kauma/src/utils/poly.rs
2024-11-25 14:19:41 +01:00

1329 lines
40 KiB
Rust

use crate::utils::field::ByteArray;
use base64::prelude::*;
use std::{str::FromStr, u128, u8, usize};
use std::{
cmp::Ordering,
ops::{Add, Div, Mul},
};
use anyhow::{anyhow, Ok, Result};
use serde_json::Value;
use super::field::FieldElement;
#[derive(Debug, serde::Serialize, serde::Deserialize)]
pub struct Polynomial {
polynomial: Vec<FieldElement>,
}
impl Polynomial {
pub const fn new(polynomial: Vec<FieldElement>) -> Self {
Self { polynomial }
}
pub fn degree(&self) -> usize {
self.polynomial.len()
}
pub fn from_c_array(array: &Value) -> Self {
let mut polynomial: Vec<FieldElement> = vec![];
let c_array: Vec<String> = array
.as_array()
.expect("Input is not an array")
.iter()
.map(|x| {
x.as_str()
.expect("Array element is not a string")
.to_string()
})
.collect();
eprintln!("{:?}", c_array);
for coefficient in c_array {
polynomial.push(FieldElement::new(
BASE64_STANDARD
.decode(coefficient)
.expect("Error on poly decode:"),
));
}
Self { polynomial }
}
pub fn to_c_array(self) -> Vec<String> {
let mut output: Vec<String> = vec![];
for coeff in self.polynomial {
output.push(BASE64_STANDARD.encode(coeff));
}
output
}
pub fn pow(mut self, mut exponent: u128) -> Polynomial {
let mut result: Polynomial = Polynomial::new(vec![FieldElement::new(
polynomial_2_block(vec![0], "gcm").unwrap(),
)]);
if exponent == 1 {
eprintln!("special case 1: {:02X?}", self.clone());
return self;
}
if exponent == 0 {
let result = Polynomial::new(vec![FieldElement::new(
polynomial_2_block(vec![0], "gcm").unwrap(),
)]);
eprintln!("Returned value is: {:02X?}", result);
return result;
}
//eprintln!("Initial result: {:?}", result);
while exponent > 0 {
//eprintln!("Current exponent: {:02X}", exponent);
if exponent & 1 == 1 {
let temp = &self * &result;
//eprintln!("Mult");
//eprintln!("After mod: {:?}", temp);
result = temp
}
let temp_square = &self * &self;
//eprintln!("Square");
//eprintln!("After squaring: {:?}", temp_square);
self = temp_square;
//eprintln!("After mod: {:?}", self);
exponent >>= 1;
}
//eprintln!("result in powmod before reduction: {:02X?}", result);
while !result.polynomial.is_empty()
&& result
.polynomial
.last()
.unwrap()
.as_ref()
.iter()
.all(|&x| x == 0)
{
result.polynomial.pop();
}
//eprintln!("result in powmod after reduction: {:02X?}", result);
if result.is_empty() {
result = Polynomial::new(vec![FieldElement::new(vec![0; 16])]);
}
result
}
pub fn pow_mod(mut self, mut exponent: u128, modulus: Polynomial) -> Polynomial {
let mut result: Polynomial = Polynomial::new(vec![FieldElement::new(
polynomial_2_block(vec![0], "gcm").unwrap(),
)]);
if exponent == 1 {
eprintln!("special case 1: {:02X?}", self.clone().div(&modulus).1);
return self.div(&modulus).1;
}
if exponent == 0 {
let result = Polynomial::new(vec![FieldElement::new(
polynomial_2_block(vec![0], "gcm").unwrap(),
)]);
eprintln!("Returned value is: {:02X?}", result);
return result;
}
//eprintln!("Initial result: {:?}", result);
while exponent > 0 {
//eprintln!("Current exponent: {:02X}", exponent);
if exponent & 1 == 1 {
let temp = &self * &result;
//eprintln!("After multiplication: {:?}", temp);
result = temp.div(&modulus).1;
//eprintln!("After mod: {:?}", result);
}
let temp_square = &self * &self;
//eprintln!("After squaring: {:?}", temp_square);
self = temp_square.div(&modulus).1;
//eprintln!("After mod: {:?}", self);
exponent >>= 1;
}
eprintln!("result in powmod before reduction: {:02X?}", result);
while !result.polynomial.is_empty()
&& result
.polynomial
.last()
.unwrap()
.as_ref()
.iter()
.all(|&x| x == 0)
{
result.polynomial.pop();
}
