_encoding().

◆ m_public_key

PointGFp Botan::EC_PublicKey::m_public_key
protected

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