#include <ec_group.h>

Classes
class	Mul2Table
	Table for computing gx + hy. More...

Public Member Functions
const std::shared_ptr< EC_Group_Data > &	_data () const

bool	a_is_minus_3 () const

bool	a_is_zero () const

BigInt	cube_mod_order (const BigInt &x) const

std::vector< uint8_t >	DER_encode () const

std::vector< uint8_t >	DER_encode (EC_Group_Encoding form) const

	EC_Group ()

	EC_Group (const BigInt &p, const BigInt &a, const BigInt &b, const BigInt &base_x, const BigInt &base_y, const BigInt &order, const BigInt &cofactor, const OID &oid=OID())

	EC_Group (const EC_Group &)

	EC_Group (const OID &oid)

	EC_Group (const OID &oid, const BigInt &p, const BigInt &a, const BigInt &b, const BigInt &base_x, const BigInt &base_y, const BigInt &order)

	EC_Group (const uint8_t ber[], size_t ber_len)

	EC_Group (EC_Group &&)=default

	EC_Group (std::span< const uint8_t > ber)

	EC_Group (std::string_view pem_or_oid)

EC_Group_Engine	engine () const

const BigInt &	get_a () const

const BigInt &	get_b () const

const BigInt &	get_cofactor () const

const OID &	get_curve_oid () const

const BigInt &	get_g_x () const

const BigInt &	get_g_y () const

const BigInt &	get_order () const

size_t	get_order_bits () const

size_t	get_order_bytes () const

const BigInt &	get_p () const

size_t	get_p_bits () const

size_t	get_p_bytes () const

bool	has_cofactor () const

bool	initialized () const

BigInt	inverse_mod_order (const BigInt &x) const

BigInt	mod_order (const BigInt &x) const

BigInt	multiply_mod_order (const BigInt &x, const BigInt &y) const

BigInt	multiply_mod_order (const BigInt &x, const BigInt &y, const BigInt &z) const

EC_Group &	operator= (const EC_Group &)

EC_Group &	operator= (EC_Group &&)=default

bool	operator== (const EC_Group &other) const

std::string	PEM_encode (EC_Group_Encoding form=EC_Group_Encoding::Explicit) const

size_t	point_size (EC_Point_Format format) const

EC_Group_Source	source () const

BigInt	square_mod_order (const BigInt &x) const

bool	used_explicit_encoding () const

bool	verify_group (RandomNumberGenerator &rng, bool strong=false) const

	~EC_Group ()

Static Public Member Functions
static size_t	clear_registered_curve_data ()

static EC_Group	EC_Group_from_PEM (std::string_view pem)

static OID	EC_group_identity_from_order (const BigInt &order)

static std::shared_ptr< EC_Group_Data >	EC_group_info (const OID &oid)

static EC_Group	from_name (std::string_view name)

static EC_Group	from_OID (const OID &oid)

static EC_Group	from_PEM (std::string_view pem)

static const std::set< std::string > &	known_named_groups ()

static bool	supports_application_specific_group ()

static bool	supports_named_group (std::string_view name)

Detailed Description

Class representing an elliptic curve

The internal representation is stored in a shared_ptr, so copying an EC_Group is inexpensive.

Definition at line 87 of file ec_group.h.

Constructor & Destructor Documentation

◆ EC_Group() [1/9]

Botan::EC_Group::EC_Group	(	const BigInt &	p,
		const BigInt &	a,
		const BigInt &	b,
		const BigInt &	base_x,
		const BigInt &	base_y,
		const BigInt &	order,
		const BigInt &	cofactor,
		const OID &	oid = OID() )

Construct elliptic curve from the specified parameters

This is used for example to create custom (application-specific) curves.

Some build configurations do not support application specific curves, in which case this constructor will throw an exception. You can check for this situation beforehand using the function EC_Group::supports_application_specific_group()

Parameters

p	the elliptic curve p
a	the elliptic curve a param
b	the elliptic curve b param
base_x	the x coordinate of the base point
base_y	the y coordinate of the base point
order	the order of the base point
cofactor	the cofactor
oid	an optional OID used to identify this curve

Warning: This constructor is deprecated and will be removed in Botan 4; support for cofactors > 1 is deprecated and will be removed; support for prime fields > 521 bits is deprecated and will be removed.; Support for explicitly encoded curve parameters is deprecated. An OID must be assigned.

Definition at line 419 of file ec_group.cpp.

                                   {
   if(oid.has_value()) {
      m_data = ec_group_data().lookup_or_create(
         p, a, b, base_x, base_y, order, cofactor, oid, EC_Group_Source::ExternalSource);
   } else {
      m_data = ec_group_data().lookup_or_create_without_oid(
         p, a, b, base_x, base_y, order, cofactor, EC_Group_Source::ExternalSource);
   }
}

References Botan::ExternalSource, and Botan::OID::has_value().

Referenced by EC_Group(), EC_Group(), EC_Group(), EC_Group(), EC_Group(), EC_Group_from_PEM(), from_name(), from_OID(), from_PEM(), operator=(), operator=(), operator==(), and ~EC_Group().

◆ EC_Group() [2/9]

Botan::EC_Group::EC_Group	(	const OID &	oid,
		const BigInt &	p,
		const BigInt &	a,
		const BigInt &	b,
		const BigInt &	base_x,
		const BigInt &	base_y,
		const BigInt &	order )

Construct elliptic curve from the specified parameters

This is used for example to create custom (application-specific) curves.

Some build configurations do not support application specific curves, in which case this constructor will throw an exception. You can check for this situation beforehand using the function EC_Group::supports_application_specific_group()

Unlike the deprecated constructor, this constructor imposes additional restrictions on the parameters, namely:

An object identifier must be provided
The prime must be at least 192 bits and at most 512 bits, and a multiple of 32 bits. Currently, as long as BOTAN_DISABLE_DEPRECATED_FEATURES is not set, this constructor accepts primes as small as 128 bits - this lower bound will be removed in the next major release.
As an extension of the above restriction, the prime can also be exactly the 521-bit Mersenne prime (2**521-1) or exactly the 239-bit prime used in X9.62 239 bit groups (2**239 - 2**143 - 2**95 + 2**47 - 1)
The prime must be congruent to 3 modulo 4
The group order must have the same bit length as the prime. It is allowed for the order to be larger than p, but they must have the same bit length.
Only prime order curves (with cofactor == 1) are allowed

Warning: use only elliptic curve parameters that you trust

Parameters

oid	an object identifier used to identify this curve
p	the elliptic curve prime (at most 521 bits)
a	the elliptic curve a param
b	the elliptic curve b param
base_x	the x coordinate of the group generator
base_y	the y coordinate of the group generator
order	the order of the group

Definition at line 436 of file ec_group.cpp.

