Boolean Functions

Synonyms

Binary functions

Related Concepts

Reed–Muller Codes; Stream Cipher; Symmetric Cryptography

Definition

Functions mapping binary vectors of a given length to bits

Background

Symmetric cryptography

Theory

Boolean functions play a central role in the design of many symmetric cryptosystems [4] and in their security. In stream ciphers (Combination Generator, Filter Generators, …), they usually combine the outputs to several linear feedback shift registers, or they filter (and combine) the contents of a single one. Their output produces then the pseudo-random sequence which is used in a Vernam-like cipher (i.e., which is bitwise added to the plaintext to produce the ciphertext). In block ciphers (see the entries on these ciphers), the S-boxes are designed by appropriate composition of nonlinear Boolean functions.

An n-variable Boolean functionf(x) is a function from the set ${F}_{{2}^{n}}$ of all binary vectors of length n (also called words) $x = ({x}_{1},\ldots,{x}_{n})$, to...