The Pythagorean cipher is a cryptosystem of classical cryptography, older in time than other systems such as the Caesar cipher. It was described by the Pythagoreans based on the music theory pioneered by Pythagoras, and was widely used by the Greek empire during the Second Punic War.
According to Plutarch, the Roman empire preferred to adopt the Caesar cipher because it was simpler than the Pythagorean cipher, and also because of the limitations of this type of cipher due to the problem of the wolf fifth, which caused errors in the decryption process derived from the deviation by the Pythagorean comma. A description of the procedure can be found in Plutarch's work, in addition to a comparison with the Spartan scytale cipher.
According to other historians, this cipher required cryptologists or scribes versed in music theory and with a highly educated musical ear. And although it allowed it to be transmitted over great distances using different musical instruments of the time, other systems prevailed.
The philosopher Plato refers in a fragment of his dialogues to a predecessor system to that of Pythagoras used by the Atlanteans. Even in it, an evident influence is suggested in its definition and use. Because there are no documents on Atlantis, nor about its real existence, this statement cannot be corroborated.
The improvement of the musical notation systems produced in the Middle Ages allowed this type of classical cipher to spread, in addition to allowing the proliferation of variants. But equally, the problems derived from the temperament resulting from the Pythagorean tuning, caused problems to be constantly incurred during decryption, although the cryptogram was transmitted in writing on a staff and not through the emission of sounds using a musical instrument. In addition, the constant confusion in the encryption criteria at a time when there were no consensuses such as just intonation. At that time there were no musical standards, and it complicated the encryption method even though both parties were in possession of the symmetrical key and procedure.
According to some chronicles, the cryptosystem was crucial during the Muslim invasion of Al-Andalus, being used for the transmission of important military messages. Some chroniclers of the time assure that, thanks to the little diffusion of it, there were many cultures that were unaware of this encryption method, which played in favor of being a strength for cryptanalysts.
During the Renaissance, thanks to the appearance of new temperaments, Pythagorean cipher was preferred by some cryptogoles over the Vigenère cipher. There was a lively debate about the susceptibility of both cryptosystems to frequency analysis, and the number of cryptograms needed to break either method. The truth is that the simplicity of the classical substitution systems was a great advantage over the procedure based on music theory, which required a greater learning curve. On the other hand, oral transmission was not presented as an advantage, in fact, they ended up sending the messages through a written musical encoding. What also seemed a contradiction compared to the original description of the procedure according to various sources.
urrently, the Pythagorean cipher only has pedagogical interest, being studied as an introductory section within the classical cryptosystems. It is true that there are some scholars who argue that at the time it was defined, it was an advanced cryptosystem for its time and highly robust when compared to other contemporary methods. But equally, there are many who believe that its complexity was not justified, as there are simpler and more agile alternatives that offer equivalent security.