Joint Intelligence Training Center
Cryptology 406: Classic Ciphers
Laboratory Session 5: ALBERTI CIPHER DISK
In this exercise the student will learn to encipher and decipher short messages using the Alberti cipher disk. NOTE: You can complete this assignment at home. No field work required.
Algorithm: A formula, or step-by-step procedure, for solving a mathematical problem.
Base Plate: the larger, fixed Alberti disk. Plaintext is always read on the base plate.
Ciphertext: the encrypted version of a message that the sender wishes to transmit to the receiver(s).
Decipher (decrypt, decode): to convert a ciphertext message to plain text.
Encipher (encrypt, encode): to convert a plaintext message to ciphertext.
Frequency analysis: In cryptanalysis, the study of the frequency and patterns of letters or groups of letters in a ciphertext. The method is used as an aid in breaking classic ciphers.
Key (keytext): in cryptography, the key is a piece of information (a parameter) that determines the functional output of a cryptographic algorithm or cipher. Without the key, an algorithm will have no result. In encryption, the key specifies a particular transformation of plaintext into ciphertext, or vice versa during decryption.
Monoalphabetic cipher: any cipher based on substitution, using a single substitution alphabet over the entire message.
Plaintext: an unencrypted message that the sender wishes to transmit to the receiver(s).
Polyalphabetic cipher: any cipher based on substitution, using multiple substitution alphabets.
Rotor: the smaller, movable Alberti disk. Ciphertext is always read on the rotor.
Leon Battista Alberti (1404–1472) was an Italian author, artist, architect, poet, priest, linguist, philosopher and general Renaissance polymath. Being an accomplished cryptographer, he
> published the earliest book on cryptanalysis in western Europe,
> created the first polyalphabetic cipher (now known as the Alberti cipher) and
> invented the first encryption machine (the Alberti Cipher Disk).
His polyalphabetic cipher was the most significant advance in cryptography since Julius Caesar's time. For this, cryptography historian David Kahn* christened Alberti the "Father of Western Cryptography."
Alberti cipher disk (left); Templar cipher disk (right)
Alberti was active in Italian Freemasonry. This led him into a relationship with the Knights Templar that remains unclear. Historians speculate that he designed the Templar Cipher Disk and taught the Knights how to use it to secure their clandestine communications. Both devices work using the same principals.
* David Kahn, The Codebreakers: the story of secret writing. New York: MacMillan, 1967, (still in print; very entertaining; highly recommended).
IV. How the Alberti Cipher Disk Works
Initially the Rotor (red) is aligned with the Baseplate (blue) so that all the letters and numbers match (red 'A' opposite blue 'A', etc.). If the Rotor is turned one space clockwise, this puts red '9' opposite blue 'A', etc. In Example 1 the KEY is '9' because we set '9' on the rotor under 'A' on the baseplate and leave it at this setting for the entire message.
Example 1: Clockwise Rotor shift (left); Enciphered message (right)
The plaintext message is now composed from the baseplate (blue). It's ciphertext equivalent is read from the rotor (red).
This is identical to the simple and ancient monoalphabetic substitution method called the Caesar shift cipher. In this system every 'A' is encrypted as '9', every 'B' is encrypted as 'A', etc. While this encipherment may discourage the casual kibitzer, it provides no security against a cryptanalyst with only rudimentary skills.
Adding another key, we alternate the first clockwise shift with a second, counter- clockwise shift to 'B'. Now the KEY is '9B' which reflects these alternating clockwise/counterclockwise shifts.
Example 2: Counterclockwise Rotor shift (left); Enciphered message (right)
The additional shift produces an improved ciphertext. The plaintext 'A' can now appear as either '9' or 'B' in the ciphertext. Plaintext 'T' can appear in ciphertext as either 'U' or 'S'. While this encryption would not deter a skilled cryptanalyst for very long, the significant difference is that this is now a polyalphabetic cipher, albeit the simplest version of its type. The polyalphabetic system has unlimited substitution possibilities, based on the length of the key being used.
V. Frequency Analysis
The frequency distribution of the letters in our written language is a useful tool in the analysis of substitution ciphers. The following chart illustrates the relative frequency of letters used in the English language. 'E' is the most commonly used letter, followed by 'T', 'A', 'O' and 'I' respectively.
Normal English language letter frequency
Monoalphabetic ciphers can disguise the plaintext, but they cannot alter the frequency, or pattern, of the letters being used. Polyalphabetic ciphers, properly used, can redistribute the letter frequency, increasing the security of the cipher.
The following chart compares the frequency distributions of the examples used above.
Note that in the polyalphabetic cipher (Example 2) the distribution is spread among more letters (10 vs 9) and is more evenly distributed (or flatter) than in the monoalphabetic equivalent (Example 1). Now consider the following, a polyalphabetic cipher using a five-character key. The five disks represent each setting of the key.
The resulting frequency distribution (Example 3) is flatter yet with little resemblance to the monoalphabetic distribution.
VI. Constructing an Alberti Cipher Disk
The Alberti Cipher Disk is a simple device. Print the following illustration then carefully cut out the disk and the baseplate. Place the rotor on top of the base plate then pin them together at their common rotation axis. A cheap stud earring makes a good center pin.
Alberti cipher disk: rotor (left); baseplate (right)
With any cipher, encryption and decryption is easiest using a blank form designed especially for this purpose. You can view and print a blank form for this exercise by clicking here.
VII. Deciphering a Message
You are an intelligence officer for OSS, the legendary wartime intelligence organization. ROMEO, a trusted field agent, has transmitted the following message, encrypted using the Alberti cipher disk:
QTAMW IOLF3 XUEP0 TXWYI 6Y42M 0FKYC 9YXVN VFV51 YJY1D Q1XKW A9YNS AUWI9
Follow these step to decipher the message.
