26 times, when the second rotor returns to its original position. The first wheel’s 26 revolutions of 26 letters each means that 26 × 26, or 676 letters, will be enciphered through a different wiring maze. Only at the 677th will the internal maze be the same as for the first letter. (The alphabet, of course, has only 26 letters, and many of these will repeat in the ciphertext. But if the plaintext consisted only of
a
’s, the sequence of ciphertext letters would start to repeat only at the 677th
a
.)
Using the same principle, more rotors can be added, each one lengthening the period by a factor of 26. Four rotors produce a period of 456,976 letters; five rotors, a period of 11,881,376.
To decipher a message in such a machine, the cipher clerk obviously needs to know the starting positions of the rotors. This crucial information, called the key, must be agreed upon by sender and receiver in advance of any communication between them. Often a key takes the form of a list of starting positions for each day in a month; the sheets of paper bearing this list are distributed by couriers to all the radio or telegraph stations that will encipher or decipher their communications with the same machine. A key can encompass other elements as well. If, for example, the rotors are removable, so that they can be inserted into the machine in varying orders, the keywill specify the order of the rotors from left to right. Without the key the decipherer would not be able to read the message except by playing codebreaker.
The mechanism that Scherbius offered the navy in the spring of 1918 was a sample multirotor machine. His memorandum explained the rotor principle and then his chief point: the impracticability of the enemy’s solving a message even if he had the machine:
The key variation is so great that, without knowledge of the key, even with an available plaintext and ciphertext and with the possession of a machine, the key cannot be found, since it is impossible to run through 6 billion (seven rotors) or 100 trillion (thirteen rotors) keys [rotor starting positions]. If the examination of each telegram takes half a minute in a 24-hour workday, this would require 5.8 years with a simultaneous employment of 100 machines of seven rotors and 14.5 years for 1,000 machines of eight rotors.
He noted, correctly, that “it would only make sense to search for a key in this way when it is known that unknown cryptograms have the same key. And when the same key is maintained for a long time.”
The naval staff examined Scherbius’s machine and found that it afforded “good security, even if compromised.” But it decided not to buy it “because with the present kind of naval cipher traffic, the use of machines is not worthwhile.” Instead it recommended that the Foreign Office examine the machine to see if it were suitable for diplomatic correspondence. The price of a ten-rotor machine, measuring 12 by 5½ by 4¾ inches, with an attached typewriter to print the output, was 4,000 to 5,000 marks, or $1,600 to $2,000 (about $14,400 to $18,000 in 1991 dollars), and delivery time was eight weeks. This price, Scherbius said, could be reduced to 1,400 to 1,800 marks, or $560 to $720 ($5,000 to $6,500 in 1991 dollars), if a thousand machines were bought.
But the Foreign Office was not interested either. This may have discouraged Scherbius, but it did not defeat him. The cryptography bug had bitten him.
Scherbius was born on October 20, 1878, in Frankfurt-am-Main, the son of a small businessman. He graduated from that city’s
Ober-realschule
, a type of secondary school that emphasized mathematics, natural sciences, and modern languages; most of its graduates went into engineering. After studying electricity for the 1901–02 winter semester at the Technical College in Munich, Scherbius matriculated May 13, 1902, at the Technical College in Hanover. He studied one or two courses at a time for several months, among them Electrical Installations
a
’s, the sequence of ciphertext letters would start to repeat only at the 677th
a
.)
Using the same principle, more rotors can be added, each one lengthening the period by a factor of 26. Four rotors produce a period of 456,976 letters; five rotors, a period of 11,881,376.
To decipher a message in such a machine, the cipher clerk obviously needs to know the starting positions of the rotors. This crucial information, called the key, must be agreed upon by sender and receiver in advance of any communication between them. Often a key takes the form of a list of starting positions for each day in a month; the sheets of paper bearing this list are distributed by couriers to all the radio or telegraph stations that will encipher or decipher their communications with the same machine. A key can encompass other elements as well. If, for example, the rotors are removable, so that they can be inserted into the machine in varying orders, the keywill specify the order of the rotors from left to right. Without the key the decipherer would not be able to read the message except by playing codebreaker.
The mechanism that Scherbius offered the navy in the spring of 1918 was a sample multirotor machine. His memorandum explained the rotor principle and then his chief point: the impracticability of the enemy’s solving a message even if he had the machine:
The key variation is so great that, without knowledge of the key, even with an available plaintext and ciphertext and with the possession of a machine, the key cannot be found, since it is impossible to run through 6 billion (seven rotors) or 100 trillion (thirteen rotors) keys [rotor starting positions]. If the examination of each telegram takes half a minute in a 24-hour workday, this would require 5.8 years with a simultaneous employment of 100 machines of seven rotors and 14.5 years for 1,000 machines of eight rotors.
He noted, correctly, that “it would only make sense to search for a key in this way when it is known that unknown cryptograms have the same key. And when the same key is maintained for a long time.”
The naval staff examined Scherbius’s machine and found that it afforded “good security, even if compromised.” But it decided not to buy it “because with the present kind of naval cipher traffic, the use of machines is not worthwhile.” Instead it recommended that the Foreign Office examine the machine to see if it were suitable for diplomatic correspondence. The price of a ten-rotor machine, measuring 12 by 5½ by 4¾ inches, with an attached typewriter to print the output, was 4,000 to 5,000 marks, or $1,600 to $2,000 (about $14,400 to $18,000 in 1991 dollars), and delivery time was eight weeks. This price, Scherbius said, could be reduced to 1,400 to 1,800 marks, or $560 to $720 ($5,000 to $6,500 in 1991 dollars), if a thousand machines were bought.
But the Foreign Office was not interested either. This may have discouraged Scherbius, but it did not defeat him. The cryptography bug had bitten him.
Scherbius was born on October 20, 1878, in Frankfurt-am-Main, the son of a small businessman. He graduated from that city’s
Ober-realschule
, a type of secondary school that emphasized mathematics, natural sciences, and modern languages; most of its graduates went into engineering. After studying electricity for the 1901–02 winter semester at the Technical College in Munich, Scherbius matriculated May 13, 1902, at the Technical College in Hanover. He studied one or two courses at a time for several months, among them Electrical Installations
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