1260 lines
37 KiB
Rust
1260 lines
37 KiB
Rust
use cryptonum::signed::SCN;
|
||
use num::{BigUint,ToPrimitive,Zero};
|
||
use std::fmt;
|
||
use std::fmt::Write;
|
||
use std::cmp::Ordering;
|
||
use std::ops::*;
|
||
|
||
/// In case you were wondering, it stands for "Unsigned Crypto Num".
|
||
#[derive(Clone,Debug,PartialEq,Eq)]
|
||
pub struct UCN {
|
||
pub(crate) contents: Vec<u64>
|
||
}
|
||
|
||
#[derive(Clone,Debug,PartialEq,Eq)]
|
||
pub struct BarrettUCN {
|
||
pub(crate) u: UCN,
|
||
pub(crate) k: usize,
|
||
pub(crate) m: UCN
|
||
}
|
||
|
||
impl UCN {
|
||
pub fn zero() -> UCN {
|
||
UCN{ contents: vec![] }
|
||
}
|
||
|
||
pub fn bits(&self) -> usize {
|
||
self.contents.len() * 64
|
||
}
|
||
|
||
pub fn is_zero(&self) -> bool {
|
||
self.contents.len() == 0
|
||
}
|
||
|
||
pub fn is_odd(&self) -> bool {
|
||
if self.contents.len() == 0 {
|
||
false
|
||
} else {
|
||
(self.contents[0] & 1) == 1
|
||
}
|
||
}
|
||
|
||
pub fn is_even(&self) -> bool {
|
||
if self.contents.len() == 0 {
|
||
false
|
||
} else {
|
||
(self.contents[0] & 1) == 0
|
||
}
|
||
}
|
||
|
||
fn clean(&mut self) {
|
||
loop {
|
||
match self.contents.pop() {
|
||
None =>
|
||
break,
|
||
Some(0) =>
|
||
continue,
|
||
Some(x) => {
|
||
self.contents.push(x);
|
||
break
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
fn expand(&mut self, rhs: &UCN) {
|
||
while self.contents.len() < rhs.contents.len() {
|
||
self.contents.push(0);
|
||
}
|
||
}
|
||
|
||
pub fn from_str(x: &str) -> UCN {
|
||
let mut outvec = Vec::new();
|
||
let mut worker = 0;
|
||
let mut shift = 0;
|
||
|
||
for c in x.chars().rev() {
|
||
match c.to_digit(16) {
|
||
None =>
|
||
panic!("Bad character in string: {}", c),
|
||
Some(v) => {
|
||
worker = worker + ((v as u64) << shift);
|
||
shift += 4;
|
||
}
|
||
}
|
||
if shift == 64 {
|
||
outvec.push(worker);
|
||
worker = 0;
|
||
shift = 0;
|
||
}
|
||
}
|
||
outvec.push(worker);
|
||
let mut res = UCN{ contents: outvec };
|
||
res.clean();
|
||
res
|
||
}
|
||
|
||
pub fn modinv(&self, phi: &UCN) -> UCN {
|
||
let x = SCN::from(self.clone());
|
||
let y = SCN::from(phi.clone());
|
||
let (d, a, _b) = x.egcd(y);
|
||
|
||
if d == SCN::from(1 as u8) {
|
||
if a.is_negative() {
|
||
(a + SCN::from(phi.clone())).value
|
||
} else {
|
||
a.value
|
||
}
|
||
} else {
|
||
UCN::zero()
|
||
}
|
||
}
|
||
|
||
pub fn barrett_u(&self) -> BarrettUCN {
|
||
let k = self.contents.len();
|
||
let b = UCN::from(1 as u8) << (64 * 2 * k);
|
||
let u = b / self;
|
||
BarrettUCN{ u: u, k: k, m: self.clone() }
|
||
}
|
||
|
||
pub fn reduce(&self, u: &BarrettUCN) -> UCN {
|
||
// 1. q1←⌊x/bk−1⌋, q2←q1 · μ, q3←⌊q2/bk+1⌋.
|
||
let q1 = self >> (64 * (u.k - 1));
|
||
let q2 = q1 * &u.u;
|
||
let q3 = q2 >> (64 * (u.k + 1));
|
||
// 2. r1←x mod bk+1, r2←q3 · m mod bk+1, r←r1 − r2.
|
||
// 3. If r<0 then r←r+bk+1.
|
||
let mut r1 = self.clone();
|
||
r1.contents.resize(u.k + 1, 0);
|
||
let mut r2 = q3 * &u.m;
|
||
r2.contents.resize(u.k + 1, 0);
|
||
let mut r = if r1 >= r2 {
|
||
r1 - r2
|
||
} else {
|
||
let mut bk1cont = Vec::with_capacity(u.k + 1);
|
||
bk1cont.resize(u.k, 0);
|
||
bk1cont.push(1);
|
||
(r1 + UCN{ contents: bk1cont }) - r2
|
||
};
|
||
// 4. Whiler≥mdo:r←r−m.
