Archimedes cipher

The Archimedean cipher is a classical cryptography cryptosystem, older in time than other systems such as the Caesar cipher. It was described by Archimedes of Syracuse based on the arithmetic spiral, or Archimedean spiral, which the Greek mathematician himself studied in depth.

According to Plutarch, the Greek sage perfectly mastered both the Spartan Scythal and the Pythagorean cipher. But due to the intrusion of the first methods of cryptanalysis, it is said that Archimedes devised a more intricate method. Although precisely because of its complexity, historians of the time believe that this cryptosystem was weighed down compared to other simpler alternatives, and for this reason it received little diffusion in ancient times. A description of the procedure can be found in Plutarch's work, as well as a comparison with the Spartan Scythian cipher.

This application is based on the original version, using two discrete and concentric variations of the Archimedean spiral are used, in which the initial step of the polar angle is out of phase between them, seeking an interlocking without collisions, thanks to which both spirals can feed back to each other. yes depending on the key. In this first version, Archimedes uses the number 27 as the maximum length for the spirals.

The choice of the length of the spiral has been the result of debate among thinkers and scholars throughout the centuries. Some historians believe that the choice of the number 27 was made premeditated so that the number of discrete positions on the horizontal axis of the spiral was 12 positions, making them coincide with the number of gods of Olympus: according to the mythology of ancient Greece . The latter made it easier to memorize part of the symmetric key.

Among the large number of theories and hypotheses that exist about the mechanical device found in the 20th century in a shipwreck near the Greek island of Antikythera, there are many historians who attribute its invention and manufacture to Archimedes himself. And there are also many experts who believe that the real function of the mechanism was to allow an Archimedean cipher to be carried out in an automated manner.