shamirsecret.rb

require "openssl"

class ShamirSecret
  attr_reader :_coefficients
  attr_reader :secretdata

  def initialize(threshold, secretdata=nil)
    @threshold = threshold
    @secretdata = secretdata
    @_coefficients = []

    if secretdata
      secretdata.each_char do |secretbyte|
        thesecoefficients = secretbyte+OpenSSL::Random.random_bytes(@threshold-1)
        @_coefficients << thesecoefficients
      end
    end
  end

  def is_valid_share(share)
    raise "Share is of incorrect length: #{share.size}" if share.size !=2
    raise "Must initialize coefficient before checking is_valid_share" unless @_coefficients
    raise "Must initialize coefficient before checking is_valid_share" if @_coefficients.size != share[1].size

    x  = share[0]
    fx = share[1]

    correctshare = compute_share(x)

    correctshare == share
  end

  def compute_share(x)
    raise "x should be integer" unless x.class == Fixnum
    raise "x must be between 1 and 255" if x <= 0 || x  >256
    raise "@_coefficient must be initialized" if @_coefficients.empty?

    sharebytes = []

    @_coefficients.each do |thiscoefficient|
      thisshare = _f(x,thiscoefficient)
      sharebytes << thisshare
    end
    
    return x, sharebytes
  end

  def recover_secretdata(shares)
    newshares = []

    shares.each do |share|
      newshares << share unless newshares.include?(share)
    end

    shares = newshares

    if @threshold > shares.size
      raise "Threshold: #{@threshold} is smaller than the number of uniquie shares: #{shares.size}"
    end

    if @secretdata
      raise "Recovoring secretdata when some is stored. Use check_share instead"
    end

    xs = []

    shares.each do |share|
      if xs.include?(share[0])
        raise "Different shares with the same first byte: #{share[0]}"
      end

      if share[1].size != shares[0][1].size
        raise "Shares have different lengths!"
      end
      
      xs << share[0]
    end

    mycoefficients = []
    mysecretdata = ''

    shares[0][1].size.times.each do |byte_to_use|
      fxs = []
      shares.each do |share|
        fxs << share[1][byte_to_use]
      end

      resulting_poly = _full_lagrange(xs,fxs)

      if resulting_poly[0..@threshold-1] + [0]*(shares.size - @threshold) != resulting_poly
        raise "Share do not match. Cannot decode"
      end

      mycoefficients << resulting_poly.map{|p| p.chr}.join

      mysecretdata += resulting_poly[0].chr
    end

    @_coefficients = mycoefficients
    @secretdata = mysecretdata
  end

  private

  def _f(x, coefs_bytes)
    raise "invalid share index value. cannot be 0" if x == 0

    accumulator = 0

    x_i = 1

    coefs_bytes.each_byte do |c|
      accumulator = _gf256_add(accumulator, _gf256_mul(c, x_i))
      x_i = _gf256_mul(x_i, x)
    end

    return accumulator
  end

  def _multiply_polynomials(a,b)
    resultterms = []

    termpadding = []

    b.each do |bterm|
      thisvalue = termpadding.clone

      a.each do |aterm|
	val = _gf256_mul(aterm, bterm)
        thisvalue << _gf256_mul(aterm, bterm)
      end
        
      resultterms = _add_polynomials(resultterms, thisvalue)
      
      termpadding << 0
    end

    return resultterms
  end

  def _add_polynomials(a,b)
    if a.size < b.size
      a = a + [0]*(b.size - a.size)
    elsif a.size > b.size
      b = b + [0]*(a.size - b.size)
    end

    result = []

    a.size.times do |pos|
      result << _gf256_add(a[pos], b[pos])
    end

    return result
  end

  def _full_lagrange(xs, fxs)
    returnedcoefficients = []

    fxs.size.times do |i|
      this_polynomial = [1]

      fxs.size.times do |j|
        next if i == j

        denominator = _gf256_sub(xs[i], xs[j])

        this_term = [_gf256_div(xs[j], denominator), _gf256_div(1, denominator)]

        this_polynomial = _multiply_polynomials(this_polynomial, this_term)
      end

      this_polynomial = _multiply_polynomials(this_polynomial, [fxs[i]]) if fxs[i]

