Class: ECDSA::Group

Inherits:
Object
  • Object
show all
Defined in:
lib/ecdsa/group.rb,
lib/ecdsa/group/nistp192.rb,
lib/ecdsa/group/nistp224.rb,
lib/ecdsa/group/nistp256.rb,
lib/ecdsa/group/nistp384.rb,
lib/ecdsa/group/nistp521.rb,
lib/ecdsa/group/secp112r1.rb,
lib/ecdsa/group/secp112r2.rb,
lib/ecdsa/group/secp128r1.rb,
lib/ecdsa/group/secp128r2.rb,
lib/ecdsa/group/secp160k1.rb,
lib/ecdsa/group/secp160r1.rb,
lib/ecdsa/group/secp160r2.rb,
lib/ecdsa/group/secp192k1.rb,
lib/ecdsa/group/secp192r1.rb,
lib/ecdsa/group/secp224k1.rb,
lib/ecdsa/group/secp224r1.rb,
lib/ecdsa/group/secp256k1.rb,
lib/ecdsa/group/secp256r1.rb,
lib/ecdsa/group/secp384r1.rb,
lib/ecdsa/group/secp521r1.rb

Constant Summary collapse

Nistp192 = 
new(
  name: 'nistp192',
  p: 62771017353866807638357894232076664160839087_00390324961279,
  a: -3,
  b: 0x64210519_e59c80e7_0fa7e9ab_72243049_feb8deec_c146b9b1,
  g: [0x188da80e_b03090f6_7cbf20eb_43a18800_f4ff0afd_82ff1012,
      0x07192b95_ffc8da78_631011ed_6b24cdd5_73f977a1_1e794811],
  n: 62771017353866807638357894231760590137671947_73182842284081,
  h: nil,  # cofactor not given in NIST document
)
Nistp224 = 
new(
  name: 'nistp224',
  p: 26959946667150639794667015087019630673557916_260026308143510066298881,
  a: -3,
  b: 0xb4050a85_0c04b3ab_f5413256_5044b0b7_d7bfd8ba_270b3943_2355ffb4,
  g: [0xb70e0cbd_6bb4bf7f_321390b9_4a03c1d3_56c21122_343280d6_115c1d21,
      0xbd376388_b5f723fb_4c22dfe6_cd4375a0_5a074764_44d58199_85007e34],
  n: 26959946667150639794667015087019625940457807_714424391721682722368061,
  h: nil,  # cofactor not given in NIST document
)
Nistp256 = 
new(
  name: 'nistp256',
  p: 11579208921035624876269744694940757353008614_3415290314195533631308867097853951,
  a: -3,
  b: 0x5ac635d8_aa3a93e7_b3ebbd55_769886bc_651d06b0_cc53b0f6_3bce3c3e_27d2604b,
  g: [0x6b17d1f2_e12c4247_f8bce6e5_63a440f2_77037d81_2deb33a0_f4a13945_d898c296,
      0x4fe342e2_fe1a7f9b_8ee7eb4a_7c0f9e16_2bce3357_6b315ece_cbb64068_37bf51f5],
  n: 11579208921035624876269744694940757352999695_5224135760342422259061068512044369,
  h: nil,  # cofactor not given in NIST document
)
Nistp384 = 
new(
  name: 'nistp384',
  p: 39402006196394479212279040100143613805079739_27046544666794829340424572177149687032904726_6088258938001861606973112319,
  a: -3,
  b: 0xb3312fa7_e23ee7e4_988e056b_e3f82d19_181d9c6e_fe814112_0314088f_5013875a_c656398d_8a2ed19d_2a85c8ed_d3ec2aef,
  g: [0xaa87ca22_be8b0537_8eb1c71e_f320ad74_6e1d3b62_8ba79b98_59f741e0_82542a38_5502f25d_bf55296c_3a545e38_72760ab7,
      0x3617de4a_96262c6f_5d9e98bf_9292dc29_f8f41dbd_289a147c_e9da3113_b5f0b8c0_0a60b1ce_1d7e819d_7a431d7c_90ea0e5f,
     ],
  n: 39402006196394479212279040100143613805079739_27046544666794690527962765939911326356939895_6308152294913554433653942643,
  h: nil,  # cofactor not given in NIST document
)
Nistp521 = 
new(
  name: 'nistp521',
  p: 68647976601306097149819007990813932172694353_00143305409394463459185543183397656052122559_64066145455497729631139148085803712198799971_6643812574028291115057151,
  a: -3,
  b: 0x051_953eb961_8e1c9a1f_929a21a0_b68540ee_a2da725b_99b315f3_b8b48991_8ef109e1_56193951_ec7e937b_1652c0bd_3bb1bf07_3573df88_3d2c34f1_ef451fd4_6b503f00,
  g: [0x00c6_858e06b7_0404e9cd_9e3ecb66_2395b442_9c648139_053fb521_f828af60_6b4d3dba_a14b5e77_efe75928_fe1dc127_a2ffa8de_3348b3c1_856a429b_f97e7e31_c2e5bd66,
