Class: BLS::Fp12

Inherits:
Object
  • Object
show all
Includes:
FQP
Defined in:
lib/bls/field.rb

Overview

Finite extension field over irreducible polynomial. Fp6(w) / (w2 - γ) where γ = v

Constant Summary collapse

ZERO = 
Fp12.new([Fp6::ZERO, Fp6::ZERO])
ONE = 
Fp12.new([Fp6::ONE, Fp6::ZERO])
FROBENIUS_COEFFICIENTS = 
[
  Fp2.new([
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x1904d3bf02bb0667c231beb4202c0d1f0fd603fd3cbd5f4f7b2443d784bab9c4f67ea53d63e7813d8d0775ed92235fb8,
            0x00fc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3
          ]),
  Fp2.new([
            0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffff,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2,
            0x06af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09
          ]),
  Fp2.new([
            0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995,
            0x05b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116
          ]),
  Fp2.new([
            0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x00fc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3,
            0x1904d3bf02bb0667c231beb4202c0d1f0fd603fd3cbd5f4f7b2443d784bab9c4f67ea53d63e7813d8d0775ed92235fb8
          ]),
  Fp2.new([
            0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x06af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09,
            0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2
          ]),
  Fp2.new([
            0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x05b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116,
            0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995
          ])
].freeze

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Methods included from FQP

#==, #add, #conjugate, #div, #negate, #pow, #subtract, #to_bytes, #to_hex, #zero?

Constructor Details

#initialize(coeffs) ⇒ Fp12

Returns a new instance of Fp12.

Raises:

  • (ArgumentError) 


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# File 'lib/bls/field.rb', line 448

def initialize(coeffs)
  raise ArgumentError, 'Expected array with 2 elements' unless coeffs.size == 2

  @coeffs = coeffs
end

Instance Attribute Details

#coeffs ⇒ Object (readonly)

Returns the value of attribute coeffs.



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# File 'lib/bls/field.rb', line 446

def coeffs
  @coeffs
end

Class Method Details

.from_tuple(t) ⇒ Object 



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# File 'lib/bls/field.rb', line 454

def self.from_tuple(t)
  Fp12.new([Fp6.from_tuple(t[0...6]), Fp6.from_tuple(t[6...12])])
end

Instance Method Details

#cyclotomic_exp(n) ⇒ Object 



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# File 'lib/bls/field.rb', line 583

def cyclotomic_exp(n)
  z = Fp12::ONE
  i = BLS_X_LEN - 1
  while i >= 0
    z = z.cyclotomic_square
    z *= self unless BLS.bit_get(n, i).zero?
    i -= 1
  end
  z
end

#cyclotomic_square ⇒ Object 



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# File 'lib/bls/field.rb', line 570

def cyclotomic_square
  c0, c1 = coeffs
  c0c0, c0c1, c0c2 = c0.coeffs
  c1c0, c1c1, c1c2 = c1.coeffs
  t3, t4 = fp4_square(c0c0, c1c1)
  t5, t6 = fp4_square(c1c0, c0c2)
  t7, t8 = fp4_square(c0c1, c1c2)
  t9 = t8.mul_by_non_residue
  Fp12.new([
             Fp6.new([(t3 - c0c0) * 2 + t3, (t5 - c0c1) * 2 + t5, (t7 - c0c2) * 2 + t7]),
             Fp6.new([(t9 + c1c0) * 2 + t9, (t4 + c1c1) * 2 + t4, (t6 + c1c2) * 2 + t6])])
end

#final_exponentiate ⇒ Object 



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# File 'lib/bls/field.rb', line 558

def final_exponentiate
  t0 = frobenius_map(6) / self
  t1 = t0.frobenius_map(2) * t0
  t2 = t1.cyclotomic_exp(Curve::X).conjugate
  t3 = t1.cyclotomic_square.conjugate * t2
  t4 = t3.cyclotomic_exp(Curve::X).conjugate
  t5 = t4.cyclotomic_exp(Curve::X).conjugate
  t6 = t5.cyclotomic_exp(Curve::X).conjugate * t2.cyclotomic_square
  (t2 * t5).frobenius_map(2) * (t4 * t1).frobenius_map(3) *
    (t6 * t1.conjugate).frobenius_map(1) * t6.cyclotomic_exp(Curve::X).conjugate * t3.conjugate * t1
end

#frobenius_map(power) ⇒ Object 



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# File 'lib/bls/field.rb', line 546

def frobenius_map(power)
  c0, c1 = coeffs
  r0 = c0.frobenius_map(power)
  c1_0, c1_1, c1_2 = c1.frobenius_map(power).coeffs
  Fp12.new([
             r0,
             Fp6.new([
                       c1_0 * Fp12::FROBENIUS_COEFFICIENTS[power % 12],
                       c1_1 * Fp12::FROBENIUS_COEFFICIENTS[power % 12],
                       c1_2 * Fp12::FROBENIUS_COEFFICIENTS[power % 12]])])
end

#invert ⇒ Object 



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# File 'lib/bls/field.rb', line 540

def invert
  c0, c1 = coeffs
  t = (c0.square - c1.square.mul_by_non_residue).invert
  Fp12.new([c0 * t, (c1 * t).negate])
end

#multiply(other) ⇒ Object Also known as: * 



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# File 'lib/bls/field.rb', line 512

def multiply(other)
  return Fp12.new([coeffs[0] * other, coeffs[1] * other]) if other.is_a?(Integer)

  c0, c1 = coeffs
  r0, r1 = other.coeffs
  t1 = c0 * r0
  t2 = c1 * r1
  Fp12.new([t1 + t2.mul_by_non_residue, (c0 + c1) * (r0 + r1) - (t1 + t2)])
end

#multiply_by_014(o0, o1, o4) ⇒ Object 



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# File 'lib/bls/field.rb', line 523

def multiply_by_014(o0, o1, o4)
  c0, c1 = coeffs
  t0 = c0.multiply_by_01(o0, o1)
  t1 = c1.multiply_by_1(o4)
  Fp12.new([t1.mul_by_non_residue + t0, (c1 + c0).multiply_by_01(o0, o1 + o4) - t0 - t1])
end

#multiply_by_fp2(other) ⇒ Object 



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# File 'lib/bls/field.rb', line 530

def multiply_by_fp2(other)
  Fp12.new(coeffs.map{ |c| c.multiply_by_fp2(other) })
end

#square ⇒ Object 



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# File 'lib/bls/field.rb', line 534

def square
  c0, c1 = coeffs
  ab = c0 * c1
  Fp12.new([(c1.mul_by_non_residue + c0) * (c0 + c1) - ab - ab.mul_by_non_residue, ab + ab])
end