      returnedcoefficients = _add_polynomials(returnedcoefficients, this_polynomial)
    end

    return returnedcoefficients
      
  end

  GF256_EXP = [
       0x01, 0x03, 0x05, 0x0f, 0x11, 0x33, 0x55, 0xff,
       0x1a, 0x2e, 0x72, 0x96, 0xa1, 0xf8, 0x13, 0x35,
       0x5f, 0xe1, 0x38, 0x48, 0xd8, 0x73, 0x95, 0xa4,
       0xf7, 0x02, 0x06, 0x0a, 0x1e, 0x22, 0x66, 0xaa,
       0xe5, 0x34, 0x5c, 0xe4, 0x37, 0x59, 0xeb, 0x26,
       0x6a, 0xbe, 0xd9, 0x70, 0x90, 0xab, 0xe6, 0x31,
       0x53, 0xf5, 0x04, 0x0c, 0x14, 0x3c, 0x44, 0xcc,
       0x4f, 0xd1, 0x68, 0xb8, 0xd3, 0x6e, 0xb2, 0xcd,
       0x4c, 0xd4, 0x67, 0xa9, 0xe0, 0x3b, 0x4d, 0xd7,
       0x62, 0xa6, 0xf1, 0x08, 0x18, 0x28, 0x78, 0x88,
       0x83, 0x9e, 0xb9, 0xd0, 0x6b, 0xbd, 0xdc, 0x7f,
       0x81, 0x98, 0xb3, 0xce, 0x49, 0xdb, 0x76, 0x9a,
       0xb5, 0xc4, 0x57, 0xf9, 0x10, 0x30, 0x50, 0xf0,
       0x0b, 0x1d, 0x27, 0x69, 0xbb, 0xd6, 0x61, 0xa3,
       0xfe, 0x19, 0x2b, 0x7d, 0x87, 0x92, 0xad, 0xec,
       0x2f, 0x71, 0x93, 0xae, 0xe9, 0x20, 0x60, 0xa0,
       0xfb, 0x16, 0x3a, 0x4e, 0xd2, 0x6d, 0xb7, 0xc2,
       0x5d, 0xe7, 0x32, 0x56, 0xfa, 0x15, 0x3f, 0x41,
       0xc3, 0x5e, 0xe2, 0x3d, 0x47, 0xc9, 0x40, 0xc0,
       0x5b, 0xed, 0x2c, 0x74, 0x9c, 0xbf, 0xda, 0x75,
       0x9f, 0xba, 0xd5, 0x64, 0xac, 0xef, 0x2a, 0x7e,
       0x82, 0x9d, 0xbc, 0xdf, 0x7a, 0x8e, 0x89, 0x80,
       0x9b, 0xb6, 0xc1, 0x58, 0xe8, 0x23, 0x65, 0xaf,
       0xea, 0x25, 0x6f, 0xb1, 0xc8, 0x43, 0xc5, 0x54,
       0xfc, 0x1f, 0x21, 0x63, 0xa5, 0xf4, 0x07, 0x09,
       0x1b, 0x2d, 0x77, 0x99, 0xb0, 0xcb, 0x46, 0xca,
       0x45, 0xcf, 0x4a, 0xde, 0x79, 0x8b, 0x86, 0x91,
       0xa8, 0xe3, 0x3e, 0x42, 0xc6, 0x51, 0xf3, 0x0e,
       0x12, 0x36, 0x5a, 0xee, 0x29, 0x7b, 0x8d, 0x8c,
       0x8f, 0x8a, 0x85, 0x94, 0xa7, 0xf2, 0x0d, 0x17,
       0x39, 0x4b, 0xdd, 0x7c, 0x84, 0x97, 0xa2, 0xfd,
       0x1c, 0x24, 0x6c, 0xb4, 0xc7, 0x52, 0xf6, 0x01] 