      0x0118_39296a78_9a3bc004_5c8a5fb4_2c7d1bd9_98f54449_579b4468_17afbd17_273e662c_97ee7299_5ef42640_c550b901_3fad0761_353c7086_a272c240_88be9476_9fd16650],
  n: 68647976601306097149819007990813932172694353_00143305409394463459185543183397655394245057_74633321719753296399637136332111386476861244_0380340372808892707005449,
  h: nil,  # cofactor not given in NIST document
)
Secp112r1 = 
new(
  name: 'secp112r1',
  p: 0xDB7C_2ABF62E3_5E668076_BEAD208B,
  a: 0xDB7C_2ABF62E3_5E668076_BEAD2088,
  b: 0x659E_F8BA0439_16EEDE89_11702B22,
  g: [0x0948_7239995A_5EE76B55_F9C2F098,
      0xA89C_E5AF8724_C0A23E0E_0FF77500],
  n: 0xDB7C_2ABF62E3_5E7628DF_AC6561C5,
  h: 1,
)
Secp112r2 = 
new(
  name: 'secp112r2',
  p: 0xDB7C_2ABF62E3_5E668076_BEAD208B,
  a: 0x6127_C24C05F3_8A0AAAF6_5C0EF02C,
  b: 0x51DE_F1815DB5_ED74FCC3_4C85D709,
  g: [0x4BA3_0AB5E892_B4E1649D_D0928643,
      0xADCD_46F5882E_3747DEF3_6E956E97],
  n: 0x36DF_0AAFD8B8_D7597CA1_0520D04B,
  h: 4,
)
Secp128r1 = 
new(
  name: 'secp128r1',
  p: 0xFFFFFFFD_FFFFFFFF_FFFFFFFF_FFFFFFFF,
  a: 0xFFFFFFFD_FFFFFFFF_FFFFFFFF_FFFFFFFC,
  b: 0xE87579C1_1079F43D_D824993C_2CEE5ED3,
  g: [0x161FF752_8B899B2D_0C28607C_A52C5B86,
      0xCF5AC839_5BAFEB13_C02DA292_DDED7A83],
  n: 0xFFFFFFFE_00000000_75A30D1B_9038A115,
  h: 1,
)
Secp128r2 = 
new(
  name: 'secp128r2',
  p: 0xFFFFFFFD_FFFFFFFF_FFFFFFFF_FFFFFFFF,
  a: 0xD6031998_D1B3BBFE_BF59CC9B_BFF9AEE1,
  b: 0x5EEEFCA3_80D02919_DC2C6558_BB6D8A5D,
  g: [0x7B6AA5D8_5E572983_E6FB32A7_CDEBC140,
      0x27B6916A_894D3AEE_7106FE80_5FC34B44],
  n: 0x3FFFFFFF_7FFFFFFF_BE002472_0613B5A3,
  h: 4,
)
Secp160k1 = 
new(
  name: 'secp160k1',
  p: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFAC73,
  a: 0,
  b: 7,
  g: [0x3B4C382C_E37AA192_A4019E76_3036F4F5_DD4D7EBB,
      0x938CF935_318FDCED_6BC28286_531733C3_F03C4FEE],
  n: 0x01_00000000_00000000_0001B8FA_16DFAB9A_CA16B6B3,
  h: 1,
)
Secp160r1 = 
new(
  name: 'secp160r1',
  p: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_7FFFFFFF,
  a: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_7FFFFFFC,
  b: 0x1C97BEFC_54BD7A8B_65ACF89F_81D4D4AD_C565FA45,
  g: [0x4A96B568_8EF57328_46646989_68C38BB9_13CBFC82,
      0x23A62855_3168947D_59DCC912_04235137_7AC5FB32],
  n: 0x01_00000000_00000000_0001F4C8_F927AED3_CA752257,
  h: 1,
)
Secp160r2 = 
new(
  name: 'secp160r2',
  p: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFAC73,
  a: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFAC70,
  b: 0xB4E134D3_FB59EB8B_AB572749_04664D5A_F50388BA,
  g: [0x52DCB034_293A117E_1F4FF11B_30F7199D_3144CE6D,
      0xFEAFFEF2_E331F296_E071FA0D_F9982CFE_A7D43F2E],
  n: 0x01_00000000_00000000_0000351E_E786A818_F3A1A16B,
  h: 1,
)
Secp192k1 = 
new(
  name: 'secp192k1',
  p: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFEE37,
  a: 0,
  b: 3,
  g: [0xDB4FF10E_C057E9AE_26B07D02_80B7F434_1DA5D1B1_EAE06C7D,
      0x9B2F2F6D_9C5628A7_844163D0_15BE8634_4082AA88_D95E2F9D],
  n: 0xFFFFFFFF_FFFFFFFF_FFFFFFFE_26F2FC17_0F69466A_74DEFD8D,
  h: 1,
)
Secp192r1 = 
new(
  name: 'secp192r1',
  p: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFFFFF_FFFFFFFF,
  a: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFFFFF_FFFFFFFC,
  b: 0x64210519_E59C80E7_0FA7E9AB_72243049_FEB8DEEC_C146B9B1,