|
||
while &r >= &u.m {
|
||
r -= &u.m;
|
||
}
|
||
// 5. Return(r).
|
||
r
|
||
}
|
||
|
||
pub fn modexp(&self, e: &UCN, m: &UCN) -> UCN {
|
||
let mut b = self.clone() % m;
|
||
let mut eprime = e.clone();
|
||
let mut result = UCN::from(1 as u8);
|
||
|
||
loop {
|
||
if eprime.is_zero() {
|
||
return result;
|
||
}
|
||
|
||
if eprime.is_odd() {
|
||
result = (result * &b) % m;
|
||
}
|
||
|
||
b = (&b * &b) % m;
|
||
eprime >>= 1;
|
||
}
|
||
}
|
||
|
||
pub fn fastmodexp(&self, e: &UCN, mu: &BarrettUCN) -> UCN {
|
||
let mut b = self.reduce(&mu);
|
||
let mut result = UCN::from(1 as u8);
|
||
|
||
for digit in e.contents.iter() {
|
||
let mut work = *digit;
|
||
|
||
for _ in 0..64 {
|
||
if (work & 0x1) == 1 {
|
||
result = (result * &b).reduce(&mu);
|
||
}
|
||
|
||
b = (&b * &b).reduce(&mu);
|
||
|
||
work >>= 1;
|
||
}
|
||
}
|
||
|
||
result
|
||
}
|
||
|
||
pub fn to_bytes(&self, len: usize) -> Vec<u8> {
|
||
let mylen = self.contents.len() * 8;
|
||
let mut res = Vec::with_capacity(mylen);
|
||
|
||
// generate the basic data, which may be too large or too small
|
||
for val in self.contents.iter().rev() {
|
||
res.push( ((*val >> 56) & 0xFF) as u8 );
|
||
res.push( ((*val >> 48) & 0xFF) as u8 );
|
||
res.push( ((*val >> 40) & 0xFF) as u8 );
|
||
res.push( ((*val >> 32) & 0xFF) as u8 );
|
||
res.push( ((*val >> 24) & 0xFF) as u8 );
|
||
res.push( ((*val >> 16) & 0xFF) as u8 );
|
||
res.push( ((*val >> 8) & 0xFF) as u8 );
|
||
res.push( ((*val >> 0) & 0xFF) as u8 );
|
||
}
|
||
|
||
// if this is too big, then we need to pull a bit off the top
|
||
while res.len() > len {
|
||
res.remove(0);
|
||
}
|
||
|
||
// if this is too small, then we need to add some bytes to the start
|
||
while res.len() < len {
|
||
res.insert(0,0);
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
pub fn from_bytes(x: &[u8]) -> UCN {
|
||
let mut res = Vec::with_capacity( (x.len() + 7) / 8);
|
||
let mut item = 0;
|
||
let mut shift = 0;
|
||
|
||
for v in x.iter().rev() {
|
||
item |= (*v as u64) << shift;
|
||
shift += 8;
|
||
if shift == 64 {
|
||
shift = 0;
|
||
res.push(item);
|
||
item = 0;
|
||
}
|
||
}
|
||
if item != 0 {
|
||
res.push(item);
|
||
}
|
||
|
||
let mut res = UCN{ contents: res };
|
||
res.clean();
|
||
res
|
||
}
|
||
}
|
||
|
||
impl fmt::UpperHex for UCN {
|
||
fn fmt(&self, fmt: &mut fmt::Formatter) -> Result<(),fmt::Error> {
|
||
for x in self.contents.iter().rev() {
|
||
fmt.write_char(tochar_upper(x >> 60))?;
|
||
fmt.write_char(tochar_upper(x >> 56))?;
|
||
fmt.write_char(tochar_upper(x >> 52))?;
|
||
fmt.write_char(tochar_upper(x >> 48))?;
|
||
fmt.write_char(tochar_upper(x >> 44))?;
|
||
fmt.write_char(tochar_upper(x >> 40))?;
|
||
fmt.write_char(tochar_upper(x >> 36))?;
|
||
fmt.write_char(tochar_upper(x >> 32))?;
|
||
fmt.write_char(tochar_upper(x >> 28))?;
|
||
fmt.write_char(tochar_upper(x >> 24))?;
|
||
fmt.write_char(tochar_upper(x >> 20))?;
|
||
fmt.write_char(tochar_upper(x >> 16))?;
|
||
fmt.write_char(tochar_upper(x >> 12))?;
|
||
fmt.write_char(tochar_upper(x >> 8))?;
|
||
fmt.write_char(tochar_upper(x >> 4))?;
|
||
fmt.write_char(tochar_upper(x >> 0))?;
|
||
}
|
||
if self.contents.len() == 0 {
|
||
fmt.write_char('0')?;
|
||
}
|
||
Ok(())
|
||
}
|
||
}
|
||
|
||
fn tochar_upper(x: u64) -> char {
|
||
match (x as u8) & (0xF as u8) {
|
||
0x0 => '0',
|
||
0x1 => '1',
|
||
0x2 => '2',
|
||
0x3 => '3',
|
||
0x4 => '4',
|
||
0x5 => '5',
|
||
0x6 => '6',
|
||
0x7 => '7',
|
||
0x8 => '8',
|
||
0x9 => '9',
|
||
0xA => 'A',
|
||
0xB => 'B',
|
