Class: Secp256k1::Point

Inherits:
Object
  • Object
show all
Defined in:
lib/secp256k1.rb

Overview

An elliptic curve point on secp256k1.

Stores affine coordinates (x, y) or represents the point at infinity. Scalar multiplication uses Jacobian coordinates internally with windowed-NAF for performance.

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(x, y) ⇒ Point

Returns a new instance of Point.

Parameters:

  • x (Integer, nil) —

    x-coordinate (nil for infinity)

  • y (Integer, nil) —

    y-coordinate (nil for infinity)



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# File 'lib/secp256k1.rb', line 414

def initialize(x, y)
  @x = x
  @y = y
end

Instance Attribute Details

#x ⇒ Integer? (readonly)

Returns x-coordinate (nil for infinity).

Returns:

  • (Integer, nil) —

    x-coordinate (nil for infinity)



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# File 'lib/secp256k1.rb', line 407

def x
  @x
end

#y ⇒ Integer? (readonly)

Returns y-coordinate (nil for infinity).

Returns:

  • (Integer, nil) —

    y-coordinate (nil for infinity)



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# File 'lib/secp256k1.rb', line 410

def y
  @y
end

Class Method Details

.from_bytes(bytes) ⇒ Point

Deserialise a point from compressed (33 bytes) or uncompressed (65 bytes) SEC1 encoding.

Parameters:

  • bytes (String) —

    binary string

Returns:

Raises:

  • (ArgumentError) —

    if the encoding is invalid or the point is not on the curve



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# File 'lib/secp256k1.rb', line 440

def self.from_bytes(bytes)
  bytes = bytes.b if bytes.encoding != Encoding::BINARY
  prefix = bytes.getbyte(0)

  case prefix
  when 0x04 # Uncompressed
    raise ArgumentError, 'invalid uncompressed point length' unless bytes.length == 65

    x = Secp256k1.bytes_to_int(bytes[1, 32])
    y = Secp256k1.bytes_to_int(bytes[33, 32])
    raise ArgumentError, 'x coordinate out of field range' if x >= P
    raise ArgumentError, 'y coordinate out of field range' if y >= P

    pt = new(x, y)
    raise ArgumentError, 'point is not on the curve' unless pt.on_curve?

    pt
  when 0x02, 0x03 # Compressed
    raise ArgumentError, 'invalid compressed point length' unless bytes.length == 33

    x = Secp256k1.bytes_to_int(bytes[1, 32])
    raise ArgumentError, 'x coordinate out of field range' if x >= P

    y_squared = Secp256k1.fadd(Secp256k1.fmul(Secp256k1.fsqr(x), x), 7)
    y = Secp256k1.fsqrt(y_squared)
    raise ArgumentError, 'invalid point: x not on curve' if y.nil?

    # Ensure y-parity matches prefix
    y = Secp256k1.fneg(y) if (y.odd? ? 0x03 : 0x02) != prefix

    new(x, y)
  else
    raise ArgumentError, "unknown point prefix: 0x#{prefix.to_s(16).rjust(2, '0')}"
  end
end

.generator ⇒ Point

The generator point G.

Returns:



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# File 'lib/secp256k1.rb', line 429

def self.generator
  @generator ||= new(GX, GY)
end

.infinity ⇒ Point

The point at infinity (additive identity).

Returns:



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# File 'lib/secp256k1.rb', line 422

def self.infinity
  new(nil, nil)
end

Instance Method Details

#==(other) ⇒ Boolean Also known as: eql?

Equality comparison.

Parameters:

Returns:

  • (Boolean) 


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# File 'lib/secp256k1.rb', line 584

def ==(other)
  return false unless other.is_a?(Point)

  if infinity? && other.infinity?
    true
  elsif infinity? || other.infinity?
    false
  else
    @x == other.x && @y == other.y
  end
end

#add(other) ⇒ Point

Point addition: self + other.

