diff_table.rb

SBox = Hash[ (0..15).to_a.zip( %w[E 2 1 3 D 9 0 6 F 4 5 A 8 C 7 B].map {|n| n.to_i(16)}) ]

# Find all pairs x and x* in delta(x')
def delta_x(xor)
  (0..15).map {|x|[x, (0..15).select { |x_star| x ^ x_star == xor }[0]] }
end

# Let's also make iterating over every index [x,y] easier...
class Array
  def each_xy
    (0...self.size).each {|x| (0...self[x].size).each {|y| yield x,y }}
  end
end

if __FILE__ == $0
  ddt = Array.new(16) { Array.new(16,0) }
  ddt.each_xy do |a,b|
    delta_x(a).each {|x,x_st| ddt[a][b] += 1 if (SBox[x] ^ SBox[x_st] == b)}
  end
  # Table now completed... That was easy.
  printf("    " + "%3d"*16+"\n", *((0..15).to_a))
  printf("    " + "---"*16+"\n")
  ddt.each_with_index do |row,i|
      printf("%2d |"+"%3d"*16+"\n",i, *row )
  end
end

#       0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
#     ------------------------------------------------
#  0 | 16  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
#  1 |  0  0  2  0  4  0  2  0  0  0  0  2  4  0  0  2
#  2 |  0  2  0  0  0  0  0  2  0  0  2  0  0  2  2  6
#  3 |  0  2  0  4  0  2  0  0  0  2  0  4  0  2  0  0
#  4 |  0  4  2  2  0  2  0  2  2  0  0  2  0  0  0  0
#  5 |  0  0  0  4  0  0  0  4  0  0  0  0  2  2  2  2
#  6 |  0  0  0  0  2  0  2  0  2  0  2  0  2  2  2  2
#  7 |  0  0  4  2  2  0  0  0  4  2  0  0  0  0  2  0
#  8 |  0  2  0  0  2  4  2  2  0  2  0  0  0  2  0  0
#  9 |  0  6  0  0  0  0  2  0  0  0  2  4  0  2  0  0
# 10 |  0  0  2  0  0  0  0  2  4  0  4  2  0  0  2  0
# 11 |  0  0  0  0  2  2  2  2  0  0  0  0  4  0  4  0
# 12 |  0  0  2  0  0  2  4  0  2  0  0  0  2  2  2  0
# 13 |  0  0  2  2  2  0  2  0  0  2  6  0  0  0  0  0
# 14 |  0  0  2  2  0  0  0  0  2  6  0  0  0  0  0  4
# 15 |  0  0  0  0  2  4  0  2  0  2  0  2  2  2  0  0