                                        {
   BOTAN_ARG_CHECK(oid.has_value(), "An OID is required for creating an EC_Group");
 
   // TODO(Botan4) remove this and require 192 bits minimum
#if defined(BOTAN_DISABLE_DEPRECATED_FEATURES)
   constexpr size_t p_bits_lower_bound = 192;
#else
   constexpr size_t p_bits_lower_bound = 128;
#endif
 
   BOTAN_ARG_CHECK(p.bits() >= p_bits_lower_bound, "EC_Group p too small");
   BOTAN_ARG_CHECK(p.bits() <= 521, "EC_Group p too large");
 
   if(p.bits() == 521) {
      const auto p521 = BigInt::power_of_2(521) - 1;
      BOTAN_ARG_CHECK(p == p521, "EC_Group with p of 521 bits must be 2**521-1");
   } else if(p.bits() == 239) {
      const auto x962_p239 = []() {
         BigInt p239;
         for(size_t i = 0; i != 239; ++i) {
            if(i < 47 || ((i >= 94) && (i != 143))) {
               p239.set_bit(i);
            }
         }
         return p239;
      }();
 
      BOTAN_ARG_CHECK(p == x962_p239, "EC_Group with p of 239 bits must be the X9.62 prime");
   } else {
      BOTAN_ARG_CHECK(p.bits() % 32 == 0, "EC_Group p must be a multiple of 32 bits");
   }
 
   BOTAN_ARG_CHECK(p % 4 == 3, "EC_Group p must be congruent to 3 modulo 4");
 
   BOTAN_ARG_CHECK(a >= 0 && a < p, "EC_Group a is invalid");
   BOTAN_ARG_CHECK(b > 0 && b < p, "EC_Group b is invalid");
   BOTAN_ARG_CHECK(base_x >= 0 && base_x < p, "EC_Group base_x is invalid");
   BOTAN_ARG_CHECK(base_y >= 0 && base_y < p, "EC_Group base_y is invalid");
   BOTAN_ARG_CHECK(p.bits() == order.bits(), "EC_Group p and order must have the same number of bits");
 
   auto mod_p = Barrett_Reduction::for_public_modulus(p);
   BOTAN_ARG_CHECK(is_bailie_psw_probable_prime(p, mod_p), "EC_Group p is not prime");
 
   auto mod_order = Barrett_Reduction::for_public_modulus(order);
   BOTAN_ARG_CHECK(is_bailie_psw_probable_prime(order, mod_order), "EC_Group order is not prime");
 
   // This catches someone "ignoring" a cofactor and just trying to
   // provide the subgroup order
   BOTAN_ARG_CHECK((p - order).abs().bits() <= (p.bits() / 2) + 1, "Hasse bound invalid");
 
   // Check that 4*a^3 + 27*b^2 != 0
   const auto discriminant = mod_p.reduce(mod_p.multiply(4, mod_p.cube(a)) + mod_p.multiply(27, mod_p.square(b)));
   BOTAN_ARG_CHECK(discriminant != 0, "EC_Group discriminant is invalid");
 
   // Check that the generator (base_x,base_y) is on the curve; y^2 = x^3 + a*x + b
   auto y2 = mod_p.square(base_y);
   auto x3_ax_b = mod_p.reduce(mod_p.cube(base_x) + mod_p.multiply(a, base_x) + b);
   BOTAN_ARG_CHECK(y2 == x3_ax_b, "EC_Group generator is not on the curve");
 
   BigInt cofactor(1);
 
   m_data =
      ec_group_data().lookup_or_create(p, a, b, base_x, base_y, order, cofactor, oid, EC_Group_Source::ExternalSource);
}

References Botan::abs(), Botan::BigInt::bits(), BOTAN_ARG_CHECK, Botan::ExternalSource, Botan::Barrett_Reduction::for_public_modulus(), Botan::OID::has_value(), Botan::is_bailie_psw_probable_prime(), mod_order(), Botan::BigInt::power_of_2(), and Botan::BigInt::set_bit().

◆ EC_Group() [3/9]

Botan::EC_Group::EC_Group ( std::span< const uint8_t > ber )

explicit

Decode a BER encoded ECC domain parameter set

Parameters

ber	the bytes of the BER encoding

Definition at line 507 of file ec_group.cpp.

                                             {
   auto data = BER_decode_EC_group(ber, EC_Group_Source::ExternalSource);
   m_data = data.first;
   m_explicit_encoding = data.second;
}

References Botan::ExternalSource.

◆ EC_Group() [4/9]

Botan::EC_Group::EC_Group	(	const uint8_t	ber[],
		size_t	ber_len )

inline

Definition at line 184 of file ec_group.h.

184: EC_Group(std::span{ber, ber_len}) {}

Botan::EC_Group::EC_Group

EC_Group()

References EC_Group().

◆ EC_Group() [5/9]

Botan::EC_Group::EC_Group ( const OID & oid )

inlineexplicit

Create an EC domain by OID (or throw if unknown)

Parameters

oid	the OID of the EC domain to create

Definition at line 190 of file ec_group.h.

190{ *this = EC_Group::from_OID(oid); }

Botan::EC_Group::from_OID

static EC_Group from_OID(const OID &oid)

Definition ec_group.cpp:360

References EC_Group(), and from_OID().

◆ EC_Group() [6/9]

Botan::EC_Group::EC_Group ( std::string_view pem_or_oid )

explicit

Create an EC domain from PEM encoding (as from PEM_encode()), or from an OID name (eg "secp256r1", or "1.2.840.10045.3.1.7")

Parameters

pem_or_oid PEM-encoded data, or an OID

Warning: Support for PEM in this function is deprecated. Use EC_Group::from_PEM or EC_Group::from_OID or EC_Group::from_name

Definition at line 385 of file ec_group.cpp.

                                     {
   if(str.empty()) {
      return;  // no initialization / uninitialized
   }
 
   try {
      const OID oid = OID::from_string(str);
      if(oid.has_value()) {
         m_data = ec_group_data().lookup(oid);
      }
   } catch(...) {}
 
   if(m_data == nullptr) {
      if(str.size() > 30 && str.substr(0, 29) == "-----BEGIN EC PARAMETERS-----") {
         // OK try it as PEM ...
         const auto ber = PEM_Code::decode_check_label(str, "EC PARAMETERS");
 
         auto data = BER_decode_EC_group(ber, EC_Group_Source::ExternalSource);
         this->m_data = data.first;
         this->m_explicit_encoding = data.second;
      }
   }
 
   if(m_data == nullptr) {
      throw Invalid_Argument(fmt("Unknown ECC group '{}'", str));
   }
}

References Botan::PEM_Code::decode_check_label(), Botan::ExternalSource, Botan::fmt(), Botan::OID::from_string(), and Botan::OID::has_value().

◆ EC_Group() [7/9]

Botan::EC_Group::EC_Group ( )

default

Create an uninitialized EC_Group

References EC_Group().

Referenced by from_name(), from_OID(), and from_PEM().

◆ ~EC_Group()

Botan::EC_Group::~EC_Group ( )

default

References EC_Group().

◆ EC_Group() [8/9]

Botan::EC_Group::EC_Group ( const EC_Group & )

default

References EC_Group().

