Computer Security and Cryptography

1.1 THE LEXICON OF CRYPTOGRAPHY

The word “cryptography” is derived from the Greek words kryptos, meaning hidden, and graphien, meaning to write. Historians believe Egyptian hieroglyphics, which began about 1900 B.C.E., to be an early instance of encipherment. The key that unlocked the hieroglyphic secrets was the Rosetta Stone, discovered in 1799 in lower Egypt and now located in the British Museum in London. Francois Champollion, using the Rosetta Stone, deciphered the hieroglyphics in 1822. The books by David Kahn [1967, 1983] and Simon Singh [1999] provide extensive accounts of cryptography and its influence on history.

Every scientific discipline develops its own lexicon, and cryptography is no exception. We begin with a brief summary of the principal terms used in cryptography.

An alphabet = {a₀, a₁,…, a_m−1} is a finite set of letters; examples include

1. m = 2^r: (0,1)-sequences of fixed length rZ_r,2 = {x = (x₀, x₁, …, x_r−1): x_i = 0, 1, 0 ≤ i < r};
2. m = 2⁷: the ASCII character alphabet;
3. m = 26: the alphabet consisting of upper-case Latin letters: {A, B, …, Z}

Text is formed by concatenating letters of ; an n-gram (a₀, a₁, …, a_n−1) is the concatenation of n letters. We do not require that the text be understandable nor that it be grammatically correct relative to a natural language ...