Botan 3.7.1
Crypto and TLS for C&
Botan::EC_Group Class Referencefinal

#include <ec_group.h>

Classes

class  Mul2Table
 Table for computing g*x + h*y. 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 BigIntget_a () const
 
const BigIntget_b () const
 
const BigIntget_cofactor () const
 
const OIDget_curve_oid () const
 
const BigIntget_g_x () const
 
const BigIntget_g_y () const
 
const BigIntget_order () const
 
size_t get_order_bits () const
 
size_t get_order_bytes () const
 
const BigIntget_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_Groupoperator= (const EC_Group &)
 
EC_Groupoperator= (EC_Group &&)=default
 
bool operator== (const EC_Group &other) const
 
std::string PEM_encode () 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_DataEC_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
pthe elliptic curve p
athe elliptic curve a param
bthe elliptic curve b param
base_xthe x coordinate of the base point
base_ythe y coordinate of the base point
orderthe order of the base point
cofactorthe cofactor
oidan 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 402 of file ec_group.cpp.

409 {
410 m_data =
411 ec_group_data().lookup_or_create(p, a, b, base_x, base_y, order, cofactor, oid, EC_Group_Source::ExternalSource);
412}
const SIMD_8x32 & b

References Botan::b, and Botan::ExternalSource.

◆ 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
oidan object identifier used to identify this curve
pthe elliptic curve prime (at most 521 bits)
athe elliptic curve a param
bthe elliptic curve b param
base_xthe x coordinate of the group generator
base_ythe y coordinate of the group generator
orderthe order of the group

Definition at line 414 of file ec_group.cpp.

420 {
421 BOTAN_ARG_CHECK(oid.has_value(), "An OID is required for creating an EC_Group");
422
423 // TODO(Botan4) remove this and require 192 bits minimum
424#if defined(BOTAN_DISABLE_DEPRECATED_FEATURES)
425 constexpr size_t p_bits_lower_bound = 192;
426#else
427 constexpr size_t p_bits_lower_bound = 128;
428#endif
429
430 BOTAN_ARG_CHECK(p.bits() >= p_bits_lower_bound, "EC_Group p too small");
431 BOTAN_ARG_CHECK(p.bits() <= 521, "EC_Group p too large");
432
433 if(p.bits() == 521) {
434 const auto p521 = BigInt::power_of_2(521) - 1;
435 BOTAN_ARG_CHECK(p == p521, "EC_Group with p of 521 bits must be 2**521-1");
436 } else if(p.bits() == 239) {
437 const auto x962_p239 = []() {
438 BigInt p239;
439 for(size_t i = 0; i != 239; ++i) {
440 if(i < 47 || ((i >= 94) && (i != 143))) {
441 p239.set_bit(i);
442 }
443 }
444 return p239;
445 }();
446
447 BOTAN_ARG_CHECK(p == x962_p239, "EC_Group with p of 239 bits must be the X9.62 prime");
448 } else {
449 BOTAN_ARG_CHECK(p.bits() % 32 == 0, "EC_Group p must be a multiple of 32 bits");
450 }
451
452 BOTAN_ARG_CHECK(p % 4 == 3, "EC_Group p must be congruent to 3 modulo 4");
453
454 BOTAN_ARG_CHECK(a >= 0 && a < p, "EC_Group a is invalid");
455 BOTAN_ARG_CHECK(b > 0 && b < p, "EC_Group b is invalid");
456 BOTAN_ARG_CHECK(base_x >= 0 && base_x < p, "EC_Group base_x is invalid");
457 BOTAN_ARG_CHECK(base_y >= 0 && base_y < p, "EC_Group base_y is invalid");
458 BOTAN_ARG_CHECK(p.bits() == order.bits(), "EC_Group p and order must have the same number of bits");
459
461 BOTAN_ARG_CHECK(is_bailie_psw_probable_prime(p, mod_p), "EC_Group p is not prime");
462
464 BOTAN_ARG_CHECK(is_bailie_psw_probable_prime(order, mod_order), "EC_Group order is not prime");
465
466 // This catches someone "ignoring" a cofactor and just trying to
467 // provide the subgroup order
468 BOTAN_ARG_CHECK((p - order).abs().bits() <= (p.bits() / 2) + 1, "Hasse bound invalid");
469
470 // Check that 4*a^3 + 27*b^2 != 0
471 const auto discriminant = mod_p.reduce(mod_p.multiply(4, mod_p.cube(a)) + mod_p.multiply(27, mod_p.square(b)));
472 BOTAN_ARG_CHECK(discriminant != 0, "EC_Group discriminant is invalid");
473
474 // Check that the generator (base_x,base_y) is on the curve; y^2 = x^3 + a*x + b
475 auto y2 = mod_p.square(base_y);
476 auto x3_ax_b = mod_p.reduce(mod_p.cube(base_x) + mod_p.multiply(a, base_x) + b);
477 BOTAN_ARG_CHECK(y2 == x3_ax_b, "EC_Group generator is not on the curve");
478
479 BigInt cofactor(1);
480
481 m_data =
482 ec_group_data().lookup_or_create(p, a, b, base_x, base_y, order, cofactor, oid, EC_Group_Source::ExternalSource);
483}
#define BOTAN_ARG_CHECK(expr, msg)
Definition assert.h:29
static BigInt power_of_2(size_t n)
Definition bigint.h:830
BigInt mod_order(const BigInt &x) const
Definition ec_group.h:646
static Modular_Reducer for_public_modulus(const BigInt &m)
Definition reducer.cpp:43
BigInt abs(const BigInt &n)
Definition numthry.h:24
bool is_bailie_psw_probable_prime(const BigInt &n, const Modular_Reducer &mod_n)
Definition primality.cpp:90

References Botan::abs(), Botan::b, Botan::BigInt::bits(), BOTAN_ARG_CHECK, Botan::ExternalSource, Botan::Modular_Reducer::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
berthe bytes of the BER encoding

Definition at line 485 of file ec_group.cpp.