||
0xC => 'C',
|
||
0xD => 'D',
|
||
0xE => 'E',
|
||
0xF => 'F',
|
||
_ => panic!("the world is broken")
|
||
}
|
||
}
|
||
|
||
impl fmt::LowerHex for UCN {
|
||
fn fmt(&self, fmt: &mut fmt::Formatter) -> Result<(),fmt::Error> {
|
||
for x in self.contents.iter().rev() {
|
||
fmt.write_char(tochar_lower(x >> 60))?;
|
||
fmt.write_char(tochar_lower(x >> 56))?;
|
||
fmt.write_char(tochar_lower(x >> 52))?;
|
||
fmt.write_char(tochar_lower(x >> 48))?;
|
||
fmt.write_char(tochar_lower(x >> 44))?;
|
||
fmt.write_char(tochar_lower(x >> 40))?;
|
||
fmt.write_char(tochar_lower(x >> 36))?;
|
||
fmt.write_char(tochar_lower(x >> 32))?;
|
||
fmt.write_char(tochar_lower(x >> 28))?;
|
||
fmt.write_char(tochar_lower(x >> 24))?;
|
||
fmt.write_char(tochar_lower(x >> 20))?;
|
||
fmt.write_char(tochar_lower(x >> 16))?;
|
||
fmt.write_char(tochar_lower(x >> 12))?;
|
||
fmt.write_char(tochar_lower(x >> 8))?;
|
||
fmt.write_char(tochar_lower(x >> 4))?;
|
||
fmt.write_char(tochar_lower(x >> 0))?;
|
||
}
|
||
Ok(())
|
||
}
|
||
}
|
||
|
||
fn tochar_lower(x: u64) -> char {
|
||
match (x as u8) & (0xF as u8) {
|
||
0x0 => '0',
|
||
0x1 => '1',
|
||
0x2 => '2',
|
||
0x3 => '3',
|
||
0x4 => '4',
|
||
0x5 => '5',
|
||
0x6 => '6',
|
||
0x7 => '7',
|
||
0x8 => '8',
|
||
0x9 => '9',
|
||
0xA => 'a',
|
||
0xB => 'b',
|
||
0xC => 'c',
|
||
0xD => 'd',
|
||
0xE => 'e',
|
||
0xF => 'f',
|
||
_ => panic!("the world is broken")
|
||
}
|
||
}
|
||
|
||
//------------------------------------------------------------------------------
|
||
//
|
||
// Conversions to/from crypto nums.
|
||
//
|
||
//------------------------------------------------------------------------------
|
||
|
||
define_from!(UCN, u8);
|
||
define_from!(UCN, u16);
|
||
define_from!(UCN, u32);
|
||
define_from!(UCN, u64);
|
||
define_from!(UCN, usize);
|
||
define_into!(UCN, u8);
|
||
define_into!(UCN, u16);
|
||
define_into!(UCN, u32);
|
||
define_into!(UCN, u64);
|
||
define_into!(UCN, usize);
|
||
|
||
impl From<BigUint> for UCN {
|
||
fn from(x: BigUint) -> UCN {
|
||
UCN::from(&x)
|
||
}
|
||
}
|
||
|
||
impl<'a> From<&'a BigUint> for UCN {
|
||
fn from(inval: &BigUint) -> UCN {
|
||
let mut x = inval.clone();
|
||
let mut dest = Vec::new();
|
||
let mask = BigUint::from(0xFFFFFFFFFFFFFFFF as u64);
|
||
|
||
while !x.is_zero() {
|
||
match (&x & &mask).to_u64() {
|
||
None =>
|
||
panic!("Can't use BigUint in From<BigUint>"),
|
||
Some(val) =>
|
||
dest.push(val)
|
||
}
|
||
x >>= 64;
|
||
}
|
||
|
||
UCN{ contents: dest }
|
||
}
|
||
}
|
||
|
||
impl From<BigInt> for UCN {
|
||
fn from(x: BigInt) -> UCN {
|
||
UCN::from(&x)
|
||
}
|
||
}
|
||
|
||
impl<'a> From<&'a BigInt> for UCN {
|
||
fn from(x: &BigInt) -> UCN {
|
||
match x.to_biguint() {
|
||
None =>
|
||
panic!("Attempt to coerce negative BigInt into UCN"),
|
||
Some(x) =>
|
||
UCN::from(x)
|
||
}
|
||
}
|
||
}
|
||
|
||
impl From<UCN> for BigUint {
|
||
fn from(x: UCN) -> BigUint {
|
||
let mut result = BigUint::zero();
|
||
|
||
for part in x.contents.iter().rev() {
|
||
result <<= 64;
|
||
result += BigUint::from(*part);
|
||
}
|
||
|
||
result
|
||
}
|
||
}
|
||
|
||
impl From<UCN> for BigInt {
|
||
fn from(x: UCN) -> BigInt {
|
||
let uint = BigUint::from(x);
|
||
BigInt::from(uint)
|
||
}
|
||
}
|
||
|
||
//------------------------------------------------------------------------------
|
||
//
|
||
// Comparisons
|
||
//
|
||
//------------------------------------------------------------------------------
|
||
|
||
impl PartialOrd for UCN {
|
||
