info = """

                Factorial Encryption
                   March 26, 2006
          Copyright by Aaron Voelker, Saney

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Create a checksum from a literal using
a modified factorial function.

------------------------------------------------------

Basic encryption is intended to work as SHA-1 or Md5
checksum encryptions do. 

The difference: throw in an optional password argument
plus salt, and any cracker should be left with nowhere
to start.

------------------------------------------------------

1 -  Make an array of characters a-z + 0-9 + A-Z.

2 -  If a password is present, move letters from
     password to front of array.

3 -  Add array to the front of string to encrypt.

4 -  Get ordinal value of each character in string.

5 -  Throw each character in an avalanche style
     through the modified factorial function.
     
6 -  Calculate a 'sum' of all the results multiplayed
     by the index at which they were created.
     
7 -  Index the charset by the result of each
     factorial, multiplayed by the index, subtracted
     by the 'sum'.
     
8 -  Return 'clength' number of letters based on index
     determined by 'sum'%(length of string-'clength')
     plus the length of 'clength'.
     
"""


def factorial(x, limit=1, inc=1):
        if x <= limit:
                return limit
        return x + factorial(x-limit)


def get_fs(ords, lenx):
        sum = 0
        fs  = []
        # [LABEL 5]
        for i in range(lenx):
                f    = factorial(ords[i],-ords[(i+1)%lenx],ords[(i+2)%lenx]/10)

                # [LABEL 6]
                sum += f*(i+1)
                fs  += [f]
        return fs, sum


def mk_charset(ps = ''):
        # [LABEL 1]
        set = [chr(x) for x in range(97, 123) + range(48, 58) + range(65, 91)]

        # [LABEL 2]
        for l in ps:
                try:
                        set.remove(l)
                        set = [l] + set
                except ValueError:
                        pass
        return set


def fencrypt(x, passw=''):
        clength  = 25

        charset  = mk_charset(passw)
        charrng  = len(charset)

        # [LABEL 3]
        newx     = x + ''.join(charset)
        lenx     = len(newx)

        # [LABEL 4]
        ords     = [ord(l) for l in list(newx)]
        
        fs, sum  = get_fs(ords, lenx)

        # [LABEL 7]
        res      = ''.join( charset[ (fs[f]*(f+1)-sum)%charrng ] for f in range(lenx) )

        # [LABEL 8]
        start    = sum%(lenx-clength)
        return res[ start:start+clength ]


if __name__ == '__main__':
        print fencrypt(info)