Cryptography, from the Greek kryptós (secret) and graphein (writting) is the technique of transmitting secret information that a recipient can access without other parties being able to. Terminology is now established that we call Alice ("A") the sender, Bob ("B") the recipient and Eve ("E") the eavesdropper. The message is called plaintext and its encrypted version is called cyphertext. Cryptography consists in using a cypher (an algorithm) to turn the plaintext into cyphertext and back:
plaintext 🡒 cyphertext.
Both the destination and a Hacker will reverse this process, one legitimately and accessing the intended information, the other in violation of the intended secrecy.
An example of a cipher is, for instance, the following sequence:
which is a naively encrypted version of the original sentence, using the rot13 algorithm which rotates by 13 the Latin alphabet, i.e., a🡒n, b🡒o, c🡒p, etc. Because 13 is half the alphabet, rotating it twice brings us back to the original message: a🡒n🡒a, b🡒o🡒b, etc. This is a 13-shift version of a cipher actually used by Caesar, who was rotating the alphabet by -3 letter:
a🡒x, b🡒y, c🡒z, d🡒a, e🡒b
Such operations are described mathematically by modular arithmetics, $\oplus$, which equates two numbers $a$ and $b$ modulo $m$, written
$$a\equiv b (\mod m)$ Here is a text Caesar might have encoded: : Yhql, ylgl, ylfl in rot13, this would have given: : Irav, ivqv, ivpv in rot1 : Wfoj, wjej, wjdj One problem of such ciphers is that one can notice patterns and break them. Caesar's cipher is particularly fragile because one can try all rotations of the alphabet and see which soup of letter makes sense. This is called a "brute-force attack". == Vegenere cipher == While Caesar's cipher had only one number, the $x$ in rot$x$, to encrypt and decrypt, one can easily make the cipher more robust by using a "key", which encodes the information that encrypts the message. The simplest variation is to decide on a key, for instance:
which
The process of encryption/decryption is typically , thanks to a key (one key for "symmetric" cyphers, two for "asymmetric" ones).
It represents perfect cryptography, in the sense that it cannot be broken even with unlimited computing power (this was proven by Claude Shannon).
Asymmetric systems use a public key to encrypt a message and a private key to decrypt it