fn partial_cmp(&self, other: &UCN) -> Option<Ordering> {
|
||
Some(self.cmp(other))
|
||
}
|
||
}
|
||
|
||
impl Ord for UCN {
|
||
fn cmp(&self, other: &UCN) -> Ordering {
|
||
match self.contents.len().cmp(&other.contents.len()) {
|
||
Ordering::Equal => {
|
||
let mut me = self.contents.iter().rev();
|
||
let mut them = other.contents.iter().rev();
|
||
|
||
for (m, t) in me.zip(them) {
|
||
match m.cmp(t) {
|
||
Ordering::Equal =>
|
||
continue,
|
||
res =>
|
||
return res
|
||
}
|
||
}
|
||
|
||
Ordering::Equal
|
||
}
|
||
x => x
|
||
}
|
||
}
|
||
}
|
||
|
||
//------------------------------------------------------------------------------
|
||
//
|
||
// Bit Operations
|
||
//
|
||
//------------------------------------------------------------------------------
|
||
|
||
impl Not for UCN {
|
||
type Output = UCN;
|
||
|
||
fn not(self) -> UCN {
|
||
let mut contents = self.contents;
|
||
|
||
for x in contents.iter_mut() {
|
||
*x = !*x;
|
||
}
|
||
|
||
let mut res = UCN{ contents: contents };
|
||
res.clean();
|
||
res
|
||
}
|
||
}
|
||
|
||
impl<'a> Not for &'a UCN {
|
||
type Output = UCN;
|
||
|
||
fn not(self) -> UCN {
|
||
let res = self.clone();
|
||
res.not()
|
||
}
|
||
}
|
||
|
||
impl<'a> BitOrAssign<&'a UCN> for UCN {
|
||
fn bitor_assign(&mut self, rhs: &UCN) {
|
||
self.expand(&rhs);
|
||
{
|
||
let mut iter_me = self.contents.iter_mut();
|
||
let mut iter_tm = rhs.contents.iter();
|
||
|
||
loop {
|
||
match (iter_me.next(), iter_tm.next()) {
|
||
(Some(dest), Some(val)) =>
|
||
*dest |= val,
|
||
_ =>
|
||
break
|
||
}
|
||
}
|
||
}
|
||
self.clean();
|
||
}
|
||
}
|
||
|
||
impl<'a> BitXorAssign<&'a UCN> for UCN {
|
||
fn bitxor_assign(&mut self, rhs: &UCN) {
|
||
self.expand(&rhs);
|
||
{
|
||
let mut iter_me = self.contents.iter_mut();
|
||
let mut iter_tm = rhs.contents.iter();
|
||
|
||
loop {
|
||
match (iter_me.next(), iter_tm.next()) {
|
||
(Some(dest), Some(val)) =>
|
||
*dest ^= val,
|
||
_ =>
|
||
break
|
||
}
|
||
}
|
||
}
|
||
self.clean();
|
||
}
|
||
}
|
||
|
||
impl<'a> BitAndAssign<&'a UCN> for UCN {
|
||
fn bitand_assign(&mut self, rhs: &UCN) {
|
||
if self.contents.len() > rhs.contents.len() {
|
||
self.contents.resize(rhs.contents.len(), 0);
|
||
}
|
||
{
|
||
let mut iter_me = self.contents.iter_mut();
|
||
let mut iter_tm = rhs.contents.iter();
|
||
|
||
loop {
|
||
match (iter_me.next(), iter_tm.next()) {
|
||
(Some(dest), Some(val)) =>
|
||
*dest &= val,
|
||
_ =>
|
||
break
|
||
}
|
||
}
|
||
}
|
||
self.clean();
|
||
}
|
||
}
|
||
|
||
derive_arithmetic_operators!(UCN, BitOr, bitor, BitOrAssign, bitor_assign);
|
||
derive_arithmetic_operators!(UCN, BitXor, bitxor, BitXorAssign, bitxor_assign);
|
||
derive_arithmetic_operators!(UCN, BitAnd, bitand, BitAndAssign, bitand_assign);
|
||
|
||
//------------------------------------------------------------------------------
|
||
//
|
||
// Shifts
|
||
//
|
||
//------------------------------------------------------------------------------
|
||
|
||
impl ShlAssign<u64> for UCN {
|
||
fn shl_assign(&mut self, rhs: u64) {
|
||
let mut digits = rhs / 64;
|
||
let bits = rhs % 64;
|
||
let mut carry = 0;
|
||
|
||
// ripple the bit-level shift through
|
||
if bits != 0 {
|
||
for x in self.contents.iter_mut() {
|
||
let new_carry = *x >> (64 - bits);
|
||
*x = (*x << bits) | carry;
|
||
carry = new_carry;
|
||
}
|
||
}
|
||
|
||
// if we pulled some stuff off the end, add it back
|
||
if carry != 0 {
|
||
self.contents.push(carry);
|
||
}
|
||
|
||
// add the appropriate digits on the low side
|
||
while digits > 0 {