◆ EC_Group() [9/9]

Botan::EC_Group::EC_Group ( EC_Group && )

default

References EC_Group().

Member Function Documentation

◆ _data()

const std::shared_ptr< EC_Group_Data > & Botan::EC_Group::_data ( ) const

inline

Definition at line 451 of file ec_group.h.

451{ return m_data; }

Referenced by Botan::EC_AffinePoint::deserialize(), Botan::EC_Scalar::deserialize(), Botan::EC_AffinePoint::EC_AffinePoint(), Botan::EC_Scalar::EC_Scalar(), Botan::EC_Scalar::from_bigint(), Botan::EC_Scalar::from_bytes_mod_order(), Botan::EC_Scalar::from_bytes_with_trunc(), Botan::EC_AffinePoint::hash_to_curve_nu(), Botan::EC_AffinePoint::hash_to_curve_ro(), Botan::EC_Scalar::one(), and Botan::EC_Scalar::random().

◆ a_is_minus_3()

bool Botan::EC_Group::a_is_minus_3 ( ) const

inline

Return if a == -3 mod p

Definition at line 640 of file ec_group.h.

640{ return get_a() + 3 == get_p(); }

Botan::EC_Group::get_a

const BigInt & get_a() const

Definition ec_group.cpp:540

Botan::EC_Group::get_p

const BigInt & get_p() const

Definition ec_group.cpp:536

References a_is_minus_3(), get_a(), and get_p().

Referenced by a_is_minus_3().

◆ a_is_zero()

bool Botan::EC_Group::a_is_zero ( ) const

inline

Return if a == 0 mod p

Definition at line 645 of file ec_group.h.

645{ return get_a().is_zero(); }

Botan::BigInt::is_zero

bool is_zero() const

Definition bigint.h:457

References a_is_zero(), and get_a().

Referenced by a_is_zero().

◆ clear_registered_curve_data()

size_t Botan::EC_Group::clear_registered_curve_data ( )

static

Definition at line 187 of file ec_group.cpp.

                                             {
   return ec_group_data().clear();
}

◆ cube_mod_order()

BigInt Botan::EC_Group::cube_mod_order ( const BigInt & x ) const

inline

Definition at line 693 of file ec_group.h.

                                                                                                 {
         auto xs = EC_Scalar::from_bigint(*this, x);
         return (xs * xs * xs).to_bigint();
      }

References cube_mod_order(), and Botan::EC_Scalar::from_bigint().

Referenced by cube_mod_order().

◆ DER_encode() [1/2]

std::vector< uint8_t > Botan::EC_Group::DER_encode ( ) const

Create the DER encoding of this domain, using namedCurve format

Returns: the group information encoded as DER

Definition at line 616 of file ec_group.cpp.

                                              {
   const auto& der_named_curve = data().der_named_curve();
   // TODO(Botan4) this can be removed because an OID will always be defined
   if(der_named_curve.empty()) {
      throw Encoding_Error("Cannot encode EC_Group as OID because OID not set");
   }
 
   return der_named_curve;
}

Referenced by DER_encode(), and PEM_encode().

◆ DER_encode() [2/2]

std::vector< uint8_t > Botan::EC_Group::DER_encode ( EC_Group_Encoding form ) const

Create the DER encoding of this domain

Parameters

form	of encoding to use

Returns: the group information encoded as DER

Definition at line 626 of file ec_group.cpp.

                                                                    {
   if(form == EC_Group_Encoding::Explicit) {
      std::vector<uint8_t> output;
      DER_Encoder der(output);
      const size_t ecpVers1 = 1;
      const OID curve_type("1.2.840.10045.1.1");  // prime field
 
      const size_t p_bytes = get_p_bytes();
 
      const auto generator = EC_AffinePoint::generator(*this).serialize_uncompressed();
 
      der.start_sequence()
         .encode(ecpVers1)
         .start_sequence()
         .encode(curve_type)
         .encode(get_p())
         .end_cons()
         .start_sequence()
         .encode(get_a().serialize(p_bytes), ASN1_Type::OctetString)
         .encode(get_b().serialize(p_bytes), ASN1_Type::OctetString)
         .end_cons()
         .encode(generator, ASN1_Type::OctetString)
         .encode(get_order())
         .encode(get_cofactor())
         .end_cons();
      return output;
   } else if(form == EC_Group_Encoding::NamedCurve) {
      return this->DER_encode();
   } else if(form == EC_Group_Encoding::ImplicitCA) {
      return {0x00, 0x05};
   } else {
      throw Internal_Error("EC_Group::DER_encode: Unknown encoding");
   }
}

References DER_encode(), Botan::DER_Encoder::encode(), Botan::DER_Encoder::end_cons(), Botan::Explicit, Botan::EC_AffinePoint::generator(), get_a(), get_b(), get_cofactor(), get_order(), get_p(), get_p_bytes(), Botan::ImplicitCA, Botan::NamedCurve, Botan::OctetString, Botan::EC_AffinePoint::serialize_uncompressed(), and Botan::DER_Encoder::start_sequence().

Referenced by Botan::EC_PublicKey::DER_domain(), and Botan::TLS::Signature_Scheme::key_algorithm_identifier().

◆ EC_Group_from_PEM()

static EC_Group Botan::EC_Group::EC_Group_from_PEM ( std::string_view pem )

inlinestatic

Definition at line 217 of file ec_group.h.

                                                                                                     {
         return EC_Group::from_PEM(pem);
      }

References BOTAN_DEPRECATED, EC_Group(), EC_Group_from_PEM(), and from_PEM().

Referenced by EC_Group_from_PEM().

◆ EC_group_identity_from_order()

OID Botan::EC_Group::EC_group_identity_from_order ( const BigInt & order )

static

Definition at line 356 of file ec_named.cpp.

   {
   const uint32_t low_bits = static_cast<uint32_t>(order.word_at(0));
 
   if(low_bits == 0xFC632551 && order == BigInt("0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551")) {
      return OID{1, 2, 840, 10045, 3, 1, 7};
   }
 
   if(low_bits == 0xCCC52973 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) {
      return OID{1, 3, 132, 0, 34};
   }
 
   if(low_bits == 0x91386409 && order == BigInt("0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409")) {
      return OID{1, 3, 132, 0, 35};
   }
 
   if(low_bits == 0x9E60FC09 && order == BigInt("0xE95E4A5F737059DC60DF5991D45029409E60FC09")) {
      return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 1};
   }
 
   if(low_bits == 0x9AC4ACC1 && order == BigInt("0xC302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1")) {
      return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 3};
   }
 
   if(low_bits == 0xA5A7939F && order == BigInt("0xD7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F")) {
      return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 5};
   }
 
   if(low_bits == 0x974856A7 && order == BigInt("0xA9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7")) {
      return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 7};
   }
 
   if(low_bits == 0x44C59311 && order == BigInt("0xD35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D482EC7EE8658E98691555B44C59311")) {
      return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 9};
   }
 