485 {
486 auto data = BER_decode_EC_group(ber, EC_Group_Source::ExternalSource);
487 m_data = data.first;
488 m_explicit_encoding = data.second;
489}

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}) {}

◆ EC_Group() [5/9]

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

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

Parameters
oidthe OID of the EC domain to create

Definition at line 190 of file ec_group.h.

190{ *this = EC_Group::from_OID(oid); }
static EC_Group from_OID(const OID &oid)
Definition ec_group.cpp:343

◆ 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_oidPEM-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 368 of file ec_group.cpp.

368 {
369 if(str.empty()) {
370 return; // no initialization / uninitialized
371 }
372
373 try {
374 const OID oid = OID::from_string(str);
375 if(oid.has_value()) {
376 m_data = ec_group_data().lookup(oid);
377 }
378 } catch(...) {}
379
380 if(m_data == nullptr) {
381 if(str.size() > 30 && str.substr(0, 29) == "-----BEGIN EC PARAMETERS-----") {
382 // OK try it as PEM ...
383 const auto ber = PEM_Code::decode_check_label(str, "EC PARAMETERS");
384
385 auto data = BER_decode_EC_group(ber, EC_Group_Source::ExternalSource);
386 this->m_data = data.first;
387 this->m_explicit_encoding = data.second;
388 }
389 }
390
391 if(m_data == nullptr) {
392 throw Invalid_Argument(fmt("Unknown ECC group '{}'", str));
393 }
394}
static OID from_string(std::string_view str)
Definition asn1_oid.cpp:86
secure_vector< uint8_t > decode_check_label(DataSource &source, std::string_view label_want)
Definition pem.cpp:49
std::string fmt(std::string_view format, const T &... args)
Definition fmt.h:53

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

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

◆ ~EC_Group()

Botan::EC_Group::~EC_Group ( )
default

◆ EC_Group() [8/9]

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

◆ EC_Group() [9/9]

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

Member Function Documentation

◆ _data()

◆ a_is_minus_3()

bool Botan::EC_Group::a_is_minus_3 ( ) const
inline

Return if a == -3 mod p

Definition at line 636 of file ec_group.h.

636{ return get_a() + 3 == get_p(); }
const BigInt & get_a() const
Definition ec_group.cpp:518
const BigInt & get_p() const
Definition ec_group.cpp:514

◆ a_is_zero()

bool Botan::EC_Group::a_is_zero ( ) const
inline

Return if a == 0 mod p

Definition at line 641 of file ec_group.h.

641{ return get_a().is_zero(); }
bool is_zero() const
Definition bigint.h:458

◆ clear_registered_curve_data()

size_t Botan::EC_Group::clear_registered_curve_data ( )
static

Definition at line 182 of file ec_group.cpp.

182 {
183 return ec_group_data().clear();
184}

◆ cube_mod_order()

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

Definition at line 689 of file ec_group.h.

689 {
690 auto xs = EC_Scalar::from_bigint(*this, x);
691 return (xs * xs * xs).to_bigint();
692 }
static EC_Scalar from_bigint(const EC_Group &group, const BigInt &bn)
Definition ec_scalar.cpp:65

◆ 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 594 of file ec_group.cpp.

594 {
595 const auto& der_named_curve = data().der_named_curve();
596 // TODO(Botan4) this can be removed because an OID will always be defined
597 if(der_named_curve.empty()) {
598 throw Encoding_Error("Cannot encode EC_Group as OID because OID not set");
599 }
600
601 return der_named_curve;
602}
const std::vector< uint8_t > & der_named_curve() const

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
formof encoding to use
Returns
the group information encoded as DER

Definition at line 604 of file ec_group.cpp.