1. Determine the key (see below).
2. Copy the ciphertext and the key into a blank form.
3. Use the Alberti cipher disk to derive the plaintext message.
You refer to a top secret list and confirm that the key for this message is HTVMJE6. Enter both the ciphertext and the repetitive key in the appropriate boxes on the form. Turn the rotor until the first key character ('H') is aligned under the 'A' on the outer baseplate. Find the first ciphertext character ('Q') on the rotor. Above 'Q' on the rotor you find 'J' on the base plate. This is the first character in the plaintext message. You write 'J' in the first box on the plaintext line.
To find the second plaintext letter, turn the rotor until the second key character ('T') is aligned under the 'A' on the baseplate. The second ciphertext character (also 'T') is now aligned under 'A' on the baseplate. 'A' therefore is the second character in the plaintext message, so write 'A' in the second box on the plaintext line. Complete this example to read the secret message. A few additional plaintext letters are inserted as an aid in this exercise.
Historical Note: The Royal Navy used the Alberti cipher (British Naval Cypher No. 2) until early 1942, when they discovered that the Germans had broken the code and were reading their secret messages.
VIII. Things to Think About
The Vigenere cipher is an historical descendant of the Alberti cipher. Theoretically the two methods are identical. the only practical difference is that the Vigenere employs a table of shifted alphabets rather than a rotor device.
As with most ciphers a longer key increases the strength and security of the ciphertext. In fact, the ultimate key, one that is unique, used only once, is random and the same length as the message produces an unbreakable ciphertext. This is the definition of a one-time pad cipher.
IX. Date-Name-Key Algorithm
Any cipher, even the one-time pad, is only as secure as its key. Several ciphers with perfect key security have been developed in recent years, including Private Key Encryption (see GC1KBPY). With all classic ciphers, however, including the Alberti, security of the key is the weakest link. The problem is, of course, that both the sender and the receiver of any encrypted message must share a common key. This means that the key must be distributed among all parties who need to communicate using the cipher.
Historically the most common approach to this problem is to distribute a list of keys to all users in a network. In World War II, for example, the Kriegsmarine (German Navy) used the supposedly unbreakable Enigma Machine cipher protect its radio communications. Every ship in their fleet carried a booklet that listed the daily rotor settings (a type of key) and was updated quarterly. The British codebreakers at Bletchley Park made little progress on the Enigma cipher until the Royal Navy adopted the tactic of capturing unarmed German weather reporting ships in the North Atlantic. This gave them access to the rotor settings as well as the rotors, which they disassembled to study their internal wiring patterns.
A practical alternative is to develop an algorithm to generate the key. In the following example, the date that the message is sent is combined with the sender's name (in this case, 'ROMEO') to generate the key.
The above table illustrates how ROMEO generates the key for his messages to be sent on 15 June 2009. In the 'DATE' line (red) he copies the date in the standard seven-character format. To the right he enters the numerical equivalent (N.E.) of each character. Numbers are used at their face values. Letters are assigned values according to position (A=1, B=2, ..., Z=26).
In the 'NAME' line (blue) ROMEO copies his code name, repetitively, under each character in the 'DATE' line. To the right he again enters the N.E. of each character.
On the bottom line he sums the N.E. values in each column using mod 26 arithmetic. This means that if the sum exceeds 26 (the number of letters in the English alphabet) we subtract 26 from the sum and use the difference.
Example 1: U (21) + E (5) = 26 (Z)
Examle 2: N (14) + O (15) = 29 - 26 = 3 (C)
Mod 26 arithmetic keeps the N.E. sums in the range of 1 to 26. Finally, ROMEO generates his key (STWZCRX) by assigning letter equivalents to each of the mod 26 sums.
This is not a practical alternative for a large network with many spies. Without knowing who sent a message the receiver may have to generate numerous keys before hitting on the correct key that allows decipherment. For a small spy ring with just a few correspondents this method works quite well.
X. Laboratory Assignment
You control a small network of agents that includes ROMEO, a veteran who monitors the activities of KAOS enemy spies in the Nashville area. On 25 APR 69 you receive a wireless message from ROMEO. He has established a new dead drop in White House, Tennessee. The following Alberti encryption provides you with its location and description.
Y10XM XMXU1 UZQT6 LL96V W4T6S CJQS8 FKF8B 6B68V 2E75T U51Y7 Z1KVV TS5V7
0G1B6 1BZ4X 6WD9A WW510 EZ1FX T5DZB AXFQB UCF1C RCZBC 4714L BE5X6 UR95V
A1WGC FD4R1 GA316 T2TZ1 WT4DX 11BC1 9Y536 410GA 0AXP8 X0L7D 4ZOA0 BC19X
Use the Date-Name-Key algorithm described in Section IX to generate the key. Follow ROMEO's instructions to complete this assignment.
XI. Extra Credit
One week later ROMEO sends you the following message:
ZVNT7 ZX4T3 HVC4V 7IMRF 13UHX N319R JYPXA 44IUU LFZSZ QYLIZ 87Y94 5AU6T
7F1A4 ATTX2 Z32YU 1A9UC IZ1X4 UBFV8 FA4EN 95828 3J6B5 A96F6 LBBQG J41Z5
WCNC1 0W4G3 1HERS 1TZC8 Z86RR AG99D U281R 83N0Z 8BT3Y U1Z5T 311E0 SULNY
018U2 Y1CE5 B3YUX GF4JW RX0AX 7XZ1F 9Q5J5 GB673 URXGA X3H10 1D4GI VFYVC
7QQ1E VTHY1 C744L K7GH8 U3SQK
Again use the Date-Name-Key algorithm to generate the key. Follow ROMEO's encrypted instructions to earn extra credit for your efforts.