   if(low_bits == 0xE9046565 && order == BigInt("0x8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565")) {
      return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 11};
   }
 
   if(low_bits == 0x9CA90069 && order == BigInt("0xAADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069")) {
      return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 13};
   }
 
   if(low_bits == 0xC6D655E1 && order == BigInt("0xF1FD178C0B3AD58F10126DE8CE42435B53DC67E140D2BF941FFDD459C6D655E1")) {
      return OID{1, 2, 250, 1, 223, 101, 256, 1};
   }
 
   if(low_bits == 0xB761B893 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893")) {
      return OID{1, 2, 643, 7, 1, 2, 1, 1, 1};
   }
 
   if(low_bits == 0x1F10B275 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275")) {
      return OID{1, 2, 643, 7, 1, 2, 1, 2, 1};
   }
 
   if(low_bits == 0xCA16B6B3 && order == BigInt("0x100000000000000000001B8FA16DFAB9ACA16B6B3")) {
      return OID{1, 3, 132, 0, 9};
   }
 
   if(low_bits == 0xCA752257 && order == BigInt("0x100000000000000000001F4C8F927AED3CA752257")) {
      return OID{1, 3, 132, 0, 8};
   }
 
   if(low_bits == 0xF3A1A16B && order == BigInt("0x100000000000000000000351EE786A818F3A1A16B")) {
      return OID{1, 3, 132, 0, 30};
   }
 
   if(low_bits == 0x74DEFD8D && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D")) {
      return OID{1, 3, 132, 0, 31};
   }
 
   if(low_bits == 0xB4D22831 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) {
      return OID{1, 2, 840, 10045, 3, 1, 1};
   }
 
   if(low_bits == 0x769FB1F7 && order == BigInt("0x10000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7")) {
      return OID{1, 3, 132, 0, 32};
   }
 
   if(low_bits == 0x5C5C2A3D && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) {
      return OID{1, 3, 132, 0, 33};
   }
 
   if(low_bits == 0xD0364141 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141")) {
      return OID{1, 3, 132, 0, 10};
   }
 
   if(low_bits == 0x39D54123 && order == BigInt("0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123")) {
      return OID{1, 2, 156, 10197, 1, 301};
   }
 
   if(low_bits == 0x48D8DD31 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFE5FB1A724DC80418648D8DD31")) {
      return OID{1, 2, 840, 10045, 3, 1, 2};
   }
 
   if(low_bits == 0xF640EC13 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFF7A62D031C83F4294F640EC13")) {
      return OID{1, 2, 840, 10045, 3, 1, 3};
   }
 
   if(low_bits == 0x88909D0B && order == BigInt("0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF9E5E9A9F5D9071FBD1522688909D0B")) {
      return OID{1, 2, 840, 10045, 3, 1, 4};
   }
 
   if(low_bits == 0xBC582063 && order == BigInt("0x7FFFFFFFFFFFFFFFFFFFFFFF800000CFA7E8594377D414C03821BC582063")) {
      return OID{1, 2, 840, 10045, 3, 1, 5};
   }
 
   if(low_bits == 0x46526551 && order == BigInt("0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF975DEB41B3A6057C3C432146526551")) {
      return OID{1, 2, 840, 10045, 3, 1, 6};
   }
 
   if(low_bits == 0x0433555D && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5B3CA4FB94E7831B4FC258ED97D0BDC63B568B36607CD243CE153F390433555D")) {
      return OID{1, 3, 6, 1, 4, 1, 25258, 4, 3};
   }
 
   return OID();
}

References Botan::BigInt::word_at().

◆ EC_group_info()

std::shared_ptr< EC_Group_Data > Botan::EC_Group::EC_group_info ( const OID & oid )

static

Definition at line 15 of file ec_named.cpp.

                                                                   {
   // secp256r1
   if(oid == OID{1, 2, 840, 10045, 3, 1, 7}) {
      return load_EC_group_info(
         "0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",
         "0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",
         "0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",
         "0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296",
         "0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5",
         "0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",
         oid);
   }
 
   // secp384r1
   if(oid == OID{1, 3, 132, 0, 34}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC",
         "0xB3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF",
         "0xAA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7",
         "0x3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973",
         oid);
   }
 
   // secp521r1
   if(oid == OID{1, 3, 132, 0, 35}) {
      return load_EC_group_info(
         "0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
         "0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC",
         "0x51953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00",
         "0xC6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66",
         "0x11839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650",
         "0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",
         oid);
   }
 
   // brainpool160r1
   if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 1}) {
      return load_EC_group_info(
         "0xE95E4A5F737059DC60DFC7AD95B3D8139515620F",
         "0x340E7BE2A280EB74E2BE61BADA745D97E8F7C300",
         "0x1E589A8595423412134FAA2DBDEC95C8D8675E58",
         "0xBED5AF16EA3F6A4F62938C4631EB5AF7BDBCDBC3",
         "0x1667CB477A1A8EC338F94741669C976316DA6321",
         "0xE95E4A5F737059DC60DF5991D45029409E60FC09",
         oid);
   }
 
   // brainpool192r1
   if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 3}) {
      return load_EC_group_info(
         "0xC302F41D932A36CDA7A3463093D18DB78FCE476DE1A86297",
         "0x6A91174076B1E0E19C39C031FE8685C1CAE040E5C69A28EF",
         "0x469A28EF7C28CCA3DC721D044F4496BCCA7EF4146FBF25C9",
         "0xC0A0647EAAB6A48753B033C56CB0F0900A2F5C4853375FD6",
         "0x14B690866ABD5BB88B5F4828C1490002E6773FA2FA299B8F",
         "0xC302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1",
         oid);
   }
 
   // brainpool224r1
   if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 5}) {
      return load_EC_group_info(
         "0xD7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FF",
         "0x68A5E62CA9CE6C1C299803A6C1530B514E182AD8B0042A59CAD29F43",
         "0x2580F63CCFE44138870713B1A92369E33E2135D266DBB372386C400B",
         "0xD9029AD2C7E5CF4340823B2A87DC68C9E4CE3174C1E6EFDEE12C07D",
         "0x58AA56F772C0726F24C6B89E4ECDAC24354B9E99CAA3F6D3761402CD",
         "0xD7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F",
         oid);
   }
 
   // brainpool256r1
   if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 7}) {
      return load_EC_group_info(
         "0xA9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377",
         "0x7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9",
         "0x26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6",
         "0x8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262",
         "0x547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997",
         "0xA9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7",
         oid);
   }
 
