Module: JOSE::JWA::X448

Extended by:
X448
Included in:
X448
Defined in:
lib/jose/jwa/x448.rb

Constant Summary collapse

C_p = 
((2 ** 448) - (2 ** 224) - 1).to_bn.freeze
C_A = 
156326.to_bn.freeze
C_order = 
((2 ** 446) + 0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d).to_bn.freeze
C_cofactor = 
4.to_bn.freeze
C_u = 
5.to_bn.freeze
C_v = 
355293926785568175264127502063783334808976399387714271831880898435169088786967410002932673765864550910142774147268105838985595290606362.to_bn.freeze
C_bits = 
448.to_bn.freeze
C_bytes = 
((C_bits + 7) / 8)[0].freeze
C_bit_steps = 
(C_bits-1).to_i.downto(0).to_a.freeze
C_byte_steps = 
(C_bytes-1).to_i.downto(0).to_a.freeze
C_a24 = 
((C_A - 2) / 4)[0].freeze
C_scalarbytes = 
C_bytes
C_coordinatebytes = 
C_bytes
C_one = 
1.to_bn.freeze
C_zero = 
0.to_bn.freeze
C_F = 
JOSE::JWA::FieldElement.new(C_one, C_p).freeze
C_F_one = 
C_F
C_F_zero = 
C_F.make(C_zero).freeze
C_F_a24 = 
C_F.make(C_a24).freeze

Instance Method Summary collapse

Instance Method Details

#clamp_scalar(scalar) ⇒ Object 



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# File 'lib/jose/jwa/x448.rb', line 25

def clamp_scalar(scalar)
  scalar = coerce_coordinate_bytes!(scalar)
  scalar.setbyte(0, scalar.getbyte(0) & 252)
  scalar.setbyte(55, scalar.getbyte(55) | 128)
  return C_F.from_bytes(scalar, C_bits)
end

#coerce_coordinate_bn!(coordinate) ⇒ Object

Raises:

  • (ArgumentError) 


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# File 'lib/jose/jwa/x448.rb', line 110

def coerce_coordinate_bn!(coordinate)
  raise ArgumentError, "coordinate size must be #{C_coordinatebytes} bytes" if not valid_coordinate?(coordinate)
  coordinate = coordinate.value if coordinate.is_a?(JOSE::JWA::FieldElement)
  coordinate = coordinate.to_bn if not coordinate.is_a?(OpenSSL::BN) and coordinate.respond_to?(:to_bn)
  coordinate = OpenSSL::BN.new(coordinate.reverse, 2) if coordinate.respond_to?(:bytesize)
  return coordinate
end

#coerce_coordinate_bytes!(coordinate) ⇒ Object

Raises:

  • (ArgumentError) 


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# File 'lib/jose/jwa/x448.rb', line 126

def coerce_coordinate_bytes!(coordinate)
  raise ArgumentError, "coordinate size must be #{C_coordinatebytes} bytes" if not valid_coordinate?(coordinate)
  coordinate = coordinate.to_bytes(C_bits) if coordinate.is_a?(JOSE::JWA::FieldElement)
  coordinate = coordinate.to_bn if not coordinate.is_a?(OpenSSL::BN) and coordinate.respond_to?(:to_bn)
  coordinate = coordinate.to_s(2).rjust(C_bytes, JOSE::JWA::ZERO_PAD).reverse if coordinate.is_a?(OpenSSL::BN)
  return coordinate
end

#coerce_coordinate_fe!(coordinate) ⇒ Object 



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# File 'lib/jose/jwa/x448.rb', line 142

def coerce_coordinate_fe!(coordinate)
  return coordinate if coordinate.is_a?(JOSE::JWA::FieldElement) and coordinate.p == C_p
  coordinate = coerce_coordinate_bn!(coordinate)
  return C_F.make(coordinate)
end

#coerce_scalar_bn!(scalar) ⇒ Object

Raises:

  • (ArgumentError) 


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# File 'lib/jose/jwa/x448.rb', line 118

def coerce_scalar_bn!(scalar)
  raise ArgumentError, "scalar size must be #{C_scalarbytes} bytes" if not valid_scalar?(scalar)
  scalar = scalar.value if scalar.is_a?(JOSE::JWA::FieldElement)
  scalar = scalar.to_bn if not scalar.is_a?(OpenSSL::BN) and scalar.respond_to?(:to_bn)
  scalar = OpenSSL::BN.new(scalar.reverse, 2) if scalar.respond_to?(:bytesize)
  return scalar
end

#coerce_scalar_bytes!(scalar) ⇒ Object

Raises:

  • (ArgumentError) 


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# File 'lib/jose/jwa/x448.rb', line 134

def coerce_scalar_bytes!(scalar)
  raise ArgumentError, "scalar size must be #{C_scalarbytes} bytes" if not valid_scalar?(scalar)
  scalar = scalar.to_bytes(C_bits) if scalar.is_a?(JOSE::JWA::FieldElement)
  scalar = scalar.to_bn if not scalar.is_a?(OpenSSL::BN) and scalar.respond_to?(:to_bn)
  scalar = scalar.to_s(2).rjust(C_bytes, JOSE::JWA::ZERO_PAD).reverse if scalar.is_a?(OpenSSL::BN)
  return scalar
end

#coerce_scalar_fe!(scalar) ⇒ Object 



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# File 'lib/jose/jwa/x448.rb', line 148

def coerce_scalar_fe!(scalar)
  return scalar if scalar.is_a?(JOSE::JWA::FieldElement) and scalar.p == C_p
  scalar = coerce_scalar_bn!(scalar)
  return C_F.make(scalar)
end

#cswap(swap, x_2, x_3) ⇒ Object 



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# File 'lib/jose/jwa/x448.rb', line 32

def cswap(swap, x_2, x_3)
  iswap = (-swap.x.to_i) & 0xff
  x_2 = x_2.to_bytes(C_bits)
  x_3 = x_3.to_bytes(C_bits)
  C_byte_steps.each do |i|
    x_2i = x_2.getbyte(i)
    x_3i = x_3.getbyte(i)
    s = iswap & (x_2i ^ x_3i)
    x_2.setbyte(i, x_2i ^ s)
    x_3.setbyte(i, x_3i ^ s)
  end
  x_2 = C_F.from_bytes(x_2, C_bits)
  x_3 = C_F.from_bytes(x_3, C_bits)
  return x_2, x_3
end

#curve448(k, u) ⇒ Object 



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# File 'lib/jose/jwa/x448.rb', line 48

def curve448(k, u)
  x_1 = u
  x_2 = C_F_one
  z_2 = C_F_zero
  x_3 = u
  z_3 = C_F_one
  swap = C_F_zero

  C_bit_steps.each do |t|
    k_t = (k >> t) & 1
    swap ^= k_t
    x_2, x_3 = cswap(swap, x_2, x_3)
    z_2, z_3 = cswap(swap, z_2, z_3)
    swap = k_t

    a = x_2 + z_2
    aa = a.sqr
    b = x_2 - z_2
    bb = b.sqr
    e = aa - bb
    c = x_3 + z_3
    d = x_3 - z_3
    da = d * a
    cb = c * b
    x_3 = (da + cb).sqr
    z_3 = x_1 * (da - cb).sqr
    x_2 = aa * bb
    z_2 = e * (aa + C_F_a24 * e)
  end

  x_2, x_3 = cswap(swap, x_2, x_3)
  z_2, z_3 = cswap(swap, z_2, z_3)

  return x_2 / z_2
end

#keypair(sk = nil) ⇒ Object 



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# File 'lib/jose/jwa/x448.rb', line 95

def keypair(sk = nil)
  sk ||= SecureRandom.random_bytes(C_bytes)
  sk = clamp_scalar(sk)
  pk = sk_to_pk(sk)
  return pk, sk.to_bytes(C_bits)
end

#shared_secret(pk, sk) ⇒ Object 



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# File 'lib/jose/jwa/x448.rb', line 102

def shared_secret(pk, sk)
  return x448(sk, pk)
end

#sk_to_pk(sk) ⇒ Object 



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# File 'lib/jose/jwa/x448.rb', line 106

def sk_to_pk(sk)
  return x448_base(sk)
end

#valid_coordinate?(coordinate) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/jose/jwa/x448.rb', line 154

def valid_coordinate?(coordinate)
  return true if coordinate.is_a?(JOSE::JWA::FieldElement) and coordinate.p == C_p
  if not coordinate.is_a?(OpenSSL::BN) and coordinate.respond_to?(:to_bn)
    coordinate = coordinate.to_bn
  end
  ubytes = 0
  if coordinate.is_a?(OpenSSL::BN)
    if coordinate.num_bytes > C_coordinatebytes
      ubytes = coordinate.num_bytes
    else
      ubytes = C_coordinatebytes
    end
  end
  ubytes = coordinate.bytesize if coordinate.respond_to?(:bytesize)
  return !!(ubytes == C_coordinatebytes)
end

#valid_scalar?(scalar) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/jose/jwa/x448.rb', line 171

def valid_scalar?(scalar)
  return true if scalar.is_a?(JOSE::JWA::FieldElement) and scalar.p == C_p
  if not scalar.is_a?(OpenSSL::BN) and scalar.respond_to?(:to_bn)
    scalar = scalar.to_bn
  end
  kbytes = 0
  if scalar.is_a?(OpenSSL::BN)
    if scalar.num_bytes > C_scalarbytes
      kbytes = scalar.num_bytes
    else
      kbytes = C_scalarbytes
    end
  end
  kbytes = scalar.bytesize if scalar.respond_to?(:bytesize)
  return !!(kbytes == C_scalarbytes)
end

#x448(sk, pk) ⇒ Object 



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# File 'lib/jose/jwa/x448.rb', line 84

def x448(sk, pk)
  u = coerce_coordinate_fe!(pk)
  k = clamp_scalar(sk)
  r = curve448(k, u)
  return r.to_bytes(C_bits)
end

#x448_base(sk) ⇒ Object 



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# File 'lib/jose/jwa/x448.rb', line 91

def x448_base(sk)
  return x448(sk, C_u)
end