|
||
self.contents.insert(0,0);
|
||
digits -= 1;
|
||
}
|
||
}
|
||
}
|
||
|
||
impl Shl<u64> for UCN {
|
||
type Output = UCN;
|
||
|
||
fn shl(self, rhs: u64) -> UCN {
|
||
let mut copy = self.clone();
|
||
copy.shl_assign(rhs);
|
||
copy
|
||
}
|
||
}
|
||
|
||
derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, usize);
|
||
derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, u32);
|
||
derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, u16);
|
||
derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, u8);
|
||
|
||
impl ShrAssign<u64> for UCN {
|
||
fn shr_assign(&mut self, rhs: u64) {
|
||
let mut digits = rhs / 64;
|
||
let bits = rhs % 64;
|
||
|
||
// remove the appropriate digits on the low side
|
||
while (digits > 0) && (self.contents.len() > 0) {
|
||
self.contents.remove(0);
|
||
digits -= 1;
|
||
}
|
||
// ripple the shifts over
|
||
let mut carry = 0;
|
||
let mask = !(0xFFFFFFFFFFFFFFFF << bits);
|
||
|
||
for x in self.contents.iter_mut().rev() {
|
||
let base = *x >> bits;
|
||
let (new_carry, _) = (*x & mask).overflowing_shl((64-bits) as u32);
|
||
*x = base | carry;
|
||
carry = new_carry;
|
||
}
|
||
// in this case, we just junk the extra carry bits, but we do need to
|
||
// cleanup possible zeros at the end.
|
||
self.clean();
|
||
}
|
||
}
|
||
|
||
impl Shr<u64> for UCN {
|
||
type Output = UCN;
|
||
|
||
fn shr(self, rhs: u64) -> UCN {
|
||
let mut copy = self.clone();
|
||
copy.shr_assign(rhs);
|
||
copy
|
||
}
|
||
}
|
||
|
||
derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, usize);
|
||
derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, u32);
|
||
derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, u16);
|
||
derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, u8);
|
||
|
||
derive_signed_shift_operators!(UCN, usize, isize);
|
||
derive_signed_shift_operators!(UCN, u64, i64);
|
||
derive_signed_shift_operators!(UCN, u32, i32);
|
||
derive_signed_shift_operators!(UCN, u16, i16);
|
||
derive_signed_shift_operators!(UCN, u8, i8);
|
||
|
||
//------------------------------------------------------------------------------
|
||
//
|
||
// Addition, Subtraction and Multiplication
|
||
//
|
||
//------------------------------------------------------------------------------
|
||
|
||
impl<'a> AddAssign<&'a UCN> for UCN {
|
||
fn add_assign(&mut self, rhs: &UCN) {
|
||
let mut iter_tm = rhs.contents.iter();
|
||
let mut stolen = None;
|
||
let mut carry = 0;
|
||
|
||
// loop through every element on the left hand side, breaking early
|
||
// on if we right the end of the left hand side.
|
||
{
|
||
let mut iter_me = self.contents.iter_mut();
|
||
loop {
|
||
match(iter_me.next(), iter_tm.next()) {
|
||
(None, None) =>
|
||
break,
|
||
(Some(dest), None) => {
|
||
let dest128 = *dest as u128;
|
||
let newdest = dest128 + carry;
|
||
*dest = newdest as u64;
|
||
carry = newdest >> 64;
|
||
}
|
||
(None, Some(x)) => {
|
||
stolen = Some(*x);
|
||
break;
|
||
}
|
||
(Some(dest), Some(r)) => {
|
||
let newdest = (*dest as u128) + (*r as u128) + carry;
|
||
*dest = newdest as u64;
|
||
carry = newdest >> 64;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
// if we accidentally stole something form the right iterator,
|
||
// push it back on.
|
||
if let Some(x) = stolen {
|
||
let stolen128 = (x as u128) + carry;
|
||
self.contents.push(stolen128 as u64);
|
||
carry = stolen128 >> 64;
|
||
}
|
||
// now loop through any remaining items on the right hand side,
|
||
// pushing them onto the result.