   // brainpool320r1
   if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 9}) {
      return load_EC_group_info(
         "0xD35E472036BC4FB7E13C785ED201E065F98FCFA6F6F40DEF4F92B9EC7893EC28FCD412B1F1B32E27",
         "0x3EE30B568FBAB0F883CCEBD46D3F3BB8A2A73513F5EB79DA66190EB085FFA9F492F375A97D860EB4",
         "0x520883949DFDBC42D3AD198640688A6FE13F41349554B49ACC31DCCD884539816F5EB4AC8FB1F1A6",
         "0x43BD7E9AFB53D8B85289BCC48EE5BFE6F20137D10A087EB6E7871E2A10A599C710AF8D0D39E20611",
         "0x14FDD05545EC1CC8AB4093247F77275E0743FFED117182EAA9C77877AAAC6AC7D35245D1692E8EE1",
         "0xD35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D482EC7EE8658E98691555B44C59311",
         oid);
   }
 
   // brainpool384r1
   if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 11}) {
      return load_EC_group_info(
         "0x8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A71874700133107EC53",
         "0x7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F90F8AA5814A503AD4EB04A8C7DD22CE2826",
         "0x4A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62D57CB4390295DBC9943AB78696FA504C11",
         "0x1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10E8E826E03436D646AAEF87B2E247D4AF1E",
         "0x8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129280E4646217791811142820341263C5315",
         "0x8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565",
         oid);
   }
 
   // brainpool512r1
   if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 13}) {
      return load_EC_group_info(
         "0xAADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3",
         "0x7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA",
         "0x3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723",
         "0x81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D0098EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822",
         "0x7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F8111B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892",
         "0xAADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069",
         oid);
   }
 
   // frp256v1
   if(oid == OID{1, 2, 250, 1, 223, 101, 256, 1}) {
      return load_EC_group_info(
         "0xF1FD178C0B3AD58F10126DE8CE42435B3961ADBCABC8CA6DE8FCF353D86E9C03",
         "0xF1FD178C0B3AD58F10126DE8CE42435B3961ADBCABC8CA6DE8FCF353D86E9C00",
         "0xEE353FCA5428A9300D4ABA754A44C00FDFEC0C9AE4B1A1803075ED967B7BB73F",
         "0xB6B3D4C356C139EB31183D4749D423958C27D2DCAF98B70164C97A2DD98F5CFF",
         "0x6142E0F7C8B204911F9271F0F3ECEF8C2701C307E8E4C9E183115A1554062CFB",
         "0xF1FD178C0B3AD58F10126DE8CE42435B53DC67E140D2BF941FFDD459C6D655E1",
         oid);
   }
 
   // gost_256A
   if(oid == OID{1, 2, 643, 7, 1, 2, 1, 1, 1} || oid == OID{1, 2, 643, 2, 2, 35, 1} || oid == OID{1, 2, 643, 2, 2, 36, 0}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD94",
         "0xA6",
         "0x1",
         "0x8D91E471E0989CDA27DF505A453F2B7635294F2DDF23E3B122ACC99C9E9F1E14",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893",
         OID{1, 2, 643, 7, 1, 2, 1, 1, 1});
   }
 
   // gost_512A
   if(oid == OID{1, 2, 643, 7, 1, 2, 1, 2, 1}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4",
         "0xE8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760",
         "0x3",
         "0x7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275",
         oid);
   }
 
   // secp160k1
   if(oid == OID{1, 3, 132, 0, 9}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",
         "0x0",
         "0x7",
         "0x3B4C382CE37AA192A4019E763036F4F5DD4D7EBB",
         "0x938CF935318FDCED6BC28286531733C3F03C4FEE",
         "0x100000000000000000001B8FA16DFAB9ACA16B6B3",
         oid);
   }
 
   // secp160r1
   if(oid == OID{1, 3, 132, 0, 8}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC",
         "0x1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45",
         "0x4A96B5688EF573284664698968C38BB913CBFC82",
         "0x23A628553168947D59DCC912042351377AC5FB32",
         "0x100000000000000000001F4C8F927AED3CA752257",
         oid);
   }
 
   // secp160r2
   if(oid == OID{1, 3, 132, 0, 30}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC70",
         "0xB4E134D3FB59EB8BAB57274904664D5AF50388BA",
         "0x52DCB034293A117E1F4FF11B30F7199D3144CE6D",
         "0xFEAFFEF2E331F296E071FA0DF9982CFEA7D43F2E",
         "0x100000000000000000000351EE786A818F3A1A16B",
         oid);
   }
 
   // secp192k1
   if(oid == OID{1, 3, 132, 0, 31}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37",
         "0x0",
         "0x3",
         "0xDB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D",
         "0x9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D",
         "0xFFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D",
         oid);
   }
 
   // secp192r1
   if(oid == OID{1, 2, 840, 10045, 3, 1, 1}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
         "0x64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1",
         "0x188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012",
         "0x7192B95FFC8DA78631011ED6B24CDD573F977A11E794811",
         "0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",
         oid);
   }
 
   // secp224k1
   if(oid == OID{1, 3, 132, 0, 32}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D",
         "0x0",
         "0x5",
         "0xA1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C",
         "0x7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5",
         "0x10000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7",
         oid);
   }
 
   // secp224r1
   if(oid == OID{1, 3, 132, 0, 33}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
         "0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
         "0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
         "0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
         oid);
   }
 
   // secp256k1
   if(oid == OID{1, 3, 132, 0, 10}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F",
         "0x0",
         "0x7",
         "0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798",
         "0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",
         oid);
   }
 
   // sm2p256v1
   if(oid == OID{1, 2, 156, 10197, 1, 301}) {
      return load_EC_group_info(
         "0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF",
         "0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC",
         "0x28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93",
         "0x32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7",
         "0xBC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0",
         "0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123",
         oid);
   }
 
   // x962_p192v2
   if(oid == OID{1, 2, 840, 10045, 3, 1, 2}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
         "0xCC22D6DFB95C6B25E49C0D6364A4E5980C393AA21668D953",
         "0xEEA2BAE7E1497842F2DE7769CFE9C989C072AD696F48034A",
         "0x6574D11D69B6EC7A672BB82A083DF2F2B0847DE970B2DE15",
         "0xFFFFFFFFFFFFFFFFFFFFFFFE5FB1A724DC80418648D8DD31",
         oid);
   }
 
   // x962_p192v3
   if(oid == OID{1, 2, 840, 10045, 3, 1, 3}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
         "0x22123DC2395A05CAA7423DAECCC94760A7D462256BD56916",
         "0x7D29778100C65A1DA1783716588DCE2B8B4AEE8E228F1896",
         "0x38A90F22637337334B49DCB66A6DC8F9978ACA7648A943B0",
         "0xFFFFFFFFFFFFFFFFFFFFFFFF7A62D031C83F4294F640EC13",
         oid);
   }
 
   // x962_p239v1
   if(oid == OID{1, 2, 840, 10045, 3, 1, 4}) {
      return load_EC_group_info(
         "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",
         "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",
         "0x6B016C3BDCF18941D0D654921475CA71A9DB2FB27D1D37796185C2942C0A",
         "0xFFA963CDCA8816CCC33B8642BEDF905C3D358573D3F27FBBD3B3CB9AAAF",
         "0x7DEBE8E4E90A5DAE6E4054CA530BA04654B36818CE226B39FCCB7B02F1AE",
         "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF9E5E9A9F5D9071FBD1522688909D0B",
         oid);
   }
 