Parameters:

Returns:



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# File 'lib/secp256k1.rb', line 558

def add(other)
  return other if infinity?
  return self if other.infinity?

  jp1 = [@x, @y, 1]
  jp2 = [other.x, other.y, 1]
  jp_result = Secp256k1.jp_add(jp1, jp2)
  affine = Secp256k1.jp_to_affine(jp_result)
  return self.class.infinity if affine.nil?

  self.class.new(affine[0], affine[1])
end

#hash ⇒ Object 



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# File 'lib/secp256k1.rb', line 597

def hash
  infinity? ? 0 : [@x, @y].hash
end

#infinity? ⇒ Boolean

Whether this is the point at infinity.

Returns:

  • (Boolean) 


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# File 'lib/secp256k1.rb', line 479

def infinity?
  @x.nil?
end

#mul(scalar) ⇒ Point

Scalar multiplication: self * scalar (variable-time, wNAF).

Suitable for public scalars only (e.g. signature verification). For secret-scalar paths use #mul_ct.

Parameters:

  • scalar (Integer) —

    the scalar multiplier

Returns:

  • (Point) —

    the resulting point



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# File 'lib/secp256k1.rb', line 520

def mul(scalar)
  return self.class.infinity if scalar.zero? || infinity?

  scalar %= N
  return self.class.infinity if scalar.zero?

  jp = Secp256k1.scalar_multiply_wnaf(scalar, @x, @y)
  affine = Secp256k1.jp_to_affine(jp)
  return self.class.infinity if affine.nil?

  self.class.new(affine[0], affine[1])
end

#mul_ct(scalar) ⇒ Point

Constant-time scalar multiplication: self * scalar (Montgomery ladder).

Processes all 256 bits unconditionally so execution time does not depend on the scalar value. Use this for secret-scalar paths: key generation, signing, and ECDH shared-secret derivation.

Parameters:

  • scalar (Integer) —

    the secret scalar multiplier

Returns:

  • (Point) —

    the resulting point



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# File 'lib/secp256k1.rb', line 541

def mul_ct(scalar)
  return self.class.infinity if scalar.zero? || infinity?

  scalar %= N
  return self.class.infinity if scalar.zero?

  jp = Secp256k1.scalar_multiply_ct(scalar, @x, @y)
  affine = Secp256k1.jp_to_affine(jp)
  return self.class.infinity if affine.nil?

  self.class.new(affine[0], affine[1])
end

#negate ⇒ Point

Point negation: -self.

Returns:



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# File 'lib/secp256k1.rb', line 574

def negate
  return self if infinity?

  self.class.new(@x, Secp256k1.fneg(@y))
end

#on_curve? ⇒ Boolean

Whether this point lies on the secp256k1 curve (y² = x³ + 7).

Returns:

  • (Boolean) 


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# File 'lib/secp256k1.rb', line 486

def on_curve?
  return true if infinity?

  lhs = Secp256k1.fsqr(@y)
  rhs = Secp256k1.fadd(Secp256k1.fmul(Secp256k1.fsqr(@x), @x), 7)
  lhs == rhs
end

#to_octet_string(format = :compressed) ⇒ String

Serialise the point in SEC1 format.

Parameters:

  • format (:compressed, :uncompressed) (defaults to: :compressed)

Returns:

  • (String) —

    binary string (33 or 65 bytes)

Raises:

  • (RuntimeError) —

    if the point is at infinity



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# File 'lib/secp256k1.rb', line 499

def to_octet_string(format = :compressed)
  raise 'cannot serialise point at infinity' if infinity?

  case format
  when :compressed
    prefix = @y.odd? ? "\x03".b : "\x02".b
    prefix + Secp256k1.int_to_bytes(@x, 32)
  when :uncompressed
    "\x04".b + Secp256k1.int_to_bytes(@x, 32) + Secp256k1.int_to_bytes(@y, 32)
  else
    raise ArgumentError, "unknown format: #{format}"
  end
end