algebraic_immunity_rs

A Rust library to compute the algebraic immunity and restructes algebraic immunity of Boolean functions.

Reference:
"Computing the Restricted Algebraic Immunity, and Application to WPB Functions"
Luca Bonamino and Pierrick Méaux. IACR ePrint 2025/1779.

Installation

Add the dependency to your Cargo.toml:

[dependencies]
algebraic_immunity = "0.3.0"

Usage

From BooleanFunction struct.

use alebraic_immunity::boolean_functions::BooleanFunction;
let ve = vec![0,1,0,0];
let bf = BooleanFuntion::from_truth_table(ve.clone());

let immunity = bf.algebraic_immunity();
assert_eq!(immunity, 1);

let restricted_immunity = bf.restricted_algebraic_immunity(vec![0,1,2]);
assert_eq!(restricted_immunity, 1);

Directly from AlgebraicImmunity and RestrictedAlgebraicImmunity structs.

use algebraic_immunity::ai::{AlgebraicImmunity, RestrictedAlgebraicImmunity};

let ve = vec![0,1,0,0];
let immunity = AlgebraicImmunity::algebraic_immunity(ve, 2);
assert_eq!(immunity, 1);

let restricted_immunity = RestrictedAlgebraicImmunity::algebraic_immunity(ve, vec![0,1,2], 2);
assert_eq!(restricted_immunity, 1);

use algebraic_immunity::ai::{AlgebraicImmunity, RestrictedAlgebraicImmunity};

let ve = vec![
        1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,
        1,0,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,1,1,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,1,1,
        1,0,1,0,1,0,0,0,0,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,
        0,1,1,0,1,1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,
        1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,
        1,0,0,1,0,0,0,0,0,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,0,1,1,1,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0,0,0,1,0,0,1,0,1,0,1,0,
        1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,1,0,1,0,0,
        0,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,1,1,1,0,1,1,0,0,1,1,0,1,0,1,0,1,1,1,1,0,1,
        0,0,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,1,1,1,1,1,1,0,0,1,0,1,
        1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,0,1,1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,1,0,1,0,1,
        1,0,0,1,1,1,0,0,0,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,1,1,1,1,1,0,0,1,1,
        0,0,1,0,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,1,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,
        0,0,0,0,1,0,1,0,0,0,1,0,0,1,1,1,1,0,1,1,0,1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0,1,
        0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0,0,0,1,1,1,1,0,0,1,0,0,1,1,1,
        1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,1,0,0,1,1,1
    ];
let immunity = AlgebraicImmunity::algebraic_immunity(ve, 10);
assert_eq!(immunity, 5);


let ve = vec![
        1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,
        1,0,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,1,1,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,1,1,
        1,0,1,0,1,0,0,0,0,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,
        0,1,1,0,1,1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,
        1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,
        1,0,0,1,0,0,0,0,0,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,0,1,1,1,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0,0,0,1,0,0,1,0,1,0,1,0,
        1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,1,0,1,0,0,
        0,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,1,1,1,0,1,1,0,0,1,1,0,1,0,1,0,1,1,1,1,0,1,
        0,0,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,1,1,1,1,1,1,0,0,1,0,1,
        1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,0,1,1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,1,0,1,0,1,
        1,0,0,1,1,1,0,0,0,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,1,1,1,1,1,0,0,1,1,
        0,0,1,0,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,1,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,
        0,0,0,0,1,0,1,0,0,0,1,0,0,1,1,1,1,0,1,1,0,1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0,1,
        0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0,0,0,1,1,1,1,0,0,1,0,0,1,1,1,
        1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,1,0,0,1,1,1
    ];
let restricted_immunity = RestrictedAlgebraicImmunity::algebraic_immunity(ve, vec![1, 2, 6, 100, 200],10);
assert_eq!(restricted_immunity, 1);

License

MIT