eprintln!("result in powmod after reduction: {:02X?}", result);
if result.is_empty() {
result = Polynomial::new(vec![FieldElement::new(vec![0; 16])]);
}
result
}
// Returns (quotient, remainder)
pub fn div(&self, rhs: &Self) -> (Self, Self) {
// Div by zero check ommitted since data is guaranteed to be non 0
eprintln!("{:?}, {:?}", self.polynomial.len(), rhs.polynomial.len());
if self.polynomial.len() < rhs.polynomial.len() {
return (
Polynomial::new(vec![FieldElement::new(vec![0; 16])]),
self.clone(),
);
}
let mut remainder = self.clone();
let divisor = rhs;
let dividend_deg = remainder.polynomial.len() - 1;
let divisor_deg = divisor.polynomial.len() - 1;
if dividend_deg < divisor_deg {
return (
Polynomial::new(vec![FieldElement::new(
polynomial_2_block(vec![0; 16], "gcm").unwrap(),
)]),
remainder,
);
}
let mut quotient_coeffs =
vec![
FieldElement::new(polynomial_2_block(vec![0; 16], "gcm").unwrap());
dividend_deg - divisor_deg + 1
];
while remainder.polynomial.len() >= divisor.polynomial.len() {
let deg_diff = remainder.polynomial.len() - divisor.polynomial.len();
let leading_dividend = remainder.polynomial.last().unwrap();
let leading_divisor = divisor.polynomial.last().unwrap();
let quot_coeff = leading_dividend / leading_divisor;
quotient_coeffs[deg_diff] = quot_coeff.clone();
let mut subtrahend =
vec![FieldElement::new(polynomial_2_block(vec![0; 16], "gcm").unwrap()); deg_diff];
subtrahend.extend(
divisor
.polynomial
.iter()
.map(|x| x.clone() * quot_coeff.clone()),
);
let subtrahend_poly = Polynomial::new(subtrahend);
remainder = remainder + subtrahend_poly;
while !remainder.polynomial.is_empty()
&& remainder
.polynomial
.last()
.unwrap()
.as_ref()
.iter()
.all(|&x| x == 0)
{
remainder.polynomial.pop();
}
}
if remainder.is_empty() {
remainder = Polynomial::new(vec![FieldElement::new(vec![0; 16])]);
}
(Polynomial::new(quotient_coeffs), remainder)
}
fn is_zero(&self) -> bool {
for field_element in &self.polynomial {
if !field_element.is_zero() {
return false;
}
}
true
}
pub fn monic(mut self) -> Self {
let divident = self.polynomial.last().unwrap().clone();
for fieldelement in &mut self.polynomial.iter_mut() {
*fieldelement = fieldelement.clone() / divident.clone();
}
while !self.polynomial.is_empty()
&& self
.polynomial
.last()
.unwrap()
.as_ref()
.iter()
.all(|&x| x == 0)
{
self.polynomial.pop();
}
if self.is_empty() {
self = Polynomial::new(vec![FieldElement::new(vec![0; 16])]);
}
self
}
pub fn sqrt(self) -> Self {
let mut result = vec![];
for (position, element) in self.polynomial.iter().enumerate() {
if position % 2 == 0 {
result.push(element.clone().pow(2u128.pow(127)));
}
}
Polynomial::new(result)
}
pub fn diff(mut self) -> Self {
// Pop first element
// Check if the polynomial is 1 or less. In this case, output would be [] without check
// Output should be [0; 16] however
if self.polynomial.len() > 1 {
self.polynomial.remove(0);
} else {
return Polynomial::new(vec![FieldElement::new(vec![0; 16])]);
}
for (position, element) in self.polynomial.iter_mut().enumerate() {
// Set all uneven degrees to 0, as they were the even degrees before
// As we are in GF128, this means they become 0 after mul with even number
if position % 2 == 1 {
*element = FieldElement::new(vec![0; 16]);
}
}
while !self.polynomial.is_empty()
&& self
.polynomial
.last()
.unwrap()
.as_ref()
.iter()
.all(|&x| x == 0)
{
self.polynomial.pop();
}
if self.is_empty() {
self = Polynomial::new(vec![FieldElement::new(vec![0; 16])]);
}
self
}
}
impl Clone for Polynomial {
fn clone(&self) -> Self {
Polynomial {
polynomial: self.polynomial.clone(),
}
}
}
impl Mul for Polynomial {
type Output = Self;
fn mul(self, rhs: Self) -> Self::Output {
