Class: BLS::Fp6

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

Overview

Finite extension field over irreducible polynomial. Fp2(v) / (v^3 - ξ) where ξ = u + 1

Constant Summary collapse

ZERO = 
Fp6.new([Fp2::ZERO, Fp2::ZERO, Fp2::ZERO])
ONE = 
Fp6.new([Fp2::ONE, Fp2::ZERO, Fp2::ZERO])
FROBENIUS_COEFFICIENTS_1 = 
[
  Fp2.new([
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,
            0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac
          ]),
  Fp2.new([
            0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,
          ]),
  Fp2.new([
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
          ]),
  Fp2.new([
            0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,
            0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe
          ])
].freeze
FROBENIUS_COEFFICIENTS_2 = 
[
  Fp2.new([
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ]),
  Fp2.new([
            0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffff,
            0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
          ])
].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) ⇒ Fp6

Returns a new instance of Fp6.

Raises:

  • (ArgumentError) 


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# File 'lib/bls/field.rb', line 308

def initialize(coeffs)
  raise ArgumentError, 'Expected array with 3 elements' unless coeffs.size == 3

  @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 306

def coeffs
  @coeffs
end

Class Method Details

.from_tuple(t) ⇒ Object 



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# File 'lib/bls/field.rb', line 314

def self.from_tuple(t)
  Fp6.new([Fp2.new(t[0...2]), Fp2.new(t[2...4]), Fp2.new(t[4...6])])
end

Instance Method Details

#frobenius_map(power) ⇒ Object 



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# File 'lib/bls/field.rb', line 432

def frobenius_map(power)
  Fp6.new([
            coeffs[0].frobenius_map(power),
            coeffs[1].frobenius_map(power) * Fp6::FROBENIUS_COEFFICIENTS_1[power % 6],
            coeffs[2].frobenius_map(power) * Fp6::FROBENIUS_COEFFICIENTS_2[power % 6]
          ])
end

#invert ⇒ Object 



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# File 'lib/bls/field.rb', line 423

def invert
  c0, c1, c2 = coeffs
  t0 = c0.square - (c2 * c1).mul_by_non_residue
  t1 = c2.square.mul_by_non_residue - (c0 * c1)
  t2 = c1.square - c0 * c2
  t4 = ((c2 * t1 + c1 * t2).mul_by_non_residue + c0 * t0).invert
  Fp6.new([t4 * t0, t4 * t1, t4 * t2])
end

#mul_by_non_residue ⇒ Object

Multiply by quadratic non-residue v.



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# File 'lib/bls/field.rb', line 376

def mul_by_non_residue
  Fp6.new([coeffs[2].mul_by_non_residue, coeffs[0], coeffs[1]])
end

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



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# File 'lib/bls/field.rb', line 380

def multiply(other)
  return Fp6.new([coeffs[0] * other, coeffs[1] * other, coeffs[2] * other]) if other.is_a?(Integer)

  c0, c1, c2 = coeffs
  r0, r1, r2 = other.coeffs
  t0 = c0 * r0
  t1 = c1 * r1
  t2 = c2 * r2

  Fp6.new([
            t0 + ((c1 + c2) * (r1 + r2) - (t1 + t2)).mul_by_non_residue,
            (c0 + c1) * (r0 + r1) - (t0 + t1) + t2.mul_by_non_residue,
            t1 + ((c0 + c2) * (r0 + r2) - (t0 + t2))
          ])
end

#multiply_by_01(b0, b1) ⇒ Object

Sparse multiplication.



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# File 'lib/bls/field.rb', line 403

def multiply_by_01(b0, b1)
  c0, c1, c2 = coeffs
  t0 = c0 * b0
  t1 = c1 * b1
  Fp6.new([((c1 + c2) * b1 - t1).mul_by_non_residue + t0, (b0 + b1) * (c0 + c1) - t0 - t1, (c0 + c2) * b0 - t0 + t1])
end

#multiply_by_1(b1) ⇒ Object

Sparse multiplication.



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# File 'lib/bls/field.rb', line 398

def multiply_by_1(b1)
  Fp6.new([coeffs[2].multiply(b1).mul_by_non_residue, coeffs[0] * b1, coeffs[1] * b1])
end

#multiply_by_fp2(other) ⇒ Object 



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# File 'lib/bls/field.rb', line 410

def multiply_by_fp2(other)
  Fp6.new(coeffs.map { |c| c * other })
end

#square ⇒ Object 



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# File 'lib/bls/field.rb', line 414

def square
  c0, c1, c2 = coeffs
  t0 = c0.square
  t1 = c0 * c1 * 2
  t3 = c1 * c2 * 2
  t4 = c2.square
  Fp6.new([t3.mul_by_non_residue + t0, t4.mul_by_non_residue + t1, t1 + (c0 - c1 + c2).square + t3 - t0 - t4])
end