What are they?

The Numbered Key Cipher By BION

I've been having a lot of fun with a cipher type I call the "numbered key cipher", and I hope the reader will enjoy constructing and solving this type too. To construct a numbered key cipher start with a key word, phrase, sentence, or paragraph, extend it by appending any missing letters in alphabetical order, then number the resulting extended key, perhaps starting in the middle of the key and wrapping around to the beginning. Each plaintext letter is then encrypted by one of the numbers in the key.

Here's an example:

key: "I like ciphers."

extended key: ilikeciphersabdfgjmnoqtuvwxyz

shifted extended key: mnoqtuvwxyzilikeciphersabdfgj

numbered key:

00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21

m n o q t u v w x y z i l i k e c i p h e r

22 23 24 25 26 27 28

s a b d f g j

encryption table:

a 23 h 19 o 02 v 06

b 24 i 11, 13, 17 p 18 w 07

c 16 j 28 q 03 x 08

d 25 k 14 r 21 y 09

e 15, 20 l 12 s 22 z 10

f 26 m 00 t 04

g 27 n 01 u 05

Plaintext: The road to success is always under construction.

Worksheet:

04 19 20 21 02 23 25 04 02 22 05 16 16 15 22 22 11 22 23 12 07 23

t h e r o a d t o s u c c e s s i s a l w a

09 22 05 01 25 20 21 16 02 01 22 04 21 05 16 04 17 02 01

y s u n d e r c o n s t r u c t i o n

Cipher:

04 19 20 21 02 23 25 04 02 22 05 16 16 15 22 22 11 22 23 12 07 23

09 22 05 01 25 20 21 16 02 01 22 04 21 05 16 04 17 02 01

The degree of challenge in solving these ciphers depends on the length of the key. If you start with a key containing no repeated letters then the resulting cipher is just a simple substitution and solving it is similar to solving a Patristocrat. If you start with a key with say 64 letters than the resulting cipher has about the same difficulty as a Grandpre cipher.

The suggested plaintext length for a Numbered Key cipher is between 2.5 and 3 times the length of the extended key.

The largest number in the cipher gives you an estimate of the key length. (To simplify solving the ciphers below, I chose the shifts in their keys so the largest number gives you the exact key length.)

Here are two numbered key ciphers for the reader to solve. Note: NK-2 can be solved with nothing but the crib, but as an extra hint, the key is a short sentence from "The Great Slump of 1930" by John Maynard Keynes.

NK-1. Numbered key. Asking easy, answering hard. (prepared)

17 04 14 21 08 22 14 00 08 12 22 26 14 25 17 10 11 25 21 08 16 14

07 13 17 17 02 17 22 00 11 00 18 17 07 17 26 00 23 25 17 23 14 25

17 16 10 11 25 00 18 17 09 25 17 14 00 17 26 00 10 11 11 13 21 14

05 14 26 20 21 12 25 17 00 18 14 22 00 18 17 03 08 26 17 26 00 21

14 22 15 14 22 14 22 26 03 17 25.

NK-2. Numbered key. An illusion? (languageandyet)

15 11 56 48 50 31 31 56 50 11 56 00 53 45 39 17 26 07 17 54 54 46

45 30 21 41 37 07 53 49 28 12 25 17 20 54 38 48 49 33 17 51 51 16

48 32 17 41 30 43 56 16 43 02 14 40 30 36 54 15 11 52 29 17 32 05

15 11 56 40 36 50 39 23 40 50 11 41 22 27 25 56 52 14 51 02 12 40

30 41 43 02 29 11 41 39 08 25 09 26 37 27 11 33 23 27 17 41 22 02

17 22 25 17 41 30 05 48 15 07 16 09 32 48 11 33 17 03 40 26 31 20

17 42 27 28 12 18 49 17 36 41 52 19 21 26 15 40 27 27 09 54 15 02

17 27 23 21 14 07 52 45 05 24 23 17 24 00 20 43 54 27 17 11 56 12

24 21 56 40 30 46 31 14 26 52 15 31 04 11 33 24.

Note: This article appeared in slightly different form in The Cryptogram, MJ 2010 issue.