How a Snake Eats Its Tail

A Dip into Cryptography

All around us data is transferred faster than ever. Sensitive data is also part of our everyday life. To protect that data, we use encryption. When we encrypt data, it changes in some way that renders it useless to the possible viewer, but that can be changed back to its original state when it arrives safely to the meant receiver. These transformations rely heavily on math, and particularly on a field of math called number theory. This text takes us through the basics of cryptography both from a mathematical perspective and as a programming matter.

For as long as writing has existed, the concept of encryption has lived and developed alongside the plain text writing. The idea of rendering text seemingly incomprehensible for purposes of guarding a secret has been central especially in military use and politics. The word cipher originates from the medieval times, from words such as the latin cifra and Arabic صفر (sifr), which means “zero”. There are numerous theories on why zero would have been used to describe encryption, including that the concept of zero was not part of the roman number system and seen as a mystery among numbers. One of the oldest and most widely known ciphers used in military context is Caesars cipher, also known as Caesars shift.

Caesars shift takes one key, which is used to shift each character in the plaintext. This single key is the weakness of the cipher: once the correct shift is figured out, the whole message is revealed. Mathematically, this type of cipher can be written as a problem in modular arithmetic, which works with values wrapped up in a specific range. We’ll discuss this in more depth later.

The way we can solve the plaintext from the encrypted text is by finding the key. In the case of a Caesars cipher of value 3, finding out the key (3) lets us decrypt the whole text in one chunk. The key specifies the output of the encryption algorithm.

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