604 {
605 if(form == EC_Group_Encoding::Explicit) {
606 std::vector<uint8_t> output;
607 DER_Encoder der(output);
608 const size_t ecpVers1 = 1;
609 const OID curve_type("1.2.840.10045.1.1"); // prime field
610
611 const size_t p_bytes = get_p_bytes();
612
613 const auto generator = EC_AffinePoint::generator(*this).serialize_uncompressed();
614
615 der.start_sequence()
616 .encode(ecpVers1)
617 .start_sequence()
618 .encode(curve_type)
619 .encode(get_p())
620 .end_cons()
621 .start_sequence()
622 .encode(get_a().serialize(p_bytes), ASN1_Type::OctetString)
623 .encode(get_b().serialize(p_bytes), ASN1_Type::OctetString)
624 .end_cons()
625 .encode(generator, ASN1_Type::OctetString)
626 .encode(get_order())
627 .encode(get_cofactor())
628 .end_cons();
629 return output;
630 } else if(form == EC_Group_Encoding::NamedCurve) {
631 return this->DER_encode();
632 } else if(form == EC_Group_Encoding::ImplicitCA) {
633 return {0x00, 0x05};
634 } else {
635 throw Internal_Error("EC_Group::DER_encode: Unknown encoding");
636 }
637}
T serialize_uncompressed() const
Definition ec_apoint.h:194
static EC_AffinePoint generator(const EC_Group &group)
Return the standard group generator.
Definition ec_apoint.cpp:83
const BigInt & get_b() const
Definition ec_group.cpp:522
const BigInt & get_cofactor() const
Definition ec_group.cpp:574
const BigInt & get_order() const
Definition ec_group.cpp:562
std::vector< uint8_t > DER_encode() const
Definition ec_group.cpp:594
size_t get_p_bytes() const
Definition ec_group.cpp:502

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.

217 {
218 return EC_Group::from_PEM(pem);
219 }
static EC_Group from_PEM(std::string_view pem)
Definition ec_group.cpp:397

◆ 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.

357 {
358 const uint32_t low_bits = static_cast<uint32_t>(order.word_at(0));
359
360 if(low_bits == 0xFC632551 && order == BigInt("0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551")) {
361 return OID{1, 2, 840, 10045, 3, 1, 7};
362 }
363
364 if(low_bits == 0xCCC52973 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) {
365 return OID{1, 3, 132, 0, 34};
366 }
367
368 if(low_bits == 0x91386409 && order == BigInt("0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409")) {
369 return OID{1, 3, 132, 0, 35};
370 }
371
372 if(low_bits == 0x9E60FC09 && order == BigInt("0xE95E4A5F737059DC60DF5991D45029409E60FC09")) {
373 return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 1};
374 }
375
376 if(low_bits == 0x9AC4ACC1 && order == BigInt("0xC302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1")) {
377 return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 3};
378 }
379
380 if(low_bits == 0xA5A7939F && order == BigInt("0xD7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F")) {
381 return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 5};
382 }
383
384 if(low_bits == 0x974856A7 && order == BigInt("0xA9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7")) {
385 return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 7};
386 }
387
388 if(low_bits == 0x44C59311 && order == BigInt("0xD35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D482EC7EE8658E98691555B44C59311")) {
389 return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 9};
390 }
391
392 if(low_bits == 0xE9046565 && order == BigInt("0x8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565")) {
393 return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 11};
394 }
395
396 if(low_bits == 0x9CA90069 && order == BigInt("0xAADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069")) {
397 return OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 13};
398 }
399
400 if(low_bits == 0xC6D655E1 && order == BigInt("0xF1FD178C0B3AD58F10126DE8CE42435B53DC67E140D2BF941FFDD459C6D655E1")) {
401 return OID{1, 2, 250, 1, 223, 101, 256, 1};
402 }
403
404 if(low_bits == 0xB761B893 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893")) {
405 return OID{1, 2, 643, 7, 1, 2, 1, 1, 1};
406 }
407
408 if(low_bits == 0x1F10B275 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275")) {
409 return OID{1, 2, 643, 7, 1, 2, 1, 2, 1};
410 }
411
412 if(low_bits == 0xCA16B6B3 && order == BigInt("0x100000000000000000001B8FA16DFAB9ACA16B6B3")) {
413 return OID{1, 3, 132, 0, 9};
414 }
415
416 if(low_bits == 0xCA752257 && order == BigInt("0x100000000000000000001F4C8F927AED3CA752257")) {
417 return OID{1, 3, 132, 0, 8};
418 }
419
420 if(low_bits == 0xF3A1A16B && order == BigInt("0x100000000000000000000351EE786A818F3A1A16B")) {
421 return OID{1, 3, 132, 0, 30};
422 }
423
424 if(low_bits == 0x74DEFD8D && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D")) {
425 return OID{1, 3, 132, 0, 31};
426 }
427
428 if(low_bits == 0xB4D22831 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) {
429 return OID{1, 2, 840, 10045, 3, 1, 1};
430 }
431
432 if(low_bits == 0x769FB1F7 && order == BigInt("0x10000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7")) {
433 return OID{1, 3, 132, 0, 32};
434 }
435
436 if(low_bits == 0x5C5C2A3D && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) {
437 return OID{1, 3, 132, 0, 33};
438 }
439
440 if(low_bits == 0xD0364141 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141")) {
441 return OID{1, 3, 132, 0, 10};
442 }
443
444 if(low_bits == 0x39D54123 && order == BigInt("0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123")) {
445 return OID{1, 2, 156, 10197, 1, 301};
446 }
447
448 if(low_bits == 0x48D8DD31 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFE5FB1A724DC80418648D8DD31")) {
449 return OID{1, 2, 840, 10045, 3, 1, 2};
450 }
451
452 if(low_bits == 0xF640EC13 && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFF7A62D031C83F4294F640EC13")) {
453 return OID{1, 2, 840, 10045, 3, 1, 3};
454 }
455
456 if(low_bits == 0x88909D0B && order == BigInt("0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF9E5E9A9F5D9071FBD1522688909D0B")) {
457 return OID{1, 2, 840, 10045, 3, 1, 4};
458 }
459
460 if(low_bits == 0xBC582063 && order == BigInt("0x7FFFFFFFFFFFFFFFFFFFFFFF800000CFA7E8594377D414C03821BC582063")) {
461 return OID{1, 2, 840, 10045, 3, 1, 5};
462 }
463
464 if(low_bits == 0x46526551 && order == BigInt("0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF975DEB41B3A6057C3C432146526551")) {
465 return OID{1, 2, 840, 10045, 3, 1, 6};
466 }
467
468 if(low_bits == 0x0433555D && order == BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5B3CA4FB94E7831B4FC258ED97D0BDC63B568B36607CD243CE153F390433555D")) {
469 return OID{1, 3, 6, 1, 4, 1, 25258, 4, 3};
470 }
471
472 return OID();
473}