  g: [0x188DA80E_B03090F6_7CBF20EB_43A18800_F4FF0AFD_82FF1012,
      0x07192B95_FFC8DA78_631011ED_6B24CDD5_73F977A1_1E794811],
  n: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_99DEF836_146BC9B1_B4D22831,
  h: 1,
)
Secp224k1 = 
new(
  name: 'secp224k1',
  p: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFE56D,
  a: 0,
  b: 5,
  g: [0xA1455B33_4DF099DF_30FC28A1_69A467E9_E47075A9_0F7E650E_B6B7A45C,
      0x7E089FED_7FBA3442_82CAFBD6_F7E319F7_C0B0BD59_E2CA4BDB_556D61A5],
  n: 0x01_00000000_00000000_00000000_0001DCE8_D2EC6184_CAF0A971_769FB1F7,
  h: 1,
)
Secp224r1 = 
new(
  name: 'secp224r1',
  p: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_00000000_00000000_00000001,
  a: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFFFFF_FFFFFFFF_FFFFFFFE,
  b: 0xB4050A85_0C04B3AB_F5413256_5044B0B7_D7BFD8BA_270B3943_2355FFB4,
  g: [0xB70E0CBD_6BB4BF7F_321390B9_4A03C1D3_56C21122_343280D6_115C1D21,
      0xBD376388_B5F723FB_4C22DFE6_CD4375A0_5A074764_44D58199_85007E34],
  n: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFF16A2_E0B8F03E_13DD2945_5C5C2A3D,
  h: 1,
)
Secp256k1 = 
new(
  name: 'secp256k1',
  p: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFFC2F,
  a: 0,
  b: 7,
  g: [0x79BE667E_F9DCBBAC_55A06295_CE870B07_029BFCDB_2DCE28D9_59F2815B_16F81798,
      0x483ADA77_26A3C465_5DA4FBFC_0E1108A8_FD17B448_A6855419_9C47D08F_FB10D4B8],
  n: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_BAAEDCE6_AF48A03B_BFD25E8C_D0364141,
  h: 1,
)
Secp256r1 = 
new(
  name: 'secp256r1',
  p: 0xFFFFFFFF_00000001_00000000_00000000_00000000_FFFFFFFF_FFFFFFFF_FFFFFFFF,
  a: 0xFFFFFFFF_00000001_00000000_00000000_00000000_FFFFFFFF_FFFFFFFF_FFFFFFFC,
  b: 0x5AC635D8_AA3A93E7_B3EBBD55_769886BC_651D06B0_CC53B0F6_3BCE3C3E_27D2604B,
  g: [0x6B17D1F2_E12C4247_F8BCE6E5_63A440F2_77037D81_2DEB33A0_F4A13945_D898C296,
      0x4FE342E2_FE1A7F9B_8EE7EB4A_7C0F9E16_2BCE3357_6B315ECE_CBB64068_37BF51F5],
  n: 0xFFFFFFFF_00000000_FFFFFFFF_FFFFFFFF_BCE6FAAD_A7179E84_F3B9CAC2_FC632551,
  h: 1,
)
Secp384r1 = 
new(
  name: 'secp384r1',
  p: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFFFFF_00000000_00000000_FFFFFFFF,
  a: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFFFFF_00000000_00000000_FFFFFFFC,
  b: 0xB3312FA7_E23EE7E4_988E056B_E3F82D19_181D9C6E_FE814112_0314088F_5013875A_C656398D_8A2ED19D_2A85C8ED_D3EC2AEF,
  g: [0xAA87CA22_BE8B0537_8EB1C71E_F320AD74_6E1D3B62_8BA79B98_59F741E0_82542A38_5502F25D_BF55296C_3A545E38_72760AB7,
      0x3617DE4A_96262C6F_5D9E98BF_9292DC29_F8F41DBD_289A147C_E9DA3113_B5F0B8C0_0A60B1CE_1D7E819D_7A431D7C_90EA0E5F],
  n: 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_C7634D81_F4372DDF_581A0DB2_48B0A77A_ECEC196A_CCC52973,
  h: 1,
)
Secp521r1 = 
new(
  name: 'secp521r1',
  p: 0x01FF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF,
  a: 0x01FF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFC,
  b: 0x0051_953EB961_8E1C9A1F_929A21A0_B68540EE_A2DA725B_99B315F3_B8B48991_8EF109E1_56193951_EC7E937B_1652C0BD_3BB1BF07_3573DF88_3D2C34F1_EF451FD4_6B503F00,
  g: [0x00C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66,
      0x011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650],
  n: 0x01FF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFA_51868783_BF2F966B_7FCC0148_F709A5D0_3BB5C9B8_899C47AE_BB6FB71E_91386409,
  h: 1,
)