   // x962_p239v2
   if(oid == OID{1, 2, 840, 10045, 3, 1, 5}) {
      return load_EC_group_info(
         "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",
         "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",
         "0x617FAB6832576CBBFED50D99F0249C3FEE58B94BA0038C7AE84C8C832F2C",
         "0x38AF09D98727705120C921BB5E9E26296A3CDCF2F35757A0EAFD87B830E7",
         "0x5B0125E4DBEA0EC7206DA0FC01D9B081329FB555DE6EF460237DFF8BE4BA",
         "0x7FFFFFFFFFFFFFFFFFFFFFFF800000CFA7E8594377D414C03821BC582063",
         oid);
   }
 
   // x962_p239v3
   if(oid == OID{1, 2, 840, 10045, 3, 1, 6}) {
      return load_EC_group_info(
         "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",
         "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",
         "0x255705FA2A306654B1F4CB03D6A750A30C250102D4988717D9BA15AB6D3E",
         "0x6768AE8E18BB92CFCF005C949AA2C6D94853D0E660BBF854B1C9505FE95A",
         "0x1607E6898F390C06BC1D552BAD226F3B6FCFE48B6E818499AF18E3ED6CF3",
         "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF975DEB41B3A6057C3C432146526551",
         oid);
   }
 
   // numsp512d1
   if(oid == OID{1, 3, 6, 1, 4, 1, 25258, 4, 3}) {
      return load_EC_group_info(
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4",
         "0x1D99B",
         "0x2",
         "0x1C282EB23327F9711952C250EA61AD53FCC13031CF6DD336E0B9328433AFBDD8CC5A1C1F0C716FDC724DDE537C2B0ADB00BB3D08DC83755B205CC30D7F83CF28",
         "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5B3CA4FB94E7831B4FC258ED97D0BDC63B568B36607CD243CE153F390433555D",
         oid);
   }
 
   return std::shared_ptr<EC_Group_Data>();
}

◆ engine()

EC_Group_Engine Botan::EC_Group::engine ( ) const

Return how this EC_Group is implemented under the hood

This is mostly useful for diagnostic or debugging purposes

Definition at line 612 of file ec_group.cpp.

                                       {
   return data().engine();
}

◆ from_name()

EC_Group Botan::EC_Group::from_name ( std::string_view name )

static

Initialize an EC group from a group common name (eg "secp256r1")

Definition at line 371 of file ec_group.cpp.

                                                {
   std::shared_ptr<EC_Group_Data> data;
 
   if(auto oid = OID::from_name(name)) {
      data = ec_group_data().lookup(oid.value());
   }
 
   if(!data) {
      throw Invalid_Argument(fmt("Unknown EC_Group '{}'", name));
   }
 
   return EC_Group(std::move(data));
}

References EC_Group(), EC_Group(), Botan::fmt(), and Botan::OID::from_name().

Referenced by botan_ec_group_from_name(), Botan::create_private_key(), Botan::TLS::Signature_Scheme::key_algorithm_identifier(), Botan::TLS::Callbacks::tls_deserialize_peer_public_key(), and Botan::TLS::Callbacks::tls_generate_ephemeral_key().

◆ from_OID()

EC_Group Botan::EC_Group::from_OID ( const OID & oid )

static

Initialize an EC group from a group named by an object identifier

Definition at line 360 of file ec_group.cpp.

                                          {
   auto data = ec_group_data().lookup(oid);
 
   if(!data) {
      throw Invalid_Argument(fmt("No EC_Group associated with OID '{}'", oid.to_string()));
   }
 
   return EC_Group(std::move(data));
}

References EC_Group(), EC_Group(), Botan::fmt(), and Botan::OID::to_string().

Referenced by botan_ec_group_from_oid(), EC_Group(), and Botan::GOST_3410_PublicKey::GOST_3410_PublicKey().

◆ from_PEM()

EC_Group Botan::EC_Group::from_PEM ( std::string_view pem )

static

Initialize an EC group from the PEM/ASN.1 encoding

Definition at line 414 of file ec_group.cpp.

                                              {
   const auto ber = PEM_Code::decode_check_label(pem, "EC PARAMETERS");
   return EC_Group(ber);
}

References Botan::PEM_Code::decode_check_label(), EC_Group(), and EC_Group().

Referenced by botan_ec_group_from_pem(), and EC_Group_from_PEM().

◆ get_a()

const BigInt & Botan::EC_Group::get_a ( ) const

Return the a parameter of the elliptic curve equation

Definition at line 540 of file ec_group.cpp.

                                    {
   return data().a();
}

Referenced by a_is_minus_3(), a_is_zero(), DER_encode(), Botan::EC_PublicKey::get_int_field(), operator==(), Botan::sm2_compute_za(), and verify_group().

◆ get_b()

const BigInt & Botan::EC_Group::get_b ( ) const

Return the b parameter of the elliptic curve equation

Definition at line 544 of file ec_group.cpp.

                                    {
   return data().b();
}

Referenced by DER_encode(), Botan::EC_PublicKey::get_int_field(), operator==(), Botan::sm2_compute_za(), and verify_group().

◆ get_cofactor()

const BigInt & Botan::EC_Group::get_cofactor ( ) const

Return the cofactor

Returns: the cofactor TODO(Botan4): Remove this

Definition at line 596 of file ec_group.cpp.

                                           {
   return data().cofactor();
}

Referenced by DER_encode(), Botan::EC_PublicKey::get_int_field(), operator==(), and verify_group().

◆ get_curve_oid()

const OID & Botan::EC_Group::get_curve_oid ( ) const

Return the OID of these domain parameters

Returns: the OID

Definition at line 604 of file ec_group.cpp.

                                         {
   return data().oid();
}

Referenced by Botan::GOST_3410_PublicKey::algorithm_identifier(), and Botan::TPM2::EC_PrivateKey::create_unrestricted_transient().

◆ get_g_x()

const BigInt & Botan::EC_Group::get_g_x ( ) const

Return the x coordinate of the base point

Definition at line 588 of file ec_group.cpp.

                                      {
   return data().g_x();
}

Referenced by Botan::EC_AffinePoint::generator(), Botan::EC_PublicKey::get_int_field(), operator==(), and Botan::sm2_compute_za().

◆ get_g_y()

const BigInt & Botan::EC_Group::get_g_y ( ) const

Return the y coordinate of the base point

Definition at line 592 of file ec_group.cpp.

                                      {
   return data().g_y();
}

Referenced by Botan::EC_AffinePoint::generator(), Botan::EC_PublicKey::get_int_field(), operator==(), and Botan::sm2_compute_za().

◆ get_order()

const BigInt & Botan::EC_Group::get_order ( ) const

Return the order of the base point

Returns: order of the base point

Definition at line 584 of file ec_group.cpp.

                                        {
   return data().order();
}

Referenced by DER_encode(), Botan::EC_PublicKey::get_int_field(), operator==(), and verify_group().

◆ get_order_bits()

size_t Botan::EC_Group::get_order_bits ( ) const

Return the size of group order in bits (same as get_order().bits())

Definition at line 528 of file ec_group.cpp.

                                      {
   return data().order_bits();
}

◆ get_order_bytes()

size_t Botan::EC_Group::get_order_bytes ( ) const

Return the size of the group order in bytes (same as get_order().bytes())

Definition at line 532 of file ec_group.cpp.

                                       {
   return data().order_bytes();
}

Referenced by Botan::GOST_3410_PublicKey::_signature_element_size_for_DER_encoding().

◆ get_p()

const BigInt & Botan::EC_Group::get_p ( ) const

Return the prime modulus of the field

Definition at line 536 of file ec_group.cpp.

                                    {
   return data().p();
}

Referenced by a_is_minus_3(), DER_encode(), Botan::EC_AffinePoint::from_bigint_xy(), Botan::EC_PublicKey::get_int_field(), operator==(), and verify_group().

◆ get_p_bits()

size_t Botan::EC_Group::get_p_bits ( ) const

Return the size of p in bits (same as get_p().bits())

Definition at line 520 of file ec_group.cpp.

                                  {
   return data().p_bits();
}

Referenced by Botan::GOST_3410_PublicKey::algo_name(), and Botan::EC_PublicKey::key_length().

◆ get_p_bytes()

size_t Botan::EC_Group::get_p_bytes ( ) const

Return the size of p in bytes (same as get_p().bytes())

Definition at line 524 of file ec_group.cpp.

                                   {
   return data().p_bytes();
}

Referenced by DER_encode(), Botan::EC_AffinePoint::from_bigint_xy(), point_size(), and Botan::sm2_compute_za().

◆ has_cofactor()

bool Botan::EC_Group::has_cofactor ( ) const

Return true if the cofactor is > 1 TODO(Botan4): Remove this

Definition at line 600 of file ec_group.cpp.

                                  {
   return data().has_cofactor();
}

◆ initialized()

bool Botan::EC_Group::initialized ( ) const

inline

Definition at line 234 of file ec_group.h.

234{ return (m_data != nullptr); }

References initialized().

Referenced by initialized().

◆ inverse_mod_order()

BigInt Botan::EC_Group::inverse_mod_order ( const BigInt & x ) const

inline

Definition at line 657 of file ec_group.h.

                                                                                        {
         return EC_Scalar::from_bigint(*this, x).invert().to_bigint();
      }

References Botan::EC_Scalar::from_bigint(), and inverse_mod_order().

Referenced by inverse_mod_order().

◆ known_named_groups()

const std::set< std::string > & Botan::EC_Group::known_named_groups ( )

static

Return a set of known named EC groups

This returns the set of groups for which from_name should succeed Note that the set of included groups can vary based on the build configuration.

Definition at line 476 of file ec_named.cpp.

                                                      {
   static const std::set<std::string> named_groups = {
#if defined(BOTAN_HAS_PCURVES_BRAINPOOL256R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "brainpool256r1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_BRAINPOOL384R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "brainpool384r1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_BRAINPOOL512R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "brainpool512r1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_FRP256V1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "frp256v1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_NUMSP512D1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "numsp512d1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_SECP192R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "secp192r1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_SECP224R1) || defined(BOTAN_HAS_LEGACY_EC_POINT)
      // Not supported by pcurves_generic
      "secp224r1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_SECP256K1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "secp256k1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_SECP256R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "secp256r1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_SECP384R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "secp384r1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_SECP521R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "secp521r1",
#endif
 
#if defined(BOTAN_HAS_PCURVES_SM2P256V1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "sm2p256v1",
#endif
 
#if defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
      "brainpool192r1",
      "brainpool224r1",
      "brainpool320r1",
      "gost_256A",
      "gost_512A",
      "secp192k1",
      "x962_p192v2",
      "x962_p192v3",
      "x962_p239v1",
      "x962_p239v2",
      "x962_p239v3",
#endif
 
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      "brainpool160r1",
      "secp160k1",
      "secp160r1",
      "secp160r2",
      "secp224k1",
#endif
   };
 
   return named_groups;
}

Referenced by supports_named_group().

◆ mod_order()

BigInt Botan::EC_Group::mod_order ( const BigInt & x ) const

inline

Definition at line 650 of file ec_group.h.

                                                                                {
         return EC_Scalar::from_bytes_mod_order(*this, x.serialize()).to_bigint();
      }

References Botan::EC_Scalar::from_bytes_mod_order(), and mod_order().

Referenced by EC_Group(), and mod_order().

◆ multiply_mod_order() [1/2]

BigInt Botan::EC_Group::multiply_mod_order	(	const BigInt &	x,
		const BigInt &	y ) const

inline

Definition at line 673 of file ec_group.h.

                                                                                                          {
         auto xs = EC_Scalar::from_bigint(*this, x);
         auto ys = EC_Scalar::from_bigint(*this, y);
         return (xs * ys).to_bigint();
      }

References Botan::EC_Scalar::from_bigint(), and multiply_mod_order().

Referenced by multiply_mod_order(), and multiply_mod_order().

◆ multiply_mod_order() [2/2]

BigInt Botan::EC_Group::multiply_mod_order	(	const BigInt &	x,
		const BigInt &	y,
		const BigInt &	z ) const

inline

Definition at line 683 of file ec_group.h.

                                                                                         {
         auto xs = EC_Scalar::from_bigint(*this, x);
         auto ys = EC_Scalar::from_bigint(*this, y);
         auto zs = EC_Scalar::from_bigint(*this, z);
         return (xs * ys * zs).to_bigint();
      }

References Botan::EC_Scalar::from_bigint(), and multiply_mod_order().

◆ operator=() [1/2]

EC_Group & Botan::EC_Group::operator= ( const EC_Group & )

default

References EC_Group().

◆ operator=() [2/2]

EC_Group & Botan::EC_Group::operator= ( EC_Group && )

default

References EC_Group().

◆ operator==()

bool Botan::EC_Group::operator== ( const EC_Group & other ) const

Definition at line 666 of file ec_group.cpp.

                                                     {
   if(m_data == other.m_data) {
      return true;  // same shared rep
   }
 
   return (get_p() == other.get_p() && get_a() == other.get_a() && get_b() == other.get_b() &&
           get_g_x() == other.get_g_x() && get_g_y() == other.get_g_y() && get_order() == other.get_order() &&
           get_cofactor() == other.get_cofactor());
}

References EC_Group(), get_a(), get_b(), get_cofactor(), get_g_x(), get_g_y(), get_order(), and get_p().

◆ PEM_encode()

std::string Botan::EC_Group::PEM_encode ( EC_Group_Encoding form = EC_Group_Encoding::Explicit ) const

Return the PEM encoding

Returns: string containing PEM data

Warning: In Botan4 the form parameter will be removed and only namedCurve will be supported

TODO(Botan4) remove the argument

Definition at line 661 of file ec_group.cpp.