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.

15 {
16 // secp256r1
17 if(oid == OID{1, 2, 840, 10045, 3, 1, 7}) {
18 return load_EC_group_info(
19 "0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",
20 "0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",
21 "0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",
22 "0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296",
23 "0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5",
24 "0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",
25 oid);
26 }
27
28 // secp384r1
29 if(oid == OID{1, 3, 132, 0, 34}) {
30 return load_EC_group_info(
31 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF",
32 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC",
33 "0xB3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF",
34 "0xAA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7",
35 "0x3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F",
36 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973",
37 oid);
38 }
39
40 // secp521r1
41 if(oid == OID{1, 3, 132, 0, 35}) {
42 return load_EC_group_info(
43 "0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
44 "0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC",
45 "0x51953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00",
46 "0xC6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66",
47 "0x11839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650",
48 "0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",
49 oid);
50 }
51
52 // brainpool160r1
53 if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 1}) {
54 return load_EC_group_info(
55 "0xE95E4A5F737059DC60DFC7AD95B3D8139515620F",
56 "0x340E7BE2A280EB74E2BE61BADA745D97E8F7C300",
57 "0x1E589A8595423412134FAA2DBDEC95C8D8675E58",
58 "0xBED5AF16EA3F6A4F62938C4631EB5AF7BDBCDBC3",
59 "0x1667CB477A1A8EC338F94741669C976316DA6321",
60 "0xE95E4A5F737059DC60DF5991D45029409E60FC09",
61 oid);
62 }
63
64 // brainpool192r1
65 if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 3}) {
66 return load_EC_group_info(
67 "0xC302F41D932A36CDA7A3463093D18DB78FCE476DE1A86297",
68 "0x6A91174076B1E0E19C39C031FE8685C1CAE040E5C69A28EF",
69 "0x469A28EF7C28CCA3DC721D044F4496BCCA7EF4146FBF25C9",
70 "0xC0A0647EAAB6A48753B033C56CB0F0900A2F5C4853375FD6",
71 "0x14B690866ABD5BB88B5F4828C1490002E6773FA2FA299B8F",
72 "0xC302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1",
73 oid);
74 }
75
76 // brainpool224r1
77 if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 5}) {
78 return load_EC_group_info(
79 "0xD7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FF",
80 "0x68A5E62CA9CE6C1C299803A6C1530B514E182AD8B0042A59CAD29F43",
81 "0x2580F63CCFE44138870713B1A92369E33E2135D266DBB372386C400B",
82 "0xD9029AD2C7E5CF4340823B2A87DC68C9E4CE3174C1E6EFDEE12C07D",
83 "0x58AA56F772C0726F24C6B89E4ECDAC24354B9E99CAA3F6D3761402CD",
84 "0xD7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F",
85 oid);
86 }
87
88 // brainpool256r1
89 if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 7}) {
90 return load_EC_group_info(
91 "0xA9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377",
92 "0x7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9",
93 "0x26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6",
94 "0x8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262",
95 "0x547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997",
96 "0xA9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7",
97 oid);
98 }
99
100 // brainpool320r1
101 if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 9}) {
102 return load_EC_group_info(
103 "0xD35E472036BC4FB7E13C785ED201E065F98FCFA6F6F40DEF4F92B9EC7893EC28FCD412B1F1B32E27",
104 "0x3EE30B568FBAB0F883CCEBD46D3F3BB8A2A73513F5EB79DA66190EB085FFA9F492F375A97D860EB4",
105 "0x520883949DFDBC42D3AD198640688A6FE13F41349554B49ACC31DCCD884539816F5EB4AC8FB1F1A6",
106 "0x43BD7E9AFB53D8B85289BCC48EE5BFE6F20137D10A087EB6E7871E2A10A599C710AF8D0D39E20611",
107 "0x14FDD05545EC1CC8AB4093247F77275E0743FFED117182EAA9C77877AAAC6AC7D35245D1692E8EE1",
108 "0xD35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D482EC7EE8658E98691555B44C59311",
109 oid);
110 }
111
112 // brainpool384r1
113 if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 11}) {
114 return load_EC_group_info(
115 "0x8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A71874700133107EC53",
116 "0x7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F90F8AA5814A503AD4EB04A8C7DD22CE2826",
117 "0x4A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62D57CB4390295DBC9943AB78696FA504C11",
118 "0x1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10E8E826E03436D646AAEF87B2E247D4AF1E",
119 "0x8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129280E4646217791811142820341263C5315",
120 "0x8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565",
121 oid);
122 }
123
124 // brainpool512r1
125 if(oid == OID{1, 3, 36, 3, 3, 2, 8, 1, 1, 13}) {
126 return load_EC_group_info(
127 "0xAADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3",
128 "0x7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA",
129 "0x3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723",
130 "0x81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D0098EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822",
131 "0x7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F8111B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892",
132 "0xAADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069",
133 oid);
134 }
135
136 // frp256v1
137 if(oid == OID{1, 2, 250, 1, 223, 101, 256, 1}) {
138 return load_EC_group_info(
139 "0xF1FD178C0B3AD58F10126DE8CE42435B3961ADBCABC8CA6DE8FCF353D86E9C03",
140 "0xF1FD178C0B3AD58F10126DE8CE42435B3961ADBCABC8CA6DE8FCF353D86E9C00",
141 "0xEE353FCA5428A9300D4ABA754A44C00FDFEC0C9AE4B1A1803075ED967B7BB73F",
142 "0xB6B3D4C356C139EB31183D4749D423958C27D2DCAF98B70164C97A2DD98F5CFF",
143 "0x6142E0F7C8B204911F9271F0F3ECEF8C2701C307E8E4C9E183115A1554062CFB",
144 "0xF1FD178C0B3AD58F10126DE8CE42435B53DC67E140D2BF941FFDD459C6D655E1",
145 oid);
146 }
147
148 // gost_256A
149 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}) {
150 return load_EC_group_info(
151 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97",
152 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD94",
153 "0xA6",
154 "1",
155 "0x8D91E471E0989CDA27DF505A453F2B7635294F2DDF23E3B122ACC99C9E9F1E14",
156 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893",
157 OID{1, 2, 643, 7, 1, 2, 1, 1, 1});
158 }
159
160 // gost_512A
161 if(oid == OID{1, 2, 643, 7, 1, 2, 1, 2, 1}) {
162 return load_EC_group_info(
163 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7",
164 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4",
165 "0xE8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760",
166 "3",
167 "0x7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4",
168 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275",
169 oid);