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(opts) ⇒ Group

These parameters are defined in www.secg.org/collateral/sec2_final.pdf

Parameters:

  • opts (Hash)

Options Hash (opts):

  • :p (Object) — default: Integer —

    A prime number that defines the field used. The field will be *F<sub>p</sub>*.

  • :a (Object) — default: Integer —

    The a parameter in the curve equation (*y^2 = x^3 + ax + b*).

  • :b (Object) — default: Integer —

    The b parameter in the curve equation.

  • :g (Object) — default: Array(Integer) —

    The coordinates of the generator point, with x first.

  • :n (Object) — default: Integer —

    The order of g. This is the smallest positive integer ‘i` such that the generator point multiplied by `i` is infinity. This is also the number of different points that are on the curve.

  • :h (Object) — default: Integer —

    The cofactor (optional).



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# File 'lib/ecdsa/group.rb', line 51

def initialize(opts)
  @opts = opts

  @name = opts.fetch(:name) { '%#x' % object_id }
  @field = PrimeField.new(opts[:p])
  @param_a = opts[:a]
  @param_b = opts[:b]
  @generator = new_point(@opts[:g])
  @order = opts[:n]
  @cofactor = opts[:h]

  @param_a.is_a?(Integer) or raise ArgumentError, 'Invalid a.'
  @param_b.is_a?(Integer) or raise ArgumentError, 'Invalid b.'

  @param_a = field.mod @param_a
  @param_b = field.mod @param_b
end

Instance Attribute Details

#cofactor ⇒ Object (readonly)

The cofactor of the group. This is the number of points on the curve divided by the number of points in the group generated by the generator.



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# File 'lib/ecdsa/group.rb', line 26

def cofactor
  @cofactor
end

#field ⇒ PrimeField (readonly)

The field that coordinates on the curve belong to.

Returns:



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# File 'lib/ecdsa/group.rb', line 38

def field
  @field
end

#generator ⇒ Point (readonly)

The generator point.