|
||
for x in iter_tm {
|
||
let x128 = (*x as u128) + carry;
|
||
self.contents.push(x128 as u64);
|
||
carry = x128 >> 64;
|
||
}
|
||
// finally, if there's still a carry, push it on the end.
|
||
if carry > 0 {
|
||
self.contents.push(carry as u64);
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<'a> SubAssign<&'a UCN> for UCN {
|
||
fn sub_assign(&mut self, rhs: &UCN) {
|
||
{
|
||
let mut borrow = 0;
|
||
let mut iter_me = self.contents.iter_mut();
|
||
let mut iter_tm = rhs.contents.iter();
|
||
|
||
loop {
|
||
assert!( (borrow == 0) | (borrow == 1) );
|
||
match (iter_me.next(), iter_tm.next()) {
|
||
(None, None) if borrow == 0 =>
|
||
break,
|
||
(None, None) =>
|
||
panic!("Generated negative UCN in subtraction (1)."),
|
||
(Some(x), None) => {
|
||
if borrow == 0 {
|
||
break;
|
||
}
|
||
if *x == 0 {
|
||
*x = 0xFFFFFFFFFFFFFFFF;
|
||
borrow = 1;
|
||
} else {
|
||
*x = *x - borrow;
|
||
break;
|
||
}
|
||
}
|
||
(None, Some(_)) => {
|
||
panic!("Generated negative UCN in subtraction (2).");
|
||
}
|
||
(Some(x), Some(y)) => {
|
||
if (*x >= borrow) && ((*x - borrow) >= *y) {
|
||
*x = (*x - borrow) - *y;
|
||
borrow = 0;
|
||
} else {
|
||
let x128 = (*x as u128) + 0x10000000000000000;
|
||
let res = x128 - (*y as u128) - (borrow as u128);
|
||
*x = res as u64;
|
||
borrow = 1;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
self.clean();
|
||
}
|
||
}
|
||
|
||
impl<'a> MulAssign<&'a UCN> for UCN {
|
||
fn mul_assign(&mut self, rhs: &UCN) {
|
||
// Handle the quick and easy multiplication by zero cases first.
|
||
if self.contents.len() == 0 {
|
||
return;
|
||
}
|
||
if rhs.contents.len() == 0 {
|
||
self.contents.resize(0,0);
|
||
return;
|
||
}
|
||
|
||
// OK, do some real multiplication
|
||
let x = self.contents.clone();
|
||
let y = rhs.contents.clone();
|
||
let outlen = x.len() + y.len();
|
||
let n = y.len() - 1;
|
||
|
||
// this algorithm is 14.12 from "Handbook of Applied Cryptography"
|
||
self.contents.resize(0, 0);
|
||
self.contents.resize(outlen, 0);
|
||
for (i,xi) in x.iter().enumerate() {
|
||
let mut c = 0;
|
||
for (j,yj) in y.iter().enumerate() {
|
||
let wij = self.contents[i+j] as u128;
|
||
let xjyi = (*xi as u128) * (*yj as u128);
|
||
let uv = wij + xjyi + c;
|
||
self.contents[i+j] = uv as u64;
|
||
c = uv >> 64;
|
||
}
|
||
self.contents[i+n+1] = c as u64;
|
||
}
|
||
self.clean();
|
||
}
|
||
}
|
||
|
||
pub fn divmod(quotient: &mut Vec<u64>, remainder: &mut Vec<u64>,
|
||
inx: &Vec<u64>, iny: &Vec<u64>)
|
||
{
|
||
quotient.resize(0,0);
|
||
remainder.resize(0,0);
|
||
// This algorithm is 14.20 from "Handbook of Applied Cryptography"
|
||
//
|
||
// It requires that y[t] is not zero, which it isn't due to our invariant
|
||
// that we don't have unnecessary zeros at the end of the array. We note
|
||
// that it's also very convienent if the top bit of y[t] is set, as well,
|
||
// so we shift everything left so that things work out.
|
||
let mut xbuffer = Vec::with_capacity(inx.len() + 2);
|
||
let mut ybuffer = Vec::with_capacity(iny.len() + 2);
|
||
xbuffer.extend_from_slice(&inx);
|
||
ybuffer.extend_from_slice(&iny);
|
||
let mut x = UCN{ contents: xbuffer };
|
||
let mut y = UCN{ contents: ybuffer };
|
||
let additional_shift = iny[iny.len() - 1].leading_zeros() as usize;
|
||
x <<= additional_shift;
|
||
y <<= additional_shift;
|
||
// Once we've done this, we should be good to go with our mostly-correct
|
||
// x and y. The only trick is that the algorithm requires that n >= t. If
|
||
// this is not true, then the answer is zero, because the divisor is greater
|
||
// than the dividend.
