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|
use rug::{Complete, Integer};
use eframe::egui;
// use std::time::Instant;
fn main() {
let options = eframe::NativeOptions::default();
eframe::run_native(
"Криптографические методы защиты информации",
options,
Box::new(|_cc| Box::new(Application::default())),
);
}
enum State {
Idle,
Running(u32),
Done,
Error,
}
struct Application {
order: u32,
element: u32,
element_check: Option<bool>,
primitive_roots: Vec<u32>,
state: State,
str_num: String,
}
impl Default for Application {
fn default() -> Self {
Self {
order: 29,
element: 2,
element_check: None,
primitive_roots: Vec::new(),
state: State::Idle,
str_num: String::from("20"),
}
}
}
fn min_order(x: u32, order: u32) -> u32 {
let mut min = 0;
let mut pow = x;
for power in 1..order {
if pow == 1 {
min = power;
break;
}
pow = (pow * x) % order;
}
return min;
}
fn is_prime(x: u32) -> bool {
if x <= 1 {
return false;
}
for i in 2..x / 2 + 1 {
if x % i == 0 {
return false;
}
}
return true;
}
impl eframe::App for Application {
fn update(&mut self, ctx: &egui::Context, _frame: &mut eframe::Frame) {
let clear_state = |app: &mut Application| {
app.element_check = None;
app.state = State::Idle;
};
egui::Window::new("Задача №1").show(ctx, |ui| {
ui.horizontal(|ui| {
ui.label("Порядок поля: ");
if ui
.add(egui::DragValue::new(&mut self.order).clamp_range(2..=u32::MAX))
.changed()
{
clear_state(self);
}
});
ui.horizontal(|ui| {
ui.label("Проверяемый элемент: ");
if ui
.add(egui::DragValue::new(&mut self.element).clamp_range(1..=self.order - 1))
.changed()
{
clear_state(self);
}
});
if ui.button("Проверить элемент").clicked() {
let min = min_order(self.element, self.order);
self.element_check = Some(min == self.order - 1);
}
match self.element_check {
Some(true) => {
ui.label("Элемент является порождающим элементом");
}
Some(false) => {
ui.label("Элемент не является порождающим элементом");
}
None => {}
}
if ui.button("Рассчитать порождающие элементы").clicked() {
self.primitive_roots.clear();
self.state = if is_prime(self.order) {
State::Running(1)
} else {
State::Error
}
}
match self.state {
State::Running(current) => {
ui.label("Вычисление...");
let min = min_order(current, self.order);
if min == self.order - 1 {
self.primitive_roots.push(current);
}
self.state = if current == self.order - 1 {
State::Done
} else {
State::Running(current + 1)
}
}
State::Done => {
ui.label(format!(
"Порождающие элементы поля F_{}: {:?}",
self.order, self.primitive_roots
));
}
State::Idle => {}
State::Error => {
ui.label("Можно указать только простое число!");
}
}
});
egui::Window::new("Задача №2").show(ctx, |ui| {
ui.horizontal(|ui| {
ui.label("Число: ");
ui.add(egui::TextEdit::singleline(&mut self.str_num));
});
if ui.button("Разложить на множители").clicked() {
let number = Integer::parse(&self.str_num).unwrap().complete();
let factors = factorize(&number);
println!("Множители: {:?}", factors);
}
});
}
}
fn factorize(n: &Integer) -> Vec<Integer> {
let mut factors = Vec::new();
let mut front = vec![n.clone()];
while !front.is_empty() {
let num = front.pop().unwrap();
match lehman(&num) {
Some(factor) => {
let other = num.div_exact_ref(&factor).complete();
front.push(factor);
front.push(other);
},
None => factors.push(num)
};
}
return factors;
}
fn lehman(n: &Integer) -> Option<Integer> {
let one = &Integer::from(1u32);
let mut a = Integer::from(2u32);
let root3 = n.root_ref(3).complete();
while a <= root3 {
let (_, r) = n.div_rem_ref(&a).complete();
if r == 0 {
return Some(a);
}
a += one;
}
let root6 = n.root_ref(6).complete();
let mut k = Integer::from(1u32);
while k <= root3 {
let mut d = Integer::ZERO;
let sqrtk4 = k.sqrt_ref().complete() * 4;
let (r6sk4, _) = root6.div_rem_ref(&sqrtk4).complete();
while d <= (&r6sk4 + one).complete() {
let kn4: Integer = k.clone() * n.clone() * 4;
let sqrt_kn4 = kn4.sqrt_ref().complete();
let number = (sqrt_kn4.clone() + d.clone()).square() - kn4.clone();
if number.is_perfect_square() {
let big_a = sqrt_kn4 + d.clone();
let big_b = (big_a.square_ref() - kn4).sqrt();
let gcd1 = (big_a.clone() + big_b.clone()).gcd_ref(n).complete();
let gcd2 = (big_a.clone() - big_b.clone()).gcd_ref(n).complete();
if &gcd1 > one && &gcd1 < n {
return Some(gcd1);
}
else if &gcd2 > one && &gcd2 < n {
return Some(gcd2);
}
}
d += one;
}
k += one;
}
return None;
}
|