Returns:



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# File 'lib/ecdsa/group.rb', line 15

def generator
  @generator
end

#name ⇒ String (readonly)

The name of the group.

Returns:

  • (String) 


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# File 'lib/ecdsa/group.rb', line 11

def name
  @name
end

#order ⇒ Order (readonly)

The order of the group. This is the smallest positive integer ‘i` such that the generator point multiplied by `i` is infinity. This is also the number of different points that are on the curve.

Returns:

  • (Order) 


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# File 'lib/ecdsa/group.rb', line 21

def order
  @order
end

#param_a ⇒ Object (readonly)

The a parameter in the curve equation (*y^2 = x^3 + ax + b*).



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# File 'lib/ecdsa/group.rb', line 30

def param_a
  @param_a
end

#param_b ⇒ Integer (readonly)

The b parameter in the curve equation.

Returns:

  • (Integer) 


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# File 'lib/ecdsa/group.rb', line 34

def param_b
  @param_b
end

Instance Method Details

#bit_length ⇒ Integer

The number of bits that it takes to represent a member of the field. Log base 2 of the prime p, rounded up.

Returns:

  • (Integer) 


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# File 'lib/ecdsa/group.rb', line 97

def bit_length
  @bit_length ||= ECDSA.bit_length(field.prime)
end

#byte_length ⇒ Integer

The number of bytes that it takes to represent a member of the field. Log base 256 of the prime p, rounded up.

Returns:

  • (Integer) 


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# File 'lib/ecdsa/group.rb', line 105

def byte_length
  @byte_length ||= ECDSA.byte_length(field.prime)
end

#include?(point) ⇒ Boolean

Returns true if the point is a solution to the curve’s defining equation or if it is the infinity point.

Returns:

  • (Boolean) 


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# File 'lib/ecdsa/group.rb', line 111

def include?(point)
  return false if point.group != self
  point.infinity? or point_satisfies_equation?(point)
end

#infinity ⇒ Point Also known as: infinity_point

Returns the infinity point.

Returns:



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# File 'lib/ecdsa/group.rb', line 89

def infinity
  @infinity ||= Point.new(self, :infinity)
end

#inspect ⇒ String

Returns:

  • (String) 


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# File 'lib/ecdsa/group.rb', line 143

def inspect
  "#<#{self.class}:#{name}>"
end

#new_point(p) ⇒ Object

Creates a new point. The argument can either be an array of integers representing the coordinates, with x first, or it can be ‘:infinity`.



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# File 'lib/ecdsa/group.rb', line 72

def new_point(p)
  case p
  when :infinity
    infinity
  when Array
    x, y = p
    Point.new(self, x, y)
  when Integer
    generator.multiply_by_scalar(p)
  else
    raise ArgumentError, "Invalid point specifier #{p.inspect}."
  end
end

#partially_valid_public_key?(point) ⇒ Boolean

Returns true if the point is not infinity and it is a solution to the curve’s defining equation. This is defined in SEC1 2.0, Section 3.2.3.1: Elliptic Curve Public Key Partial Validation Primitive

Returns:

  • (Boolean) 


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# File 'lib/ecdsa/group.rb', line 129

def partially_valid_public_key?(point)
  return false if point.group != self
  return false if point.infinity?
  point_satisfies_equation?(point)
end

#solve_for_y(x) ⇒ Array

Given the x coordinate of a point, finds all possible corresponding y coordinates.

Returns:

  • (Array) 


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# File 'lib/ecdsa/group.rb', line 138

def solve_for_y(x)
  field.square_roots equation_right_hand_side x
end

#to_s ⇒ String

Returns:

  • (String) 


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# File 'lib/ecdsa/group.rb', line 148

def to_s
  inspect
end

#valid_public_key?(point) ⇒ Boolean

Returns true if the point is not infinity, it is a solution to the curve’s defining equation, and it is a multiple of G. This process is defined in SEC1 2.0, Section 3.2.2.1: Elliptic Curve Public Key Partial Validation Primitive

Returns:

  • (Boolean) 


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# File 'lib/ecdsa/group.rb', line 119

def valid_public_key?(point)
  return false if point.group != self
  return false if point.infinity?
  return false if !point_satisfies_equation?(point)
  point.multiply_by_scalar(order).infinity?
end