if self.is_zero() || rhs.is_zero() {
return Polynomial::new(vec![FieldElement::new(vec![0; 16])]);
}
let mut polynomial: Vec<FieldElement> =
vec![FieldElement::new(vec![0; 16]); self.polynomial.len() + rhs.polynomial.len() - 1];
for i in 0..self.polynomial.len() {
for j in 0..rhs.polynomial.len() {
polynomial[i + j] = &polynomial[i + j]
+ &(self.polynomial.get(i).unwrap() * rhs.polynomial.get(j).unwrap());
}
}
Polynomial::new(polynomial)
}
}
impl Mul for &Polynomial {
type Output = Polynomial;
fn mul(self, rhs: Self) -> Self::Output {
if self.is_zero() || rhs.is_zero() {
return Polynomial::new(vec![FieldElement::new(vec![0])]);
}
let mut polynomial: Vec<FieldElement> =
vec![FieldElement::new(vec![0; 16]); self.polynomial.len() + rhs.polynomial.len() - 1];
for i in 0..self.polynomial.len() {
for j in 0..rhs.polynomial.len() {
polynomial[i + j] = &polynomial[i + j]
+ &(self.polynomial.get(i).unwrap() * rhs.polynomial.get(j).unwrap());
}
}
Polynomial::new(polynomial)
}
}
impl Add for Polynomial {
type Output = Self;
fn add(self, rhs: Self) -> Self::Output {
let mut polynomial: Vec<FieldElement>;
if self.polynomial.len() > rhs.polynomial.len() {
polynomial = self.polynomial.clone();
for i in 0..rhs.polynomial.len() {
polynomial[i] = polynomial[i].clone() + rhs.polynomial[i].clone();
}
} else {
polynomial = rhs.polynomial.clone();
for i in 0..self.polynomial.len() {
polynomial[i] = polynomial[i].clone() + self.polynomial[i].clone();
}
}
while !polynomial.is_empty() && polynomial.last().unwrap().as_ref().iter().all(|&x| x == 0)
{
polynomial.pop();
}
if polynomial.is_empty() {
return Polynomial::new(vec![FieldElement::new(vec![0; 16])]);
}
Polynomial::new(polynomial)
}
}
trait IsEmpty {
fn is_empty(&self) -> bool;
}
impl IsEmpty for Polynomial {
fn is_empty(&self) -> bool {
self.polynomial.is_empty()
}
}
impl AsRef<[FieldElement]> for Polynomial {
fn as_ref(&self) -> &[FieldElement] {
&self.polynomial
}
}
impl PartialEq for Polynomial {
fn eq(&self, other: &Self) -> bool {
if self.polynomial.len() != other.polynomial.len() {
return false;
}
// Compare each coefficient
self.polynomial
.iter()
.zip(other.polynomial.iter())
.all(|(a, b)| a == b)
}
}
impl PartialOrd for Polynomial {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
match other.polynomial.len().cmp(&self.polynomial.len()) {
Ordering::Equal => {
for (field_a, field_b) in
self.as_ref().iter().rev().zip(other.as_ref().iter().rev())
{
eprintln!(
"Poly partord: {:02X?} {:02X?} ",
self.clone().to_c_array(),
other.clone().to_c_array()
);
match field_a
.reverse_bits()
.partial_cmp(&field_b.reverse_bits())
.unwrap()
{
Ordering::Equal => continue,
other => return Some(other),
}
}
Some(Ordering::Equal)
}
other => Some(other.reverse()),
}
}
}
impl Eq for Polynomial {}
impl Ord for Polynomial {
fn cmp(&self, other: &Self) -> Ordering {
match other.polynomial.len().cmp(&self.polynomial.len()) {
Ordering::Equal => {
for (field_a, field_b) in
self.as_ref().iter().rev().zip(other.as_ref().iter().rev())
{
match field_a.reverse_bits().cmp(&field_b.reverse_bits()) {
Ordering::Equal => continue,
other => return other,
}
}
Ordering::Equal
}
other => other.reverse(),
}
}
}
pub fn gcd(a: &Polynomial, b: &Polynomial) -> Polynomial {
if a.is_zero() {
return b.clone();
}
let monic_b = b.div(&a).1.monic();
return gcd(&monic_b, a);
}
pub fn sort_polynomial_array(mut polys: Vec<Polynomial>) -> Result<Vec<Polynomial>> {
// Algorithm to sort polynomials
// First sorting round
// Sorting by degree of polynomial
polys.sort();
Ok(polys)
}
pub const RED_POLY: u128 = 0x87000000_00000000_00000000_00000000;
pub fn gfmul(poly_a: &Vec<u8>, poly_b: &Vec<u8>, semantic: &str) -> Result<Vec<u8>> {