      GF256_LOG = [
        0x00, 0x00, 0x19, 0x01, 0x32, 0x02, 0x1a, 0xc6,
        0x4b, 0xc7, 0x1b, 0x68, 0x33, 0xee, 0xdf, 0x03,
        0x64, 0x04, 0xe0, 0x0e, 0x34, 0x8d, 0x81, 0xef,
        0x4c, 0x71, 0x08, 0xc8, 0xf8, 0x69, 0x1c, 0xc1,
        0x7d, 0xc2, 0x1d, 0xb5, 0xf9, 0xb9, 0x27, 0x6a,
        0x4d, 0xe4, 0xa6, 0x72, 0x9a, 0xc9, 0x09, 0x78,
        0x65, 0x2f, 0x8a, 0x05, 0x21, 0x0f, 0xe1, 0x24,
        0x12, 0xf0, 0x82, 0x45, 0x35, 0x93, 0xda, 0x8e,
        0x96, 0x8f, 0xdb, 0xbd, 0x36, 0xd0, 0xce, 0x94,
        0x13, 0x5c, 0xd2, 0xf1, 0x40, 0x46, 0x83, 0x38,
        0x66, 0xdd, 0xfd, 0x30, 0xbf, 0x06, 0x8b, 0x62,
        0xb3, 0x25, 0xe2, 0x98, 0x22, 0x88, 0x91, 0x10,
        0x7e, 0x6e, 0x48, 0xc3, 0xa3, 0xb6, 0x1e, 0x42,
        0x3a, 0x6b, 0x28, 0x54, 0xfa, 0x85, 0x3d, 0xba,
        0x2b, 0x79, 0x0a, 0x15, 0x9b, 0x9f, 0x5e, 0xca,
        0x4e, 0xd4, 0xac, 0xe5, 0xf3, 0x73, 0xa7, 0x57,
        0xaf, 0x58, 0xa8, 0x50, 0xf4, 0xea, 0xd6, 0x74,
        0x4f, 0xae, 0xe9, 0xd5, 0xe7, 0xe6, 0xad, 0xe8,
        0x2c, 0xd7, 0x75, 0x7a, 0xeb, 0x16, 0x0b, 0xf5,
        0x59, 0xcb, 0x5f, 0xb0, 0x9c, 0xa9, 0x51, 0xa0,
        0x7f, 0x0c, 0xf6, 0x6f, 0x17, 0xc4, 0x49, 0xec,
        0xd8, 0x43, 0x1f, 0x2d, 0xa4, 0x76, 0x7b, 0xb7,
        0xcc, 0xbb, 0x3e, 0x5a, 0xfb, 0x60, 0xb1, 0x86,
        0x3b, 0x52, 0xa1, 0x6c, 0xaa, 0x55, 0x29, 0x9d,
        0x97, 0xb2, 0x87, 0x90, 0x61, 0xbe, 0xdc, 0xfc,
        0xbc, 0x95, 0xcf, 0xcd, 0x37, 0x3f, 0x5b, 0xd1,
        0x53, 0x39, 0x84, 0x3c, 0x41, 0xa2, 0x6d, 0x47,
        0x14, 0x2a, 0x9e, 0x5d, 0x56, 0xf2, 0xd3, 0xab,
        0x44, 0x11, 0x92, 0xd9, 0x23, 0x20, 0x2e, 0x89,
        0xb4, 0x7c, 0xb8, 0x26, 0x77, 0x99, 0xe3, 0xa5,
        0x67, 0x4a, 0xed, 0xde, 0xc5, 0x31, 0xfe, 0x18,
        0x0d, 0x63, 0x8c, 0x80, 0xc0, 0xf7, 0x70, 0x07]


  def _gf256_add(a, b)
    val = a ^ b
    val
  end

  def _gf256_sub(a,b)
    _gf256_add(a,b)
  end

  def _gf256_mul(a,b)
    a = a.to_i
    b = b.to_i
    if a == 0 || b == 0
      return 0
    else
      GF256_EXP[(GF256_LOG[a] + GF256_LOG[b]) % 255]
    end
  end

  def _gf256_div(a,b)
    if a == 0
      return 0
    elsif b == 0
      raise ZeroDivisionError
    else
      GF256_EXP[(GF256_LOG[a] - GF256_LOG[b]) % 255]
    end
  end
end