Encoding Machines, Enigma, Mathematics

As long as the main “instrument” of cryptography and cryptology was a man, both encoding complexity and decoding speed had their natural limits, as well as high inherent error rate. This situation, however, changed dramatically with the arrival of first encoding machines, and later even more dramatically with the computer technology introduction to these fields.

Unequivocally the best known encoding machine is German Enigma with its significant role in the World War II history. Even though it still used a relatively simple cipher, substituting each letter in a message with another letter, thus a simple substitute cipher in today’s terms, the number of possible combinations (for the U-boat fleet version) reaching 76 x 1018 made it simply impossible to figure out the used combination by mere testing of all options, often a successful method until then.

As a result, if British military intelligence wanted to decode wiretapped German U-boat’s dispatches, they had to physically seize the encoding machine and the individual combination manual (what we could call a decoding key today). On top of that, they had to do it in a way that would not raise the enemy’s suspicion about the code being stolen (since he would have changed it immediately). Thanks to British Navy’s great courage and resourcefulness, the operation was successful and he Enigma code acquisition contributed greatly to the German U-boat fleet’s defeat.

A broader implementation of computer technology in cryptography and cryptology has led to even more dramatic consequences. On the theoretical plane, we are limited only by our own imagination and scientific resourcefulness today because even relatively weak home computers can perform the most complex procedures in countless interactions. Two more trends are worth noticing as well: home computer’s gradual and relatively regular increasing computing power (approximately doubled every two years), and immense superconductive computers utilized by military and other intelligence agencies (we can estimate their power only roughly and indirectly since all data relating to those computers is top secret).

As a result, contemporary cryptologists speak about so-called “life half-time” of individual ciphers. It is based on the fact that the decoding probability of each message, though encoded by a highly secure cipher at the time, increases with time, and once the cipher passes the above-mentioned “life half-time”, the decoding probability reaches an unacceptably high level.

Let our concluding anecdote be cryptology’s spread into contemporary motion-picture production, e.g. the Hollywood movie “U-571” which is based on an actual British operation leading to the Enigma acquisition, or the main storyline of the entire 24: Live Another Day Season 9.