Serial number generator for Neukey's using Damm's algorithm.

NeukeySerial.py

#!/usr/bin/env python3
from os import urandom

# Damm's weakly totally antisymetric quasigroup of order 10
# https://en.wikipedia.org/wiki/Damm_algorithm
Damm = [
  [0, 3, 1, 7, 5, 9, 8, 6, 4, 2],
  [7, 0, 9, 2, 1, 5, 4, 8, 6, 3],
  [4, 2, 0, 6, 8, 7, 1, 3, 5, 9],
  [1, 7, 5, 0, 9, 8, 3, 4, 2, 6],
  [6, 1, 2, 3, 0, 4, 5, 9, 7, 8],
  [3, 6, 7, 4, 2, 0, 9, 5, 8, 1],
  [5, 8, 6, 9, 7, 2, 0, 1, 3, 4],
  [8, 9, 4, 5, 3, 6, 2, 0, 1, 7],
  [9, 4, 3, 8, 6, 1, 7, 2, 0, 5],
  [2, 5, 8, 1, 4, 3, 6, 7, 9, 0]
]

def groupOperation(a, b):
  return Damm[a][b]

def groupProduct(digits, initial = 0):
  interim = initial
  for digit in digits:
    interim = groupOperation(interim, digit)
  return interim

def addCheckDigit(digits):
  return digits + [groupProduct(digits)]

def checkDigits(digits):
  return groupProduct(digits) == 0

def toDigits(number, base = 10):
  digits = []
  while number > 0:
    digits.append(number % base)
    number = number // base
  return digits[::-1]

def fromDigits(digits, base = 10):
  number = 0
  for digit in digits:
    number *= base
    number += digit
  return number

def addCheck(number):
  return fromDigits(addCheckDigit(toDigits(number)))

def check(number):
  return checkDigits(toDigits(number))

# Test algorithms
assert addCheck(572) == 5724
assert check(5724)
assert not check(5742)

def randomNumber(max):
  assert max < 2 ** 32
  seed = int.from_bytes(urandom(64), byteorder='big')
  return seed % max

def shuffle(list):
  n = len(list)
  for i in range(n - 1):
    j = i + randomNumber(n - i)
    list[i], list[j] = list[j], list[i]
    yield list[i]
  yield list[n - 1]

def formatGroups(number, digits = 6, groupSize = 3, separator = "."):
  numGroups = (digits + (groupSize - 1)) // groupSize
  groups = toDigits(number, 10 ** groupSize)
  groups = ([0] * (numGroups - len(groups))) + groups
  groupFormat = "{:0>" + str(groupSize) +"}"
  groups = [groupFormat.format(x) for x in groups]
  return separator.join(groups)

# Print random permutation of all serial numbers
for n in shuffle(list(range(10**5))):
  print(formatGroups(addCheck(n)))

$ time ./NeukeySerial.py > serialnumbers.txt
real  0m1.837s
user  0m1.140s
sys   0m0.696s
$ cat serialnumbers.txt | wc -l
100000
$ cat serialnumbers.txt | uniq | wc -l
100000
$ sha3sum ./serialnumbers.txt 
d3c03d2380b9b7371e0458a79fc2bef9df5f14268030924aa477682f ./serialnumbers.txt