let mut red_poly_bytes: ByteArray = ByteArray(RED_POLY.to_be_bytes().to_vec());
red_poly_bytes.0.push(0x01);
let mut poly1: ByteArray = ByteArray(poly_a.to_owned());
poly1.0.push(0x00);
let mut poly2: ByteArray = ByteArray(poly_b.to_owned());
poly2.0.push(0x00);
if semantic == "gcm" {
poly1.reverse_bits_in_bytevec();
poly2.reverse_bits_in_bytevec();
}
let mut result: ByteArray = ByteArray(vec![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]);
if poly2.LSB_is_one() {
result.xor_byte_arrays(&poly1);
}
poly2.right_shift("xex")?;
while !poly2.is_empty() {
poly1.left_shift("xex")?;
if poly1.msb_is_one() {
poly1.xor_byte_arrays(&red_poly_bytes);
}
if poly2.LSB_is_one() {
result.xor_byte_arrays(&poly1);
}
poly2.right_shift("xex")?;
}
result.0.remove(16);
if semantic == "gcm" {
result.reverse_bits_in_bytevec();
}
Ok(result.0)
}
pub fn convert_gcm_to_xex(gcm_poly: Vec<u8>) -> Result<Vec<u8>> {
let xex_poly = gcm_poly
.into_iter()
.map(|block| block.reverse_bits())
.collect();
Ok(xex_poly)
}
pub fn get_alpha_rep(num: u128) -> String {
let powers: Vec<u8> = get_coefficients(num);
//println!("{:?}", powers);
let mut alpha_rep = String::new();
if powers.len() == 1 {
return String::from_str("1").unwrap();
}
for power in powers {
alpha_rep.push_str(&format!("a^{power}"));
}
alpha_rep
}
pub fn b64_2_num(string: &String) -> Result<u128> {
let decoded: Vec<u8> = BASE64_STANDARD.decode(string)?;
let mut bytes: [u8; 16] = [0u8; 16];
bytes.copy_from_slice(&decoded);
let number: u128 = <u128>::from_ne_bytes(bytes);
Ok(number)
}
pub fn get_coefficients(num: u128) -> Vec<u8> {
let mut powers: Vec<u8> = vec![];
for shift in 0..128 {
//println!("{:?}", ((num >> shift) & 1));
if ((num >> shift) & 1) == 1 {
powers.push(shift);
}
}
powers
}
pub fn get_bit_indices_from_byte(byte: u8) -> Vec<u8> {
let mut coefficients: Vec<u8> = vec![];
for shift in 0..8 {
if ((byte >> shift) & 1) == 1 {
coefficients.push(shift);
}
}
coefficients
}
pub fn block_2_polynomial(block: Vec<u8>, semantic: &str) -> Result<Vec<u8>> {
let mut output: Vec<u8> = vec![];
match semantic {
"xex" => {
for i in 0u8..=15 {
for j in 0u8..=7 {
if (block[i as usize] >> j) & 1 == 1 {
output.push(8 * i + j);
}
}
}
output.sort();
Ok(output)
}
"gcm" => {
for i in 0u8..=15 {
for j in 0u8..=7 {
if (block[i as usize] >> j) & 1 == 1 {
output.push(8 * i + 7 - j);
}
}
}
output.sort();
Ok(output)
}
_ => Err(anyhow!("Error in b2p")),
}
}
pub fn polynomial_2_block(coefficients: Vec<u8>, semantic: &str) -> Result<Vec<u8>> {
let mut output: Vec<u8> = Vec::with_capacity(16);
output.resize(16, 0);
match semantic {
"xex" => {
for coefficient in coefficients {
let byte_position = coefficient / 8;
let bit_position = coefficient % 8;
output[byte_position as usize] ^= 1 << bit_position;
}
Ok(output)
}
"gcm" => {
for coefficient in coefficients {
let byte_position = coefficient / 8;
let bit_position = coefficient % 8;
output[byte_position as usize] ^= 1 << 7 - bit_position;
}
Ok(output)
}
_ => Err(anyhow!("Error in b2p")),
}
}
pub fn coefficients_to_byte_arr_xex(coeffs: Vec<u8>) -> Vec<u8> {
let mut byte_array: Vec<u8> = vec![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
for coeff in coeffs {
let block_num = coeff / 8;
byte_array[usize::from(block_num)] |= 1 << (coeff % 7);
}
byte_array
}
pub fn coefficient_to_binary(coefficients: Vec<u8>) -> u128 {
let mut binary_number: u128 = 0;
for coeff in coefficients {
binary_number = binary_number | (1 << coeff);
}
binary_number
}
#[cfg(test)]
mod tests {
use crate::utils::poly::b64_2_num;
use anyhow::Result;
use serde_json::json;
// Note this useful idiom: importing names from outer (for mod tests) scope.
use super::*;
#[test]
fn byte_indices_0x01() {
let byte: u8 = 0x01;
let bit_indices: Vec<u8> = vec![0];
assert_eq!(get_bit_indices_from_byte(byte), bit_indices)
}
#[test]
fn byte_indices_0x23() {
let byte: u8 = 0x23;
let bit_indices: Vec<u8> = vec![0, 1, 5];
assert_eq!(get_bit_indices_from_byte(byte), bit_indices)
}
#[test]
fn byte_indices_0x56() {
let byte: u8 = 0x56;
let bit_indices: Vec<u8> = vec![1, 2, 4, 6];
assert_eq!(get_bit_indices_from_byte(byte), bit_indices)
}
#[test]
fn coeff_to_binary() {
let coefficients: Vec<u8> = vec![12, 127, 9, 0];
let b64: &str = "ARIAAAAAAAAAAAAAAAAAgA==";
let calculated_num: u128 = coefficient_to_binary(coefficients);
assert_eq!(
BASE64_STANDARD.encode(calculated_num.to_ne_bytes()),
"ARIAAAAAAAAAAAAAAAAAgA=="
);
}
#[test]
fn test_b64_2_num() -> Result<()> {
let b64_payload: String = String::from_str("juMqbhnlBwAAAAAAAAAAAA==")?;
assert_eq!(
b64_2_num(&b64_payload)?,
2222222222222222,
"Error: Value was: {}",
b64_2_num(&b64_payload)?
);
Ok(())
}
#[test]
fn test_field_add_03() {
let json1 = json!([
"NeverGonnaGiveYouUpAAA==",
"NeverGonnaLetYouDownAA==",
"NeverGonnaRunAroundAAA==",
"AndDesertYouAAAAAAAAAA=="
]);
let json2 = json!(["KryptoanalyseAAAAAAAAA==", "DHBWMannheimAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
let sum = element2 + element1;
assert_eq!(
sum.to_c_array(),
vec![
"H1d3GuyA9/0OxeYouUpAAA==",
"OZuIncPAGEp4tYouDownAA==",
"NeverGonnaRunAroundAAA==",
"AndDesertYouAAAAAAAAAA=="
]
);
}
#[test]
fn test_field_add_multiple_zeros() {
let json1 = json!([
"AAAAAAAAAAAAAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA=="
]);
let json2 = json!(["AAAAAAAAAAAAAAAAAAAAAA==", "AAAAAAAAAAAAAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
let sum = element2 + element1;
assert_eq!(sum.to_c_array(), vec!["AAAAAAAAAAAAAAAAAAAAAA==",]);
}
#[test]
fn test_field_add_same_element() {
let json1 = json!(["NeverGonnaGiveYouUpAAA=="]);
let json2 = json!(["NeverGonnaGiveYouUpAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
let sum = element2 + element1;
assert_eq!(sum.to_c_array(), vec!["AAAAAAAAAAAAAAAAAAAAAA==",]);
}
#[test]
fn test_field_add_zero() {
let json1 = json!([
"NeverGonnaGiveYouUpAAA==",
"NeverGonnaLetYouDownAA==",
"NeverGonnaRunAroundAAA==",
"AndDesertYouAAAAAAAAAA=="
]);
let json2 = json!(["AAAAAAAAAAAAAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
let sum = element2 + element1;
assert_eq!(
sum.to_c_array(),
vec![
"NeverGonnaGiveYouUpAAA==",
"NeverGonnaLetYouDownAA==",
"NeverGonnaRunAroundAAA==",
"AndDesertYouAAAAAAAAAA=="
]
);
}
#[test]
fn test_field_add_zero_to_zero() {
let json1 = json!(["AAAAAAAAAAAAAAAAAAAAAA=="]);
let json2 = json!(["AAAAAAAAAAAAAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
let sum = element2 + element1;
assert_eq!(sum.to_c_array(), vec!["AAAAAAAAAAAAAAAAAAAAAA=="]);
}
#[test]
fn test_field_add_short_to_long() {
let json1 = json!(["AAAAAAAAAAAAAAAAAAAAAA=="]);
let json2 = json!([
"NeverGonnaGiveYouUpAAA==",
"NeverGonnaLetYouDownAA==",
"NeverGonnaRunAroundAAA==",
"AndDesertYouAAAAAAAAAA=="
]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
let sum = element2 + element1;
assert_eq!(
sum.to_c_array(),
vec![
"NeverGonnaGiveYouUpAAA==",
"NeverGonnaLetYouDownAA==",
"NeverGonnaRunAroundAAA==",
"AndDesertYouAAAAAAAAAA=="
]
);
}
#[test]
fn test_field_mul_01() {
let json1 = json!([
"JAAAAAAAAAAAAAAAAAAAAA==",
"wAAAAAAAAAAAAAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let json2 = json!(["0AAAAAAAAAAAAAAAAAAAAA==", "IQAAAAAAAAAAAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
//eprintln!("{:?}", element1);
let result = element1 * element2;
assert_eq!(
result.to_c_array(),
vec![
"MoAAAAAAAAAAAAAAAAAAAA==",
"sUgAAAAAAAAAAAAAAAAAAA==",
"MbQAAAAAAAAAAAAAAAAAAA==",
"AAhAAAAAAAAAAAAAAAAAAA=="
]
);
//assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_poly_mul_with_zero() {
let json1 = json!([
"JAAAAAAAAAAAAAAAAAAAAA==",
"wAAAAAAAAAAAAAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let json2 = json!(["AAAAAAAAAAAAAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
//eprintln!("{:?}", element1);
let result = element1 * element2;
assert_eq!(result.to_c_array(), vec!["AAAAAAAAAAAAAAAAAAAAAA=="]);
//assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_poly_pow_01() {
let json1 = json!([
"JAAAAAAAAAAAAAAAAAAAAA==",
"wAAAAAAAAAAAAAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let result = element1.pow(3);
assert_eq!(
result.to_c_array(),
vec![
"AkkAAAAAAAAAAAAAAAAAAA==",
"DDAAAAAAAAAAAAAAAAAAAA==",
"LQIIAAAAAAAAAAAAAAAAAA==",
"8AAAAAAAAAAAAAAAAAAAAA==",
"ACgCQAAAAAAAAAAAAAAAAA==",
"AAAMAAAAAAAAAAAAAAAAAA==",
"AAAAAgAAAAAAAAAAAAAAAA=="
]
);
//assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_poly_pow_with_zero() {
let json1 = json!([
"JAAAAAAAAAAAAAAAAAAAAA==",
"wAAAAAAAAAAAAAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let result = element1.pow(0);
assert_eq!(result.to_c_array(), vec!["gAAAAAAAAAAAAAAAAAAAAA=="]);
//assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_field_pow_mod_01() {
let json1 = json!([
"JAAAAAAAAAAAAAAAAAAAAA==",
"wAAAAAAAAAAAAAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let result = element1.pow(3);
assert_eq!(
result.to_c_array(),
vec![
"AkkAAAAAAAAAAAAAAAAAAA==",
"DDAAAAAAAAAAAAAAAAAAAA==",
"LQIIAAAAAAAAAAAAAAAAAA==",
"8AAAAAAAAAAAAAAAAAAAAA==",
"ACgCQAAAAAAAAAAAAAAAAA==",
"AAAMAAAAAAAAAAAAAAAAAA==",
"AAAAAgAAAAAAAAAAAAAAAA=="
]
);
//assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_field_pow_mod_with_zero() {
let json1 = json!([
"JAAAAAAAAAAAAAAAAAAAAA==",
"wAAAAAAAAAAAAAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let result = element1.pow(0);
assert_eq!(result.to_c_array(), vec!["gAAAAAAAAAAAAAAAAAAAAA=="]);
//assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_poly_div_01() {
let element1 =
FieldElement::new(BASE64_STANDARD.decode("JAAAAAAAAAAAAAAAAAAAAA==").unwrap());
let element2 =
FieldElement::new(BASE64_STANDARD.decode("wAAAAAAAAAAAAAAAAAAAAA==").unwrap());
let result = element1 / element2;
assert_eq!(BASE64_STANDARD.encode(result), "OAAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_field_poly_div_01() {
let json1 = json!([
"JAAAAAAAAAAAAAAAAAAAAA==",
"wAAAAAAAAAAAAAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let json2 = json!(["0AAAAAAAAAAAAAAAAAAAAA==", "IQAAAAAAAAAAAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
//eprintln!("{:?}", element1);
println!("Beginning the new division");
let (result, remainder) = element1.div(&element2);
assert_eq!(
result.to_c_array(),
vec!["nAIAgCAIAgCAIAgCAIAgCg==", "m85znOc5znOc5znOc5znOQ=="]
);
assert_eq!(remainder.to_c_array(), vec!["lQNA0DQNA0DQNA0DQNA0Dg=="]);
//assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_field_poly_div_larger_div() {
let json1 = json!([
"JAAAAAAAAAAAAAAAAAAAAA==",
"wAAAAAAAAAAAAAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let json2 = json!(["0AAAAAAAAAAAAAAAAAAAAA==", "IQAAAAAAAAAAAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
//eprintln!("{:?}", element1);
println!("Beginning the new division");
let (result, remainder) = element2.div(&element1);
assert_eq!(result.to_c_array(), vec!["AAAAAAAAAAAAAAAAAAAAAA=="]);
assert_eq!(
remainder.to_c_array(),
vec!["0AAAAAAAAAAAAAAAAAAAAA==", "IQAAAAAAAAAAAAAAAAAAAA=="]
);
//assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_field_poly_div_eqdeg() {
let json1 = json!(["JAAAAAAAAAAAAAAAAAAAAA==", "wAAAAAAAAAAAAAAAAAAAAA==",]);
let json2 = json!(["0AAAAAAAAAAAAAAAAAAAAA==", "IQAAAAAAAAAAAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
let (result, remainder) = element2.div(&element1);
eprintln!("{:02X?}", (&result, &remainder));
assert!(!result.is_zero());
assert!(!remainder.is_zero());
//assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_field_poly_div_eqdeg_02() {
let json1 = json!(["JAAAAAAAAAAAAAAAAAAAAA==", "wAAAAAAAAAAAAAAAAAAAAA==",]);
let json2 = json!(["KryptoanalyseAAAAAAAAA==", "DHBWMannheimAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let element2: Polynomial = Polynomial::from_c_array(&json2);
let (result, remainder) = element2.div(&element1);
eprintln!("{:02X?}", (&result, &remainder));
assert!(!result.is_zero());
assert!(!remainder.is_zero());
//assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
}
#[test]
fn test_field_poly_powmod_01() {
let json1 = json!([
"JAAAAAAAAAAAAAAAAAAAAA==",
"wAAAAAAAAAAAAAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let json2 = json!(["KryptoanalyseAAAAAAAAA==", "DHBWMannheimAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let modulus: Polynomial = Polynomial::from_c_array(&json2);
let result = element1.pow_mod(1000, modulus);
eprintln!("Result is: {:02X?}", result);
assert_eq!(result.to_c_array(), vec!["oNXl5P8xq2WpUTP92u25zg=="]);
}
#[test]
fn test_field_poly_powmod_k1() {
let json1 = json!(["JAAAAAAAAAAAAAAAAAAAAA==",]);
let json2 = json!(["KryptoanalyseAAAAAAAAA==", "DHBWMannheimAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let modulus: Polynomial = Polynomial::from_c_array(&json2);
let result = element1.pow_mod(1, modulus);
eprintln!("Result is: {:02X?}", result);
assert_eq!(result.to_c_array(), vec!["JAAAAAAAAAAAAAAAAAAAAA=="]);
}
#[test]
fn test_field_poly_powmod_k0_special() {
let json1 = json!(["NeverGonnaGiveYouUpAAA=="]);
let json2 = json!(["NeverGonnaGiveYouUpAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let modulus: Polynomial = Polynomial::from_c_array(&json2);
let result = element1.pow_mod(0, modulus);
eprintln!("Result is: {:02X?}", result);
assert_eq!(result.to_c_array(), vec!["gAAAAAAAAAAAAAAAAAAAAA=="]);
}
#[test]
fn test_field_poly_powmod_k0() {
let json1 = json!(["JAAAAAAAAAAAAAAAAAAAAA==",]);
let json2 = json!(["KryptoanalyseAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let modulus: Polynomial = Polynomial::from_c_array(&json2);
let result = element1.pow_mod(0, modulus);
eprintln!("Result is: {:02X?}", result);
assert_eq!(result.to_c_array(), vec!["gAAAAAAAAAAAAAAAAAAAAA=="]);
}
#[test]
fn test_field_pow_mod_10mill() {
let json1 = json!([
"JAAAAAAAAAAAAAAAAAAAAA==",
"wAAAAAAAAAAAAAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let json2 = json!(["KryptoanalyseAAAAAAAAA==", "DHBWMannheimAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let modulus: Polynomial = Polynomial::from_c_array(&json2);
let result = element1.pow_mod(10000000, modulus);
assert!(!result.is_zero())
}
#[test]
fn test_poly_monic() {
let json1 = json!([
"NeverGonnaGiveYouUpAAA==",
"NeverGonnaLetYouDownAA==",
"NeverGonnaRunAroundAAA==",
"AndDesertYouAAAAAAAAAA=="
]);
let expected = json!([
"edY47onJ4MtCENDTHG/sZw==",
"oaXjCKnceBIxSavZ9eFT8w==",
"1Ial5rAJGOucIdUe3zh5bw==",
"gAAAAAAAAAAAAAAAAAAAAA=="
]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let result = element1.monic();
assert_eq!(json!(result.to_c_array()), expected);
}
#[test]
fn test_poly_monic_poly_zero() {
let json1 = json!(["AAAAAAAAAAAAAAAAAAAAAA=="]);
let expected = json!(["AAAAAAAAAAAAAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let result = element1.monic();
assert_eq!(json!(result.to_c_array()), expected);
}
#[test]
fn test_poly_monic_poly_multiple_zero() {
let json1 = json!([
"AAAAAAAAAAAAAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA=="
]);
let expected = json!(["AAAAAAAAAAAAAAAAAAAAAA=="]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let result = element1.monic();
assert_eq!(json!(result.to_c_array()), expected);
}
#[test]
fn test_poly_poly_sqrt() {
let json1 = json!([
"5TxUxLHO1lHE/rSFquKIAg==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"0DEUJYdHlmd4X7nzzIdcCA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"PKUa1+JHTxHE8y3LbuKIIA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"Ds96KiAKKoigKoiKiiKAiA=="
]);
let expected = json!([
"NeverGonnaGiveYouUpAAA==",
"NeverGonnaLetYouDownAA==",
"NeverGonnaRunAroundAAA==",
"AndDesertYouAAAAAAAAAA=="
]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
eprintln!("Starting poly sqrt");
let result = element1.sqrt();
assert_eq!(json!(result.to_c_array()), expected);
}
#[test]
fn test_poly_diff() {
let json1 = json!([
"IJustWannaTellYouAAAAA==",
"HowImFeelingAAAAAAAAAA==",
"GottaMakeYouAAAAAAAAAA==",
"UnderstaaaaaaaaaaaaanQ=="
]);
let expected = json!([
"HowImFeelingAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"UnderstaaaaaaaaaaaaanQ=="
]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
eprintln!("Starting poly sqrt");
let result = element1.diff();
assert_eq!(json!(result.to_c_array()), expected);
}
#[test]
fn test_poly_diff_len1() {
let json1 = json!(["IJustWannaTellYouAAAAA==",]);
let expected = json!(["AAAAAAAAAAAAAAAAAAAAAA==",]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
eprintln!("Starting poly sqrt");
let result = element1.diff();
assert_eq!(json!(result.to_c_array()), expected);
}
#[test]
fn test_poly_diff_multi_zero() {
let json1 = json!([
"AAAAAAAAAAAAAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
"AAAAAAAAAAAAAAAAAAAAAA==",
]);
let expected = json!(["AAAAAAAAAAAAAAAAAAAAAA==",]);
let element1: Polynomial = Polynomial::from_c_array(&json1);
let result = element1.diff();
assert_eq!(json!(result.to_c_array()), expected);
}
#[test]
fn test_poly_gcd() {
let a = json!([
"DNWpXnnY24XecPa7a8vrEA==",
"I8uYpCbsiPaVvUznuv1IcA==",
"wsbiU432ARWuO93He3vbvA==",
"zp0g3o8iNz7Y+8oUxw1vJw==",
"J0GekE3uendpN6WUAuJ4AA==",
"wACd0e6u1ii4AAAAAAAAAA==",
"ACAAAAAAAAAAAAAAAAAAAA=="
]);
let b = json!([
"I20VjJmlSnRSe88gaDiLRQ==",
"0Cw5HxJm/pfybJoQDf7/4w==",
"8ByrMMf+vVj5r3YXUNCJ1g==",
"rEU/f2UZRXqmZ6V7EPKfBA==",
"LfdALhvCrdhhGZWl9l9DSg==",
"KSUKhN0n6/DZmHPozd1prw==",
"DQrRkuA9Zx279wAAAAAAAA==",
"AhCEAAAAAAAAAAAAAAAAAA=="
]);
let expected = json!([
"NeverGonnaMakeYouCryAA==",
"NeverGonnaSayGoodbyeAA==",
"NeverGonnaTellALieAAAA==",
"AndHurtYouAAAAAAAAAAAA==",
"gAAAAAAAAAAAAAAAAAAAAA=="
]);
let a: Polynomial = Polynomial::from_c_array(&a);
let b: Polynomial = Polynomial::from_c_array(&b);
let result = gcd(&a.monic(), &b.monic());
assert_eq!(json!(result.to_c_array()), expected);
}
#[test]
fn test_poly_gcd_zero() {
let a = json!(["AAAAAAAAAAAAAAAAAAAAAA==",]);
let b = json!(["AAAAAAAAAAAAAAAAAAAAAA=="]);
let expected = json!(["AAAAAAAAAAAAAAAAAAAAAA=="]);
let a: Polynomial = Polynomial::from_c_array(&a);
let b: Polynomial = Polynomial::from_c_array(&b);
let result = gcd(&a.monic(), &b.monic());
assert_eq!(json!(result.to_c_array()), expected);
}
}