Cipher Fun

by Peter Rabbit

One of the most vulnerable sources of private information is a personal telephone listing.  If this listing is lost, stolen, or copied by stealth, much mischief may result.

The following presents a procedure for telephone number encipherment that is designed to frustrate most snoops.  This procedure is an adaptation of a polyalphabetic substitution cipher devised by Giovanni Battista Della Porta, a 16^th century Italian cryptographer.  Porta's cipher table used alphabetic characters; here, it has been adapted for numbers as a polynumeric substitution cipher.

Description

The polynumeric adaptation in its simplest form is shown in Table 1:

Table 1 NUMBER 0 1 2 3 4 =========== 0-1 | 5 6 7 8 9 K 2-3 | 6 7 8 9 5 E 4-5 | 7 8 9 5 6 Y 6-7 | 8 9 5 6 7 8-9 | 9 5 6 7 8

Table 1 shows six number rows, five of which are controlled by either of two key numbers located at the left of the table.

The upper-row, containing digits 0 to 4, found above the double-line, always remains the same; the remaining five rows, located below the double-line and containing digits 5 to 9, are each arranged in a different way.

As arranged here, they are shown in their simplest form for purposes of explanation, but these arrangements are not recommended for use, due to their inherent periodicity; preferable arrangements will be shown in the following section.

Regardless of arrangement, however, the encipherment will be reciprocal for all six rows.

For example, in Table 1, in the first row, which is controlled by the key 0-1, the substitute for 7 is 2 (found above the double-line); and the substitute for 2 is 7 (found below the double-line).

Each of the five rows located below the double-line may be arranged in 120 different ways, producing a large number (120⁵) of potential encipherment tables.

Method of Employment

Table 2 shows five enciphering rows in disarranged order.

The method of disarrangement illustrated uses an easily remembered phrase, in this case a nursery rhyme: "Mary had a little lamb it's fleece..."

The order of the numbers 5 to 9 in each row is derived from the alphabetic order of the nursery rhyme letters as they appear in each row:

M A R Y H 7 5 8 9 6 A D A L I 5 7 6 9 8 T T L E L 8 9 6 5 7 A M B I T 5 8 6 7 9 S F L E E 9 7 8 5 6

Table 2 NUMBER 0 1 2 3 4 =========== 0-1 | 7 5 8 9 6 K 2-3 | 5 7 6 9 8 E 4-5 | 8 9 6 5 7 Y 6-7 | 5 8 6 7 9 8-9 | 9 7 8 5 6

The enciphering of a telephone number in this procedure will require the selection of an autokey number from 0 to 9.

This single autokey number is chosen by, and known only to, the encipherer.

In order to end up with an encipherment that resembles a genuine telephone number it is necessary to select an autokey number that will produce an encipherment not starting with 0 or 1.

Using the example of 751-2600, examination of Table 2 shows that there are four autokey choices in this particular case: 4, 5, 6, or 7.

Let us encipher the telephone number 751-2600 by using the arbitrary autokey 6 plus the first six digits of the telephone number.  Using Table 2:

Key: 6751260 Tel. #: 7512600 Cipher: 3098257

In the first line, 6 is the autokey and 751260 are the first six digits of the phone number.  The enciphered number is: 309-8257

Let us now decipher it in order to recover the original number - a simple procedure.  We begin by placing the autokey 6 over the first number of the cipher:

Key: 6 Cipher: 3098257 Tel. #: 7

Using Table 2, we find 7, the first digit of the telephone number.  This number is moved up and becomes the next key number:

Key: 67 Cipher: 3098257 Tel. #: 75

Each digit of the telephone number is moved up and becomes the key for the next number to be deciphered, until the decipherment is completed:

Key: 6751260 Cipher: 3098257 Tel. #: 7512600

Further security of the enciphered telephone number may be obtained by adding a seven digit number using non-carry addition or subtraction; that is to say:

8 + 2 = 0 (Not 10) 0 - 8 = 2 (The units digit is used, but the tens digit is ignored.)

For purposes of illustration, let us use as the additive a seven digit number representing the date of the Great San Francisco Earthquake and Fire: April 18, 1906:

Cipher: 3098257 + Additive: 4181906 Supercipher: 7179153

Subtracting the additive from the supercipher produces the cipher, which is then deciphered with the autokey and Table 2:

Supercipher: 7179153 - Additive: 4181906 Cipher: 3098257

For obvious reasons, one should not encipher every telephone number in one's collection - only the most critical ones.  As for area codes, they are best left unenciphered.