Cryptology

Abstract

Cryptology is about communication in the presence of adversaries or potential adversaries. A classical goal of cryptography is privacy. Authentication is another goal of cryptography which is any process by which you verify that someone is indeed who they claim they are. Digital signatures are a special technique for achieving authentication. Nowadays cryptography has matured and it is addressing an ever increasing number of other goals like secret sharing, fingerprinting, etc. In this chapter after a brief historical introduction where we present some most known secret-key cryptosystems—like the one-time pad, the affine and Hill’s cryptosystems—we explain the main idea of modern public-key cryptosystems whose security is based on complexity. We look in detail at the complexity of Euclidean algorithm, exponentiation and factoring of integers showing that the complexity of the first two tasks is linear while the naive trial and error method of factoring integers have exponential complexity. All this allow us then to explain in detail RSA cryptosystem. In the last section we also deal with testing primality and explain how the two primes needed for the RSA cryptosystem can be found. Several topics in cryptography will also appear in subsequent chapters: Elgamal cryptosystems in Chaps. 3 and 4, secret sharing in Chap. 6 and fingerprinting in Chap. 7.

Enigmatic words—they are all full of meaning.

Nikolai Roerich (1874–1947)