170 }
171
172 // secp160k1
173 if(oid == OID{1, 3, 132, 0, 9}) {
174 return load_EC_group_info(
175 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",
176 "0",
177 "7",
178 "0x3B4C382CE37AA192A4019E763036F4F5DD4D7EBB",
179 "0x938CF935318FDCED6BC28286531733C3F03C4FEE",
180 "0x100000000000000000001B8FA16DFAB9ACA16B6B3",
181 oid);
182 }
183
184 // secp160r1
185 if(oid == OID{1, 3, 132, 0, 8}) {
186 return load_EC_group_info(
187 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF",
188 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC",
189 "0x1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45",
190 "0x4A96B5688EF573284664698968C38BB913CBFC82",
191 "0x23A628553168947D59DCC912042351377AC5FB32",
192 "0x100000000000000000001F4C8F927AED3CA752257",
193 oid);
194 }
195
196 // secp160r2
197 if(oid == OID{1, 3, 132, 0, 30}) {
198 return load_EC_group_info(
199 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",
200 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC70",
201 "0xB4E134D3FB59EB8BAB57274904664D5AF50388BA",
202 "0x52DCB034293A117E1F4FF11B30F7199D3144CE6D",
203 "0xFEAFFEF2E331F296E071FA0DF9982CFEA7D43F2E",
204 "0x100000000000000000000351EE786A818F3A1A16B",
205 oid);
206 }
207
208 // secp192k1
209 if(oid == OID{1, 3, 132, 0, 31}) {
210 return load_EC_group_info(
211 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37",
212 "0",
213 "3",
214 "0xDB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D",
215 "0x9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D",
216 "0xFFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D",
217 oid);
218 }
219
220 // secp192r1
221 if(oid == OID{1, 2, 840, 10045, 3, 1, 1}) {
222 return load_EC_group_info(
223 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
224 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
225 "0x64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1",
226 "0x188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012",
227 "0x7192B95FFC8DA78631011ED6B24CDD573F977A11E794811",
228 "0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",
229 oid);
230 }
231
232 // secp224k1
233 if(oid == OID{1, 3, 132, 0, 32}) {
234 return load_EC_group_info(
235 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D",
236 "0",
237 "5",
238 "0xA1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C",
239 "0x7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5",
240 "0x10000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7",
241 oid);
242 }
243
244 // secp224r1
245 if(oid == OID{1, 3, 132, 0, 33}) {
246 return load_EC_group_info(
247 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
248 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
249 "0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
250 "0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
251 "0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
252 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
253 oid);
254 }
255
256 // secp256k1
257 if(oid == OID{1, 3, 132, 0, 10}) {
258 return load_EC_group_info(
259 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F",
260 "0",
261 "7",
262 "0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798",
263 "0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8",
264 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",
265 oid);
266 }
267
268 // sm2p256v1
269 if(oid == OID{1, 2, 156, 10197, 1, 301}) {
270 return load_EC_group_info(
271 "0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF",
272 "0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC",
273 "0x28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93",
274 "0x32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7",
275 "0xBC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0",
276 "0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123",
277 oid);
278 }
279
280 // x962_p192v2
281 if(oid == OID{1, 2, 840, 10045, 3, 1, 2}) {
282 return load_EC_group_info(
283 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
284 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
285 "0xCC22D6DFB95C6B25E49C0D6364A4E5980C393AA21668D953",
286 "0xEEA2BAE7E1497842F2DE7769CFE9C989C072AD696F48034A",
287 "0x6574D11D69B6EC7A672BB82A083DF2F2B0847DE970B2DE15",
288 "0xFFFFFFFFFFFFFFFFFFFFFFFE5FB1A724DC80418648D8DD31",
289 oid);
290 }
291
292 // x962_p192v3
293 if(oid == OID{1, 2, 840, 10045, 3, 1, 3}) {
294 return load_EC_group_info(
295 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
296 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
297 "0x22123DC2395A05CAA7423DAECCC94760A7D462256BD56916",
298 "0x7D29778100C65A1DA1783716588DCE2B8B4AEE8E228F1896",
299 "0x38A90F22637337334B49DCB66A6DC8F9978ACA7648A943B0",
300 "0xFFFFFFFFFFFFFFFFFFFFFFFF7A62D031C83F4294F640EC13",
301 oid);
302 }
303
304 // x962_p239v1
305 if(oid == OID{1, 2, 840, 10045, 3, 1, 4}) {
306 return load_EC_group_info(
307 "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",
308 "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",
309 "0x6B016C3BDCF18941D0D654921475CA71A9DB2FB27D1D37796185C2942C0A",
310 "0xFFA963CDCA8816CCC33B8642BEDF905C3D358573D3F27FBBD3B3CB9AAAF",
311 "0x7DEBE8E4E90A5DAE6E4054CA530BA04654B36818CE226B39FCCB7B02F1AE",
312 "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF9E5E9A9F5D9071FBD1522688909D0B",
313 oid);
314 }
315
316 // x962_p239v2
317 if(oid == OID{1, 2, 840, 10045, 3, 1, 5}) {
318 return load_EC_group_info(
319 "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",
320 "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",
321 "0x617FAB6832576CBBFED50D99F0249C3FEE58B94BA0038C7AE84C8C832F2C",
322 "0x38AF09D98727705120C921BB5E9E26296A3CDCF2F35757A0EAFD87B830E7",
323 "0x5B0125E4DBEA0EC7206DA0FC01D9B081329FB555DE6EF460237DFF8BE4BA",
324 "0x7FFFFFFFFFFFFFFFFFFFFFFF800000CFA7E8594377D414C03821BC582063",
325 oid);
326 }
327
328 // x962_p239v3
329 if(oid == OID{1, 2, 840, 10045, 3, 1, 6}) {
330 return load_EC_group_info(
331 "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",
332 "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",
333 "0x255705FA2A306654B1F4CB03D6A750A30C250102D4988717D9BA15AB6D3E",
334 "0x6768AE8E18BB92CFCF005C949AA2C6D94853D0E660BBF854B1C9505FE95A",
335 "0x1607E6898F390C06BC1D552BAD226F3B6FCFE48B6E818499AF18E3ED6CF3",
336 "0x7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF975DEB41B3A6057C3C432146526551",
337 oid);
338 }
339
340 // numsp512d1
341 if(oid == OID{1, 3, 6, 1, 4, 1, 25258, 4, 3}) {
342 return load_EC_group_info(
343 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7",
344 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4",
345 "0x1D99B",
346 "0x2",
347 "0x1C282EB23327F9711952C250EA61AD53FCC13031CF6DD336E0B9328433AFBDD8CC5A1C1F0C716FDC724DDE537C2B0ADB00BB3D08DC83755B205CC30D7F83CF28",
348 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5B3CA4FB94E7831B4FC258ED97D0BDC63B568B36607CD243CE153F390433555D",
349 oid);
350 }
351
352 return std::shared_ptr<EC_Group_Data>();
353}

