# The science of encryption: prime numbers and mod n arithmetic

• https://math.berkeley.edu

The heart of SSL – as well

as pretty much every other computer security or encoding system – is something called a

public key

encryption scheme

. The first article below describes how a public key encryption scheme works,

and the second explains the mathematics behind it: prime numbers and mod

n

arithmetic.

1. A Primer on Public-key Encryption

Adapted from a suppliment to The Atlantic magazine, September 2002. By Charles Mann.

Public-key encryption is complicated in detail but simple in outline. The article below is an

outline of the principles of the most common variant of public-key cryptography, which is known

as RSA, after the initials of its three inventors.

A few terms first: cryptology, the study of codes and ciphers, is the union of cryptography

(codemaking) and cryptanalysis (codebreaking). To cryptologists, codes and ciphers are not the

same thing. Codes are lists of prearranged substitutes for letters, words, or phrases – i.e. "meet

at the theater" for "fly to Chicago." Ciphers employ mathematical procedures called algorithms to

transform messages into unreadable jumbles. Most cryptographic algorithms use keys, which are

mathematical values that plug into the algorithm.