The E-Cipher

by Ron Miller, April 2001

E-cipher is an Efficient, Easy to use, cipher algorithm for Everyone and Everywhere.

The idea is to be able to encrypt/decrypt a message easily and conveniently while still achieving a high level of security.

The goal which this E-cipher aims at, and I believe comes closest to thus far, is to have the highest efficiency value as defined by the ease of implementation times the security level achieved, with as little as just pencil and paper at one’s disposal. As described here, done with poly-alphabets and spaces removed, encrypted messages will have greater security than those encrypted with the Enigma code machine.

The Key:

The key is any word, phrase or group of alphabetic characters.

From the key an encryption substitution alphabet (the ‘cipher-alphabet’) is formed.

This is done by using the letters in the key to produce a rearranged alphabet, by referring to the letters of the alphabets arranged as in figure 1 and following simple rules. Note that in figure 1 we have an alphabet shifted 12 places so as to start with ‘M’ over our A to Z alphabet.

This is done as follows:

1. Write down the key (without spaces)

2. Select associated letters from fig. 1 by:
for a each letter, from left to right, find the letter in the lower row of figure 1 which is below where that letter exists in the upper row. For the ‘b’ in bluesause we get a ‘P’.
If this letter has already been selected then take the next letter to its right, continuing right as needed until a remaining previously unselected letter is found. Note that the second ‘u’ in bluesauce results in a ‘J’.
If you go all the way to the right without finding an available letter then you continue the search with the first letter in the lower row at the far left.

3. Write the selected letter below the original one. Strike out the selected letter from your working copy of figure 1, indicating it has already been selected. See fig. 2

4. Once you have written down a set of letters, selected as just described, below the key, do like wise for those letters as you did for the letters of the key; and so on until all of the letters in the alphabet have all been selected for use. See fig. 3

5. Form the whole ‘Cipher Alphabet’ by writing down the selected rows of letters next to each other, one row after the other, starting with the last row first. See figure 4.

+-----------------------------------+

| MNOPQRSTUVWXYZABCDEFGHIJKL |

| ABCDEFGHIJKLMNOPQRSTUVWXYZ |

| |

| Figure 1. |

|-----------------------------------|

| |

| MNOPQRSTUVWXYZABCDEFGHIJKL |

| ABCDEF/H//KLMN///R//UVWXY/ |

| |

| key: bluesauce |

| --------- |

| PZISGOJQT |

| |

| Figure 2. |

|-----------------------------------|

| |

| key: bluesauce |

| --------- |

| PZISGOJQT |

| DNWHUCXEK |

| RBLVMYAF |

| |

| Figure 3. |

|-----------------------------------|

| |

| Cipher-Alphabet: |

| RBLVMYAFDNWHUCXEKPZISGOJQT |

| |

| Figure 4. |

+-----------------------------------+

Encrypting a message (with an overly simplified method):

First write down the alphabet a-z then below it write down the cipher-alphabet. See figure 5.

Then write the message down.

For each character in the message write below it the associated cipher-alphabet character, that is, find the letter in figure 5, which is below the same letter that you are encrypting from the source message. See figure 6.

For Decryption:

First you take the key and produce the cipher-alphabet as was done above prior to encryption.

Then you do the reverse of the Encryption character substitution. You find a letter, which is in the encrypted message in the bottom row of your version of figure 5, and take the letter above it as that of the original message.

+-----------------------------------+

| |

| abcdefghijklmnopqrstuvwxyz |

| RBLVMYAFDNWHUCXEKPZISGOJQT |

| |

| Figure 5. |

|-----------------------------------|

| |

| remove the hat |

| PMUXGM IFM FRI |

| |

| hello |

| FMHHX |

| |

| Figure 6. |

| |

+-----------------------------------+

The algorithm as described so far is that of a mono-alphabetic substitution, which is not terribly difficult for a cryptanalyst to decipher, given sufficient encrypted text, due to the fact that each letter of the message is encrypted using the same cipher-alphabet for substitution. Note how ‘e’ is always encrypted as ‘M’

So we then vary the cipher-alphabet as we encrypt.

Performing Poly-Alphabetic Encryption:

Now all we need to do is shift the relationship of the a-z alphabet and the cipher-alphabet we have in fig. 5 after each time encrypting a message character, and perform the identical shifting operation while decrypting. (A very simple consistent shift of one character position would be yet too weak.)

As part of the E-Cipher algorithm these shifts are performed by sequentially aligning the beginning of the cipher-alphabet under letters in the a-z alphabet in the order they appear in the cipher-alphabet.

To start you would note the first letter of our cipher-alphabet and align the beginning of your cipher-alphabet underneath that letter in the a-z alphabet. To do subsequent alignments you note the letter above the start of the cipher-alphabet and then find the letter to the right of it in the cipher-alphabet; this then becomes the new letter under which you then place the beginning of your cipher-alphabet, readying you for the next character encryption. This process is repeated after each single character encryption. See figure 7 for an example of sequential alignments of an a-z and cipher-alphabet. Note how the first ‘l’ is encrypted as an ‘R’ and the second as a ‘K’.

This alphabet shifting process can be easily performed by one of three aids.

- By writing down the alphabet a-z twice, end to end. Write the cipher-alphabet on another piece of paper (with the same spacing; if needed use a spacing guide of 26 ‘X’s written along the edge of a piece of paper). Then slide the cipher-alphabet along underneath the a-z alphabet according to the process described in the previous paragraph.

- Doing the same but with aid of a text editor, like notepad. This makes it easier to duplicate a-z (via cut and paste) and much better for shifting the cipher-alphabet to and fro.

- Using a code wheel. Have a fixed code wheel, with a-z on it. Then pin it to a piece of paper or card board and write the cipher-alphabet around the outside. Place a mark between the first and last letters for reference while shifting. The mechanics of shifting amounts to turning your a-z wheel, which is pinned at its center.

+---------------------------------------------------------+

| |

| Figure 7. encrypting "hello": |

| |

| abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz |

| RBLVMYAFDNWHUCXEKPZISGOJQT |

| h->K |

| |

| abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz |

| RBLVMYAFDNWHUCXEKPZISGOJQT |

| |

| e->V |

| |

| abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz |

| RBLVMYAFDNWHUCXEKPZISGOJQT |

| l->R |

| |

| abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz |

| RBLVMYAFDNWHUCXEKPZISGOJQT |

| l->K |

| |

| abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz |

| RBLVMYAFDNWHUCXEKPZISGOJQT |

| o->L |

| |

| hello |

| KVRKL |

| |

+---------------------------------------------------------+

Now the algorithm would use a different alphabetic substitution for each character position, for messages up to 26 characters long. If we were to repeat cycling through the 26 different alphabetic substitution arrangements, then every 26th character would be encrypted using the same alphabetic substitution. So with a message length of 260, we could have 26 groups of characters each having 10 other characters encrypted using the same alphabetic substitution. This is not so bad. It would be very hard to break (with frequency analysis) such a complex encryption with such small sets of similarly encoded characters widely spread through the message, even with the added help of a couple of letter patterns repeating 26 characters apart due to an associated repeat within the original text (e.g. two ‘the’s 26 letters apart). I venture to say, given the use of a strong key in the first place (8 or more characters, preferably not simply a dictionary word or two), that here, with pencil and paper, we have already obtained a security level on par with the Enigma cryptograph machines of the past. But with today’s super computers our security would still be less than safe from professionals.

So we then ‘rekey’ the cipher-alphabet after each block of 25 characters that we encrypt (or after each line from the source message).

Rekeying the Cipher Alphabet :

To rekey a cipher-alphabet we do something similar to what we did when we created the first cipher-alphabet, only this time we put the current cipher-alphabet in place of the A-Z alphabet on the bottom (see figure 8). We then use the key as before (refer to the steps 1-5 above used to produce the first cipher-alphabet with the key). If we rekey the cipher-alphabet we have been using again with the key ‘bluesauce’ we get the cipher-alphabet in figure 10, and this is the cipher-alphabet we would use for the second block of 25 characters. We then repeat this process after each subsequent block of 25 characters.

+-----------------------------------+

| MNOPQRSTUVWXYZABCDEFGHIJKL |

| RBLVMYAFDNWHUCXEKPZISGOJQT |

| |

| Figure 8. |

|-----------------------------------|

| |

| MNOPQRSTUVWXYZABCDEFGHIJKL |

| RBLVMYAFDNWHUCXEKPZISGOJQT |

| RBLVMY/F//WHUC///P//SGOJQ/ |

| R/LVMY////W/U//////////J// |

| |

| key: bluesauce |

| --------- |

| ETDZAXNKI |

| SFPCGHBQO |

| WJVRLMYU |

| |

| Figure 9. |

|-----------------------------------|

| |

| Cipher-Alphabet: |

| WJVRLMYUSFPCGHBQOETDZAXNKI |

| |

| Figure 10. |

+-----------------------------------+

Pre-Keying is a must for Truly Strong security:

As strong as this algorithm is so far, the key now is considered the weakest link. The effective amount of uniqueness and randomness in the key (and the first cipher alphabet to be used) is crucial. To achieve better results than simply using a longer key could achieve, a second ‘pre’ key is used. Hence for application of the full E-Cipher, first you use the pre-key to produce a cipher alphabet from the A-Z alphabet and then you use the regular key on it to produce the first cipher alphabet to be used to encrypt. Subsequent rekey operations are done using the regular key. See figure 11 for an example of using the two keys to produce the initial cipher alphabet to be used for doing encryption. Note that if you have the keys, you can generate the cipher alphabet(s) to be used ahead of time, provided you can safeguard them from discovery.

+-----------------------------------+

| |

| MNOPQRSTUVWXYZABCDEFGHIJKL |

| ABC/E//HIJKLMN/PQR/TUVWX// |

| ... |

| |

| Pre-Key: sparkle |

| ------- |

| GDOFYZS |

| ... |

| WXELPIJQKABVURCTMNHGDOFYZS |

| |

| MNOPQRSTUVWXYZABCDEFGHIJKL |

| WXELPI/Q//BVUR///N//DOFYZ/ |

| |

| Key: bluesauce |

| --------- |

| TSKHJCAMG |

| ... |

| PXREULIVQBZOYNDWFTSKHJCAMG |

| |

| Figure 11. |

+-----------------------------------+

That completes the description of the E-Cipher. Anything less than implementing everything described herein would be an ‘Abridged E-Cipher’.

A sample encrypted message, and the keys used to do the encryption, for you to practice on by decrypting the original message, are in figure 12 below.

+-----------------------------------+

| |

| Pre-Key: rondesc |

| |

| Key: groklings |

| |

| Encrypted message: |

| |

| HDMUM STDSR PDAXA LHSQV UQCQY |

| UYWUZ TAQBZ PQLWD TIVUH GJRAI |

| OYGDX NUSAI SFMUE QOW |

| |

| Figure 12. |

+-----------------------------------+

Download E-Cipher Test VB program to verify results and general testing.

| E-Cipher Overview | The E-Cipher | Beyond E-Cipher |