◆ 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 590 of file ec_group.cpp.

590 {
591 return data().engine();
592}
EC_Group_Engine engine() const

◆ 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 354 of file ec_group.cpp.

354 {
355 std::shared_ptr<EC_Group_Data> data;
356
357 if(auto oid = OID::from_name(name)) {
358 data = ec_group_data().lookup(oid.value());
359 }
360
361 if(!data) {
362 throw Invalid_Argument(fmt("Unknown EC_Group '{}'", name));
363 }
364
365 return EC_Group(std::move(data));
366}
static std::optional< OID > from_name(std::string_view name)
Definition asn1_oid.cpp:72
std::string name

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

Referenced by 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 343 of file ec_group.cpp.

343 {
344 auto data = ec_group_data().lookup(oid);
345
346 if(!data) {
347 throw Invalid_Argument(fmt("No EC_Group associated with OID '{}'", oid.to_string()));
348 }
349
350 return EC_Group(std::move(data));
351}

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

Referenced by 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 397 of file ec_group.cpp.

397 {
398 const auto ber = PEM_Code::decode_check_label(pem, "EC PARAMETERS");
399 return EC_Group(ber);
400}

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

◆ get_a()

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

Return the a parameter of the elliptic curve equation

Definition at line 518 of file ec_group.cpp.

518 {
519 return data().a();
520}
const BigInt & a() const

Referenced by 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 522 of file ec_group.cpp.