|
||
let n = x.contents.len();
|
||
let t = y.contents.len();
|
||
if n < t {
|
||
remainder.extend_from_slice(&inx);
|
||
return;
|
||
}
|
||
// Also, it's real convient for n and t to be greater than one, which we
|
||
// achieve by pushing a zero into the low digit. Because we do this, we
|
||
// don't have to do a lot of testing against negative indices later.
|
||
x.contents.insert(0,0);
|
||
y.contents.insert(0,0);
|
||
// 1. For j from 0 to (n-t) do: qj <- 0.
|
||
let mut q = Vec::with_capacity(n - t + 1);
|
||
q.resize(n - t + 1, 0);
|
||
// 2. While (x >= yb^(n-t)) do the following:
|
||
// q_(n-t) <- q_(n-t) + 1
|
||
// x <- x - yb^(n-t)
|
||
let ybnt = &y << (64 * (n - t));
|
||
while &x >= &ybnt {
|
||
q[n-t] = q[n-t] + 1;
|
||
x -= &ybnt;
|
||
}
|
||
// 3. For i from n down to (t + 1) do the following:
|
||
let mut i = n;
|
||
while i >= (t + 1) {
|
||
// 3.1. if xi = yt, then set q_(i-t-1) <- b - 1; otherwise set
|
||
// q_(i-t-1) <- floor((x_i * b + x_(i-1)) /y_t).
|
||
if x.contents[i] == y.contents[t] {
|
||
q[i-t-1] = 0xFFFFFFFFFFFFFFFF;
|
||
} else {
|
||
let top = ((x.contents[i] as u128)<<64) + (x.contents[i-1] as u128);
|
||
let bot = y.contents[t] as u128;
|
||
let solution = top / bot;
|
||
q[i-t-1] = solution as u64;
|
||
}
|
||
// 3.2. While (q_(i-t-1)(y_t * b + y_(t-1)) > x_i(b2) + x_(i-1)b +
|
||
// x_(i-2)) do:
|
||
// q_(i - t - 1) <- q_(i - t 1) - 1.
|
||
loop {
|
||
let qit1 = UCN{ contents: vec![q[i - t - 1]] };
|
||
let ytbyt1 = UCN{ contents: vec![y.contents[t-1], y.contents[t]] };
|
||
let left = qit1 * ytbyt1;
|
||
let right = UCN{ contents: vec![x.contents[i-2],
|
||
x.contents[i-1],
|
||
x.contents[i]] };
|
||
|
||
if left <= right {
|
||
break
|
||
}
|
||
|
||
q[i - t - 1] -= 1;
|
||
}
|
||
// 3.3. x <- x - q_(i - t - 1) * y * b^(i-t-1)
|
||
let qit1 = UCN{ contents: vec![q[i - t - 1]] };
|
||
let ybit1 = &y << (64 * (i - t - 1));
|
||
let subbit = &qit1 * &ybit1;
|
||
if subbit <= x {
|
||
x -= subbit;
|
||
} else {
|
||
// 3.4. if x < 0 then set z <- x + yb^(i-t-1) and
|
||
// q_(i-t-1) <- q(i-t-1) - 1
|
||
x -= subbit - ybit1;
|
||
q[i - t - 1] -= 1;
|
||
}
|
||
i -= 1;
|
||
}
|
||
// 4. r <- x
|
||
x >>= additional_shift;
|
||
if x.contents.len() > 0 {
|
||
// remember, we added a zero to the front of
|
||
// everything earlier; this removes it.
|
||
x.contents.remove(0);
|
||
}
|
||
remainder.append(&mut x.contents);
|
||
// 5. return (q,r)
|
||
while (q.len() > 0) && (q[q.len() - 1] == 0) {
|
||
q.pop();
|
||
}
|
||
quotient.append(&mut q);
|
||
}
|
||
|
||
impl<'a> DivAssign<&'a UCN> for UCN {
|
||
fn div_assign(&mut self, rhs: &UCN) {
|
||
let copy = self.contents.clone();
|
||
let mut dead = Vec::new();
|
||
divmod(&mut self.contents, &mut dead, ©, &rhs.contents);
|
||
}
|
||
}
|
||
|
||
impl<'a> RemAssign<&'a UCN> for UCN {
|
||
fn rem_assign(&mut self, rhs: &UCN) {
|
||
let copy = self.contents.clone();
|
||
let mut dead = Vec::new();
|
||
divmod(&mut dead, &mut self.contents, ©, &rhs.contents);
|
||
}
|
||
}
|
||
|
||
derive_arithmetic_operators!(UCN, Add, add, AddAssign, add_assign);
|
||
derive_arithmetic_operators!(UCN, Sub, sub, SubAssign, sub_assign);
|
||
derive_arithmetic_operators!(UCN, Mul, mul, MulAssign, mul_assign);
|
||
derive_arithmetic_operators!(UCN, Div, div, DivAssign, div_assign);
|
||
derive_arithmetic_operators!(UCN, Rem, rem, RemAssign, rem_assign);
|
||
|
||
//------------------------------------------------------------------------------
|
||
//
|
||
// Tests!
