# analysis of KF VMAC ROTR operations on the key
#
# values in K represent shift amounts

# number of rounds, must be >= 16
#
N = 64

# 8 32-bit pieces of the key
#
K = [ [] for i in range(8)]

# shift amount as a function of the round index
#
def Shift( i, j):
  #
  # ORIGINAL: this produces some duplicate shifts for N > 31
  #
  # return i%31
  #
  # (i%k has duplicate shifts for all possible values of k with N = 64)
  #
  # MODIFIED: no duplicate shifts
  #
  return 3*j+(i>>3) # no mod needed, max is 3*7+63//8 = 21+7 = 28

# W[i] is XOR'd with ROTR( K[j], i%31)
#
# j = i,	i=0:7
# j = i-5,	i=8:12
# j = (i-12)%3, i=13:15
# j = (63-i)%8, i=16:N-1
#
jlist = []
#
for i in range(8):
  j = i; jlist.append( j); K[j].append( Shift(i,j))
#
for i in range(8,13):
  j = i-5; jlist.append( j); K[j].append( Shift(i,j))
#
for i in range(13,16):
  j = (i-12)%3; jlist.append( j); K[j].append( Shift(i,j))
#
for i in range(16,N):
  j = (63-i)%8; jlist.append( j); K[j].append( Shift(i,j))

# debug
if 0:
  print( "i j")
  for i in range(N):
    print( i, jlist[i])

print("K rotations")
for i in range(8):
  print( "K", i, "=", K[i])

print("K rotations, sorted")
for i in range(8):
  x = ""
  if len(set(K[i])) != len(K[i]):
    x = "duplicates"
  print( "K", i, "=", sorted(K[i]), x)

print("All rotations, sorted")
A = []
for i in range(8):
  for j in range(len(K[i])):
    A.append(K[i][j])
print(sorted(A))

# results:
#
# ORIGINAL:
#  K rotations
#  K 0 = [0, 15, 23, 0, 8, 16, 24, 1]	duplicate 0
#  K 1 = [1, 13, 22, 30, 7, 15, 23, 0]
#  K 2 = [2, 14, 21, 29, 6, 14, 22, 30] duplicate 14
#  K 3 = [3, 8, 20, 28, 5, 13, 21, 29]
#  K 4 = [4, 9, 19, 27, 4, 12, 20, 28]  duplicate 4
#  K 5 = [5, 10, 18, 26, 3, 11, 19, 27]
#  K 6 = [6, 11, 17, 25, 2, 10, 18, 26]
#  K 7 = [7, 12, 16, 24, 1, 9, 17, 25]
#
# MODIFIED:
#  K rotations
#  K 0 = [0, 1, 2, 3, 4, 5, 6, 7]
#  K 1 = [3, 4, 5, 6, 7, 8, 9, 10]
#  K 2 = [6, 7, 8, 9, 10, 11, 12, 13]
#  K 3 = [9, 10, 11, 12, 13, 14, 15, 16]
#  K 4 = [12, 13, 14, 15, 16, 17, 18, 19]
#  K 5 = [15, 16, 17, 18, 19, 20, 21, 22]
#  K 6 = [18, 19, 20, 21, 22, 23, 24, 25]
#  K 7 = [21, 22, 23, 24, 25, 26, 27, 28]