522 {
523 return data().b();
524}
const BigInt & b() const

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 574 of file ec_group.cpp.

574 {
575 return data().cofactor();
576}
const BigInt & cofactor() const

Referenced by DER_encode(), Botan::ECIES_KA_Operation::derive_secret(), 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 582 of file ec_group.cpp.

582 {
583 return data().oid();
584}
const OID & oid() const

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 566 of file ec_group.cpp.

566 {
567 return data().g_x();
568}
const BigInt & g_x() const

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 570 of file ec_group.cpp.

570 {
571 return data().g_y();
572}
const BigInt & g_y() const

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 562 of file ec_group.cpp.

562 {
563 return data().order();
564}
const BigInt & order() const

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 506 of file ec_group.cpp.

506 {
507 return data().order_bits();
508}
size_t order_bits() const

◆ 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 510 of file ec_group.cpp.

510 {
511 return data().order_bytes();
512}
size_t order_bytes() const

Referenced by Botan::GOST_3410_PublicKey::_signature_element_size_for_DER_encoding(), and Botan::ECIES_KA_Operation::derive_secret().

◆ get_p()

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

Return the prime modulus of the field

Definition at line 514 of file ec_group.cpp.

514 {
515 return data().p();
516}
const BigInt & p() const

Referenced by 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 498 of file ec_group.cpp.

498 {
499 return data().p_bits();
500}
size_t p_bits() const

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 502 of file ec_group.cpp.

502 {
503 return data().p_bytes();
504}
size_t p_bytes() const

Referenced by DER_encode(), Botan::EC_AffinePoint::from_bigint_xy(), 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 578 of file ec_group.cpp.

578 {
579 return data().has_cofactor();
580}
bool has_cofactor() const

Referenced by Botan::ECIES_KA_Operation::derive_secret().

◆ initialized()

bool Botan::EC_Group::initialized ( ) const
inline

Definition at line 234 of file ec_group.h.

234{ return (m_data != nullptr); }

◆ inverse_mod_order()

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

Definition at line 653 of file ec_group.h.

653 {
654 return EC_Scalar::from_bigint(*this, x).invert().to_bigint();
655 }
BigInt to_bigint() const
Definition ec_scalar.cpp:73
EC_Scalar invert() const

◆ 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 481 of file ec_named.cpp.

481 {
482 static const std::set<std::string> named_groups = {
483#if defined(BOTAN_HAS_PCURVES_BRAINPOOL256R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
484 "brainpool256r1",
485#endif
486#if defined(BOTAN_HAS_PCURVES_BRAINPOOL384R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
487 "brainpool384r1",
488#endif
489#if defined(BOTAN_HAS_PCURVES_BRAINPOOL512R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
490 "brainpool512r1",
491#endif
492#if defined(BOTAN_HAS_PCURVES_FRP256V1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
493 "frp256v1",
494#endif
495#if defined(BOTAN_HAS_PCURVES_NUMSP512D1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
496 "numsp512d1",
497#endif
498#if defined(BOTAN_HAS_PCURVES_SECP192R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
499 "secp192r1",
500#endif
501#if defined(BOTAN_HAS_PCURVES_SECP224R1) || defined(BOTAN_HAS_LEGACY_EC_POINT)
502 "secp224r1", // not supported by pcurves_generic
503#endif
504#if defined(BOTAN_HAS_PCURVES_SECP256K1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
505 "secp256k1",
506#endif
507#if defined(BOTAN_HAS_PCURVES_SECP256R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
508 "secp256r1",
509#endif
510#if defined(BOTAN_HAS_PCURVES_SECP384R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
511 "secp384r1",
512#endif
513#if defined(BOTAN_HAS_PCURVES_SECP521R1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
514 "secp521r1",
515#endif
516#if defined(BOTAN_HAS_PCURVES_SM2P256V1) || defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
517 "sm2p256v1",
518#endif
519
520#if defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
521 "brainpool192r1",
522 "brainpool224r1",
523 "brainpool320r1",
524 "gost_256A",
525 "gost_512A",
526 "secp192k1",
527 "secp192r1",
528 "x962_p192v2",
529 "x962_p192v3",
530 "x962_p239v1",
531 "x962_p239v2",
532 "x962_p239v3",
533#endif
534
535#if defined(BOTAN_HAS_LEGACY_EC_POINT)
536 "brainpool160r1",
537 "secp160k1",
538 "secp160r1",
539 "secp160r2",
540 "secp224k1",
541#endif
542 };
543 return named_groups;
544}

Referenced by supports_named_group().

◆ mod_order()

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

Definition at line 646 of file ec_group.h.

646 {
647 return EC_Scalar::from_bytes_mod_order(*this, x.serialize()).to_bigint();
648 }
static EC_Scalar from_bytes_mod_order(const EC_Group &group, std::span< const uint8_t > bytes)
Definition ec_scalar.cpp:49

Referenced by EC_Group().

◆ multiply_mod_order() [1/2]

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

Definition at line 669 of file ec_group.h.

669 {
670 auto xs = EC_Scalar::from_bigint(*this, x);
671 auto ys = EC_Scalar::from_bigint(*this, y);
672 return (xs * ys).to_bigint();
673 }

◆ 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 679 of file ec_group.h.

