Algebraic Immunity of Boolean Functions

Synonyms

Resistance to the standard algebraic attack

Related concepts

Boolean Functions; Stream Ciphers; Symmetric Cryptography

Definition

Parameter of a Boolean function quantifying its resistance to algebraic attacks

Background

Boolean functions

Theory

A new kind of attacks, called algebraic attacks, has been introduced recently (see [2,  3]). In both the combiner and the filter model of a pseudo-random generator in a stream cipher, there exists a linear permutation $L : {\mathbb{F}}_{2}^{N}\mapsto {\mathbb{F}}_{2}^{N}$, a linear mapping $L' : {\mathbb{F}}_{2}^{N}\mapsto {\mathbb{F}}_{2}^{n}$ and an n-variable combining or filtering Boolean function f such that, denoting by ${u}_{1},\cdots \,,{u}_{N}$ the initialisation of the linear part of the pseudo-random generator and by ${({s}_{i})}_{i\geq 0}$ the pseudo-random sequence output by it, we have, for every i:

$${s}_{i} = f(L' \circ {L}^{i}({u}_{ 1},\cdots \,,{u}_{N})).$$

The general principle of algebraic attacks is to try...