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148 CHAPTER 8. POLYALPHABETIC CIPHERS
excess of 11 keyletters per minute of conversation. Or a modern business sending
2000 pages everyday needs more than 120 new pages of keywords everyday.
This is our first encounter with the key management problem. A cipher
system isn’t much good if every few days we must hand-deliver a brand-new
book full of never-been-used keys to everyone we wish to communicate with.
Even if we could develop such “books” our business would go bankrupt from
the printing and delivery costs!
The German Enigma machines of World War II fame, as well as some of
the cipher machines used by the Americans like the M-94, were, in many ways,
simply mechanical versions of multiple Vigenère ciphers. These machines used a
number of linked wheels, or “rotors,” to perform the enciphering and deciphering.
Each rotor can be thought of as giving a monoalphabetic cipher. When
coupled several such rotors combine only to give a monoalphabetic cipher. But
when one rotor rotates even one step, a new monoalphabetic cipher is created.
As long as the rotors continue to rotate, in whatever pattern, and do not come
back to their original position, an ever-longer keyword is produced. With the
5 rotors of the latter Enigma machines, the “keyword” had functional length
26 5 = 11, 881, 376, longer than the Iliad and Odyssey combined! 13 (The rotor
machines have their own weaknesses. The rotors get stolen or captured. The
setting of the rotors – how exactly they are positioned at the beginning of a
message – must be sent. And each particular type of machine has its own peculiarities.
For example, the Enigmas were unable to encipher a letter to itself.
We mustn’t overstate the power of our techniques, the weaknesses of Enigma
contributed a great deal to the Allies breaking it. But advanced versions of the
techniques we’ve developed in this chapter played an important role.)
Although the Vigenère-based Ciphers were great in their time, the development
of Friedman’s and other more sophisticated tests, coupled with the modern
need for vast quantities of keys, makes such ciphers relatively insecure.
13 A keylength of eleven million sounds large, but numbers get big fast. For a “small”
example, consider The War of the Rebellion: a compilation of the official records of the
Union and Confederate armies. Pub. under the direction of the ... Secretary of War, the
compilation of the formal reports, correspondence, orders, and returns of the Union and
Confederate Armies. In four Series, it consists of nearly 70 volumes, many in several parts,
with most of the parts between 800 and 1200 pages. For example, Volume XXIV, published
in 1889, comes in three parts, and covers “Operations in Mississippi and West Tennessee,
including those in Arkansas and Louisiana connected with the Siege of Vicksburg. January
20 - August 10, 1863.” Part III includes the Correspondences and is 1196 pages long. For
an estimate, if we assume each volume has 2 parts, each of 1000 pages, and there are 3000
characters per page, the volumes contain 420,000,000 characters in total. This is over 200,000
characters for each day of the war! Now imagine the number of characters sent during WWII.
Or during either of the Persian Gulf Wars!