679 {
680 auto xs = EC_Scalar::from_bigint(*this, x);
681 auto ys = EC_Scalar::from_bigint(*this, y);
682 auto zs = EC_Scalar::from_bigint(*this, z);
683 return (xs * ys * zs).to_bigint();
684 }

◆ operator=() [1/2]

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

◆ operator=() [2/2]

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

◆ operator==()

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

Definition at line 644 of file ec_group.cpp.

644 {
645 if(m_data == other.m_data) {
646 return true; // same shared rep
647 }
648
649 return (get_p() == other.get_p() && get_a() == other.get_a() && get_b() == other.get_b() &&
650 get_g_x() == other.get_g_x() && get_g_y() == other.get_g_y() && get_order() == other.get_order() &&
651 get_cofactor() == other.get_cofactor());
652}
const BigInt & get_g_y() const
Definition ec_group.cpp:570
const BigInt & get_g_x() const
Definition ec_group.cpp:566

References 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 ( ) const

Return the PEM encoding (always in explicit form)

Returns
string containing PEM data

Definition at line 639 of file ec_group.cpp.

639 {
640 const std::vector<uint8_t> der = DER_encode(EC_Group_Encoding::Explicit);
641 return PEM_Code::encode(der, "EC PARAMETERS");
642}
std::string encode(const uint8_t der[], size_t length, std::string_view label, size_t width)
Definition pem.cpp:39

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

◆ point_size()

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

Definition at line 694 of file ec_group.h.

694 {
695 // Hybrid and standard format are (x,y), compressed is y, +1 format byte
696 if(format == EC_Point_Format::Compressed) {
697 return (1 + get_p_bytes());
698 } else {
699 return (1 + 2 * get_p_bytes());
700 }
701 }

◆ source()

EC_Group_Source Botan::EC_Group::source ( ) const

Definition at line 586 of file ec_group.cpp.

586 {
587 return data().source();
588}
EC_Group_Source source() const

Referenced by verify_group().

◆ square_mod_order()

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

Definition at line 660 of file ec_group.h.

660 {
661 auto xs = EC_Scalar::from_bigint(*this, x);
662 xs.square_self();
663 return xs.to_bigint();
664 }

◆ 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 334 of file ec_group.cpp.

334 {
335#if defined(BOTAN_HAS_LEGACY_EC_POINT) || defined(BOTAN_HAS_PCURVES_GENERIC)
336 return true;
337#else
338 return false;
339#endif
340}

◆ 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 476 of file ec_named.cpp.

476 {
477 return EC_Group::known_named_groups().contains(std::string(name));
478}
static const std::set< std::string > & known_named_groups()
Definition ec_named.cpp:481

References known_named_groups(), and name.

Referenced by 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 654 of file ec_group.cpp.

654 {
655 const bool is_builtin = source() == EC_Group_Source::Builtin;
656
657 if(is_builtin && !strong) {
658 return true;
659 }
660
661 // TODO(Botan4) this can probably all be removed once the deprecated EC_Group
662 // constructor is removed, since at that point it no longer becomes possible
663 // to create an EC_Group which fails to satisfy these conditions
664
665 const BigInt& p = get_p();
666 const BigInt& a = get_a();
667 const BigInt& b = get_b();
668 const BigInt& order = get_order();
669
670 if(p <= 3 || order <= 0) {
671 return false;
672 }
673 if(a < 0 || a >= p) {
674 return false;
675 }
676 if(b <= 0 || b >= p) {
677 return false;
678 }
679
680 const size_t test_prob = 128;
681 const bool is_randomly_generated = is_builtin;
682
683 //check if field modulus is prime
684 if(!is_prime(p, rng, test_prob, is_randomly_generated)) {
685 return false;
686 }
687
688 //check if order is prime
689 if(!is_prime(order, rng, test_prob, is_randomly_generated)) {
690 return false;
691 }
692
693 //compute the discriminant: 4*a^3 + 27*b^2 which must be nonzero
695
696 const BigInt discriminant = mod_p.reduce(mod_p.multiply(4, mod_p.cube(a)) + mod_p.multiply(27, mod_p.square(b)));
697
698 if(discriminant == 0) {
699 return false;
700 }
701
702 //check for valid cofactor
703 if(get_cofactor() < 1) {
704 return false;
705 }
706
707#if defined(BOTAN_HAS_LEGACY_EC_POINT)
708 const EC_Point& base_point = get_base_point();
709 //check if the base point is on the curve
710 if(!base_point.on_the_curve()) {
711 return false;
712 }
713 if((base_point * get_cofactor()).is_zero()) {
714 return false;
715 }
716 //check if order of the base point is correct
717 if(!(base_point * order).is_zero()) {
718 return false;
719 }
720#endif
721
722 // check the Hasse bound (roughly)
723 if((p - get_cofactor() * order).abs().bits() > (p.bits() / 2) + 1) {
724 return false;
725 }
726
727 return true;
728}
EC_Group_Source source() const
Definition ec_group.cpp:586
bool is_prime(const BigInt &n, RandomNumberGenerator &rng, size_t prob, bool is_random)
Definition numthry.cpp:355

References Botan::abs(), Botan::b, Botan::BigInt::bits(), Botan::Builtin, Botan::Modular_Reducer::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: