Cryptanalysis of the Lorenz cipher
Encyclopedia
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
. The British Government Code and Cypher School at Bletchley Park
Bletchley Park
Bletchley Park is an estate located in the town of Bletchley, in Buckinghamshire, England, which currently houses the National Museum of Computing...
decrypted many communications between the German High Command
Oberkommando der Wehrmacht
The Oberkommando der Wehrmacht was part of the command structure of the armed forces of Nazi Germany during World War II.- Genesis :...
in Berlin and their army commands throughout occupied Europe. These were intercepted non-Morse
Morse
Morse can refer to:* Morse code, a method of coding messages into long and short beeps-Places:Canada* Morse , Saskatchewan* Morse, Saskatchewan, a hamlet* Morse No...
radio messages that had been enciphered by the Lorenz SZ
Lorenz cipher
The Lorenz SZ40, SZ42A and SZ42B were German rotor cipher machines used by the German Army during World War II. They were developed by C. Lorenz AG in Berlin. They implemented a Vernam stream cipher...
teletypewriter rotor
Rotor machine
In cryptography, a rotor machine is an electro-mechanical device used for encrypting and decrypting secret messages. Rotor machines were the cryptographic state-of-the-art for a prominent period of history; they were in widespread use in the 1920s–1970s...
cipher
Cipher
In cryptography, a cipher is an algorithm for performing encryption or decryption — a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. In non-technical usage, a “cipher” is the same thing as a “code”; however, the concepts...
attachments. British cryptographers referred to encrypted German teleprinter
Electrical telegraph
An electrical telegraph is a telegraph that uses electrical signals, usually conveyed via telecommunication lines or radio. The electromagnetic telegraph is a device for human-to-human transmission of coded text messages....
traffic as "Fish
Fish (cryptography)
Fish was the Allied codename for any of several German teleprinter stream ciphers used during World War II. Enciphered teleprinter traffic was used between German High Command and Army Group commanders in the field, so its intelligence value was of the highest strategic value to the Allies...
". They dubbed this machine and its traffic "Tunny", and the intelligence it yielded as "Ultra
Ultra
Ultra was the designation adopted by British military intelligence in June 1941 for wartime signals intelligence obtained by "breaking" high-level encrypted enemy radio and teleprinter communications at the Government Code and Cypher School at Bletchley Park. "Ultra" eventually became the standard...
".
As with the entirely separate Cryptanalysis of the Enigma
Cryptanalysis of the Enigma
Cryptanalysis of the Enigma enabled the western Allies in World War II to read substantial amounts of secret Morse-coded radio communications of the Axis powers that had been enciphered using Enigma machines. This yielded military intelligence which, along with that from other decrypted Axis radio...
, it was German operational shortcomings that allowed the initial diagnosis of the system, and a way into decryption. Unlike Enigma
Enigma machine
An Enigma machine is any of a family of related electro-mechanical rotor cipher machines used for the encryption and decryption of secret messages. Enigma was invented by German engineer Arthur Scherbius at the end of World War I...
, however, no physical machine reached allied
Allies of World War II
The Allies of World War II were the countries that opposed the Axis powers during the Second World War . Former Axis states contributing to the Allied victory are not considered Allied states...
hands until the very end of the war in Europe, long after wholesale decryption had been established.
The message characters were encoded in the 5-bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
International Telegraphy Alphabet No. 2 (ITA2). The cipher attachments implemented a type of Vernam stream cipher
Stream cipher
In cryptography, a stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream . In a stream cipher the plaintext digits are encrypted one at a time, and the transformation of successive digits varies during the encryption...
using a complex array of twelve wheels. The right hand five of these, the chi
Chi (letter)
Chi is the 22nd letter of the Greek alphabet, pronounced as in English.-Greek:-Ancient Greek:Its value in Ancient Greek was an aspirated velar stop .-Koine Greek:...
(
) wheels, changed the five bits of the incoming character, advancing one position with each one. The left hand five, the psiPsi (letter)
Psi is the 23rd letter of the Greek alphabet and has a numeric value of 700. In both Classical and Modern Greek, the letter indicates the combination /ps/ . The letter was adopted into the Old Italic alphabet, and its shape is continued into the Algiz rune of the Elder Futhark...
(
) wheels, changed the result of the chi transform further. The central two muMu (letter)
Carlos Alberto Vives Restrepo is a Grammy Award and three-time Latin Grammy Award winning-Colombian singer, composer and actor.-Biography:...
(
) or "motor" wheels determined whether the psi wheels rotated with a new character.Initially, operator errors produced a number of pairs of messages sent with the same keys, giving a so-called "depth", which often allowed manual decryption to be achieved. Such depths also allowed the complete logical structure of the machine to be worked out, a quite remarkable cryptanalytical feat on which the subsequent bulk decryption of Tunny messages relied.
Subsequently, decryption was achieved by a combination of manual and automated methods. The effect of the chi component of the key was removed with the use of machines that implemented a statistical technique. The first machine was called "Heath Robinson
Heath Robinson (codebreaking machine)
Heath Robinson was a machine used by British codebreakers at Bletchley Park during World War II to solve messages in the German teleprinter cipher used by the Lorenz SZ40/42 cipher machine; the cipher and machine were called "Tunny" by the codebreakers, who named different German teleprinter...
" and it was followed by several other "Robinsons". These were, however, slow and unreliable, and were superseded by "Colossus
Colossus computer
Not to be confused with the fictional computer of the same name in the movie Colossus: The Forbin Project.Colossus was the world's first electronic, digital, programmable computer. Colossus and its successors were used by British codebreakers to help read encrypted German messages during World War II...
" the world's first electronic, (semi-)programmable computer, ten of which were in use by the end of the war. The psi component was then removed using manual methods and machines that imitated the Tunny machine - the so-called "British Tunny" machines.
Secure Telegraphy
Electro-mechanicalElectromechanics
In engineering, electromechanics combines the sciences of electromagnetism, of electrical engineering and mechanics. Mechanical engineering in this context refers to the larger discipline which includes chemical engineering, and other related disciplines. Electrical engineering in this context...
telegraphy was developed in the 1830s and 1840s, well before telephony, and was in widespread use all over the world by the time of the Second World War
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
. An extensive system of cables were used within and between countries, but for mobile German Army Units, radio transmission was often used.
Teleprinter
Teleprinter
A teleprinter is a electromechanical typewriter that can be used to communicate typed messages from point to point and point to multipoint over a variety of communication channels that range from a simple electrical connection, such as a pair of wires, to the use of radio and microwave as the...
s at each end of the circuit consisted of a keyboard and printing mechanism, and very often a five-hole paper tape
Punched tape
Punched tape or paper tape is an obsolete form of data storage, consisting of a long strip of paper in which holes are punched to store data...
reading and punching mechanism. When used online, pressing an alphabet key at the transmitting end caused the relevant character to be printed at the receiving end. Commonly, however, the transmitting operator would prepare a message offline by punching it onto paper tape, and then going online only for the transmission of the message recorded on the tape. Typically this would be at some ten characters per second, and so occupy the line or radio channel for a shorter time than for online typing.
The characters of the message were represented by the codes of the International Telegraphy Alphabet No. 2 (ITA2). The transmission medium, either wire or radio, used asynchronous serial communication with each character signaled by a start bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
, 5 data bits and 1½ stop bits. Each bit was either a "mark" (hole in paper tape, 1 in binary or x at Bletchley Park) or a "space" (no hole in tape, binary 0 or • at Bletchley Park). For example the letter "H" would be coded as ••x•x.
| Pattern of impulses Mark = x, Space = • | Binary | Letter shift | Figure shift | BP 'shiftless' interpretation |
|---|---|---|---|---|
| ••••• | 00000 | null | null | / |
| ••x•• | 00100 | space | space | 9 |
| ••x•x | 00101 | H | # | H |
| ••••x | 00001 | T | 5 | T |
| •••xx | 00011 | O | 9 | O |
| ••xxx | 00111 | M | M | |
| ••xx• | 00110 | N | , | N |
| •••x• | 00010 | CR | CR | 3 |
| •x•x• | 01010 | R | 4 | R |
| •xxx• | 01110 | C | : | C |
| •xxxx | 01111 | V | ; | V |
| •x•xx | 01011 | G | & | G |
| •x••x | 01001 | L | ) | L |
| •xx•x | 01101 | P | 0 | P |
| •xx•• | 01100 | I | 8 | I |
| •x••• | 01000 | LF | LF | 4 |
| xx••• | 11000 | A | - | A |
| xxx•• | 11100 | U | 7 | U |
| xxx•x | 11101 | Q | 1 | Q |
| xx••x | 11001 | W | 2 | W |
| xx•xx | 11011 | FIGS | + or 5 | |
| xxxxx | 11111 | LTRS | - or 8 | |
| xxxx• | 11110 | K | ( | K |
| xx•x• | 11010 | J | ' | J |
| x••x• | 10010 | D | $ | D |
| x•xx• | 10110 | F | ! | F |
| x•xxx | 10111 | X | / | X |
| x••xx | 10011 | B | ? | B |
| x•••x | 10001 | Z | " | Z |
| x•x•x | 10101 | Y | 6 | Y |
| x•x•• | 10100 | S | ' | S |
| x•••• | 10000 | E | 3 | E |
The figure shift (FIGS) and letter shift (LETRS) characters determined how the receiving end should interpret the string of characters up to the next shift character. Because of the danger of a shift character being corrupted, some operators would send a pair of shift characters when changing from letters to numbers or vice versa. Such doubling of characters was helpful to the cryptanalysts at Bletchley Park's statistical analysis. After encipherment, shift characters had no special meaning.
For its secret transmissions, the German armed services enciphered each character using various online Geheimschreiber (secret writer) machines at both the transmitting and receiving ends. These were the Lorenz SZ (SZ for Schlüsselzusatz, meaning "cipher attachment") machine for the army, the Siemens and Halske T52
Siemens and Halske T52
The Siemens and Halske T52, also known as the Geheimfernschreiber , or Schlüsselfernschreibmaschine , was a World War II German teleprinter cipher machine...
for the air force and the Siemens T43 which was little used and never broken by the Allies. Enigma decrypts had revealed that the Germans called the wireless teleprinter transmission systems "Sägefisch" (sawfish), so the name "Fish" was adopted for this traffic. "Tunny" was the name given at Bletchley Park to the first non-Morse
Morse code
Morse code is a method of transmitting textual information as a series of on-off tones, lights, or clicks that can be directly understood by a skilled listener or observer without special equipment...
link, and it was subsequently used for all traffic enciphered with the Lorenz SZ machines.