                                                           {
   const std::vector<uint8_t> der = DER_encode(form);
   return PEM_Code::encode(der, "EC PARAMETERS");
}

References DER_encode(), and Botan::PEM_Code::encode().

◆ point_size()

size_t Botan::EC_Group::point_size ( EC_Point_Format format ) const

inline

Definition at line 698 of file ec_group.h.

                                                                                                             {
         // Hybrid and standard format are (x,y), compressed is y, +1 format byte
         if(format == EC_Point_Format::Compressed) {
            return (1 + get_p_bytes());
         } else {
            return (1 + 2 * get_p_bytes());
         }
      }

References Botan::Compressed, get_p_bytes(), and point_size().

Referenced by point_size().

◆ source()

EC_Group_Source Botan::EC_Group::source ( ) const

Definition at line 608 of file ec_group.cpp.

                                       {
   return data().source();
}

Referenced by verify_group().

◆ square_mod_order()

BigInt Botan::EC_Group::square_mod_order ( const BigInt & x ) const

inline

Definition at line 664 of file ec_group.h.

                                                                                       {
         auto xs = EC_Scalar::from_bigint(*this, x);
         xs.square_self();
         return xs.to_bigint();
      }

References Botan::EC_Scalar::from_bigint(), and square_mod_order().

Referenced by square_mod_order().

◆ supports_application_specific_group()

bool Botan::EC_Group::supports_application_specific_group ( )

static

Return true if in this build configuration it is possible to register an application specific elliptic curve.

Definition at line 351 of file ec_group.cpp.

                                                   {
#if defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
   return true;
#else
   return false;
#endif
}

Referenced by botan_ec_group_supports_application_specific_group().

◆ supports_named_group()

bool Botan::EC_Group::supports_named_group ( std::string_view name )

static

Return true if in this build configuration EC_Group::from_name(name) will succeed

Definition at line 346 of file ec_group.cpp.

                                                       {
   return EC_Group::known_named_groups().contains(std::string(name));
}

References known_named_groups().

Referenced by botan_ec_group_supports_named_group(), and Botan::create_private_key().

◆ used_explicit_encoding()

bool Botan::EC_Group::used_explicit_encoding ( ) const

inline

Return true if this EC_Group was derived from an explicit encoding

Explicit encoding of groups is deprecated; when support for explicit curves is removed in a future major release, this function will also be removed.

Definition at line 263 of file ec_group.h.

263{ return m_explicit_encoding; }

Referenced by botan_pubkey_ecc_key_used_explicit_encoding().

◆ verify_group()

bool Botan::EC_Group::verify_group	(	RandomNumberGenerator &	rng,
		bool	strong = false ) const

Verify EC_Group domain

Returns: true if group is valid. false otherwise

Definition at line 676 of file ec_group.cpp.

                                                                         {
   const bool is_builtin = source() == EC_Group_Source::Builtin;
 
   if(is_builtin && !strong) {
      return true;
   }
 
   // TODO(Botan4) this can probably all be removed once the deprecated EC_Group
   // constructor is removed, since at that point it no longer becomes possible
   // to create an EC_Group which fails to satisfy these conditions
 
   const BigInt& p = get_p();
   const BigInt& a = get_a();
   const BigInt& b = get_b();
   const BigInt& order = get_order();
 
   if(p <= 3 || order <= 0) {
      return false;
   }
   if(a < 0 || a >= p) {
      return false;
   }
   if(b <= 0 || b >= p) {
      return false;
   }
 
   const size_t test_prob = 128;
   const bool is_randomly_generated = is_builtin;
 
   //check if field modulus is prime
   if(!is_prime(p, rng, test_prob, is_randomly_generated)) {
      return false;
   }
 
   //check if order is prime
   if(!is_prime(order, rng, test_prob, is_randomly_generated)) {
      return false;
   }
 
   //compute the discriminant: 4*a^3 + 27*b^2 which must be nonzero
   auto mod_p = Barrett_Reduction::for_public_modulus(p);
 
   const BigInt discriminant = mod_p.reduce(mod_p.multiply(4, mod_p.cube(a)) + mod_p.multiply(27, mod_p.square(b)));
 
   if(discriminant == 0) {
      return false;
   }
 
   //check for valid cofactor
   if(get_cofactor() < 1) {
      return false;
   }
 
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
   const EC_Point& base_point = get_base_point();
   //check if the base point is on the curve
   if(!base_point.on_the_curve()) {
      return false;
   }
   if((base_point * get_cofactor()).is_zero()) {
      return false;
   }
   //check if order of the base point is correct
   if(!(base_point * order).is_zero()) {
      return false;
   }
#endif
 
   // check the Hasse bound (roughly)
   if((p - get_cofactor() * order).abs().bits() > (p.bits() / 2) + 1) {
      return false;
   }
 
   return true;
}

References Botan::abs(), Botan::BigInt::bits(), Botan::Builtin, Botan::Barrett_Reduction::for_public_modulus(), get_a(), get_b(), get_cofactor(), get_order(), get_p(), Botan::is_prime(), Botan::EC_Point::on_the_curve(), and source().

Referenced by Botan::EC_PublicKey::check_key().

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

src/lib/pubkey/ec_group/ec_group.h
src/lib/pubkey/ec_group/ec_group.cpp
src/lib/pubkey/ec_group/ec_named.cpp

Classes

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ EC_Group() [1/9]

◆ EC_Group() [2/9]

◆ EC_Group() [3/9]

◆ EC_Group() [4/9]

◆ EC_Group() [5/9]

◆ EC_Group() [6/9]

◆ EC_Group() [7/9]

◆ ~EC_Group()

◆ EC_Group() [8/9]

◆ EC_Group() [9/9]

Member Function Documentation

◆ _data()

◆ a_is_minus_3()

◆ a_is_zero()

◆ clear_registered_curve_data()

◆ cube_mod_order()

◆ DER_encode() [1/2]

◆ DER_encode() [2/2]

◆ EC_Group_from_PEM()

◆ EC_group_identity_from_order()

◆ EC_group_info()

◆ engine()

◆ from_name()

◆ from_OID()

◆ from_PEM()

◆ get_a()

◆ get_b()

◆ get_cofactor()

◆ get_curve_oid()

◆ get_g_x()

◆ get_g_y()

◆ get_order()

◆ get_order_bits()

◆ get_order_bytes()

◆ get_p()

◆ get_p_bits()

◆ get_p_bytes()

◆ has_cofactor()

◆ initialized()

◆ inverse_mod_order()

◆ known_named_groups()

◆ mod_order()

◆ multiply_mod_order() [1/2]

◆ multiply_mod_order() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ PEM_encode()

◆ point_size()

◆ source()

◆ square_mod_order()

◆ supports_application_specific_group()

◆ supports_named_group()

◆ used_explicit_encoding()

◆ verify_group()