|
||
//
|
||
//------------------------------------------------------------------------------
|
||
|
||
#[cfg(test)]
|
||
mod test {
|
||
use quickcheck::{Arbitrary,Gen};
|
||
use super::*;
|
||
|
||
#[test]
|
||
fn test_clean() {
|
||
let mut val1 = UCN{ contents: vec![1,0,0] };
|
||
val1.clean();
|
||
assert_eq!(val1, UCN{ contents: vec![1] });
|
||
//
|
||
let mut val2 = UCN{ contents: vec![0,0,0] };
|
||
val2.clean();
|
||
assert_eq!(val2, UCN{ contents: vec![] });
|
||
//
|
||
let mut val3 = UCN{ contents: vec![1,0,1] };
|
||
val3.clean();
|
||
assert_eq!(val3, UCN{ contents: vec![1,0,1] });
|
||
//
|
||
let mut val4 = UCN{ contents: vec![] };
|
||
val4.clean();
|
||
assert_eq!(val4, UCN{ contents: vec![] });
|
||
}
|
||
|
||
#[test]
|
||
#[allow(overflowing_literals)]
|
||
fn test_builders() {
|
||
assert_eq!(UCN{ contents: vec![] },
|
||
UCN::from(0 as u8));
|
||
assert_eq!(UCN{ contents: vec![0x7F] },
|
||
UCN::from(0x7F as u8));
|
||
assert_eq!(UCN{ contents: vec![0x7F7F] },
|
||
UCN::from(0x7F7F as u16));
|
||
assert_eq!(UCN{ contents: vec![0xCA5CADE5] },
|
||
UCN::from(0xCA5CADE5 as u32));
|
||
assert_eq!(UCN{ contents: vec![0xFFFFFFFFFFFFFFFF] },
|
||
UCN::from(0xFFFFFFFFFFFFFFFF as u64));
|
||
assert_eq!(UCN{ contents: vec![0x00000000FFFFFFFF] },
|
||
UCN::from(0xFFFFFFFFFFFFFFFF as u32));
|
||
}
|
||
|
||
quickcheck! {
|
||
fn builder_u8_upgrade_u16(x: u8) -> bool {
|
||
UCN::from(x) == UCN::from(x as u16)
|
||
}
|
||
fn builder_u16_upgrade_u32(x: u16) -> bool {
|
||
UCN::from(x) == UCN::from(x as u32)
|
||
}
|
||
fn builder_u32_upgrade_u64(x: u32) -> bool {
|
||
UCN::from(x) == UCN::from(x as u64)
|
||
}
|
||
fn builder_u8_roundtrips(x: u8) -> bool {
|
||
let thereback: u8 = UCN::from(x).into();
|
||
x == thereback
|
||
}
|
||
fn builder_u16_roundtrips(x: u16) -> bool {
|
||
let thereback: u16 = UCN::from(x).into();
|
||
x == thereback
|
||
}
|
||
fn builder_u32_roundtrips(x: u32) -> bool {
|
||
let thereback: u32 = UCN::from(x).into();
|
||
x == thereback
|
||
}
|
||
fn builder_u64_roundtrips(x: u64) -> bool {
|
||
let thereback: u64 = UCN::from(x).into();
|
||
x == thereback
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn u64_comparison_sane(x: u64, y: u64) -> bool {
|
||
let ucnx = UCN::from(x);
|
||
let ucny = UCN::from(y);
|
||
ucnx.cmp(&ucny) == x.cmp(&y)
|
||
}
|
||
fn longer_is_greater(x: u64, y: u64) -> bool {
|
||
if x == 0 {
|
||
true
|
||
} else {
|
||
let ucnx = UCN{ contents: vec![x, 1] };
|
||
let ucny = UCN::from(y);
|
||
ucnx.cmp(&ucny) == Ordering::Greater
|
||
}
|
||
}
|
||
fn self_is_equal(x: Vec<u64>) -> bool {
|
||
let val = UCN{ contents: x };
|
||
let copy = val.clone();
|
||
|
||
(&val == ©) && (val.cmp(©) == Ordering::Equal)
|
||
}
|
||
}
|
||
|
||
impl Arbitrary for UCN {
|
||
fn arbitrary<G: Gen>(g: &mut G) -> UCN {
|
||
let lenopts = [4,8]; //,16,32,48,64,112,128,240];
|
||
let mut len = *g.choose(&lenopts).unwrap();
|
||
let mut contents = Vec::with_capacity(len);
|
||
|
||
while len > 0 {
|
||
contents.push(g.gen());
|
||
len -= 1;
|
||
}
|
||
UCN{ contents: contents }
|
||
}
|
||
}
|
||
|
||
fn expand_to_match(a: &mut UCN, b: &UCN) {
|
||
assert!(a.contents.len() <= b.contents.len());
|
||
while a.contents.len() < b.contents.len() {
|
||
a.contents.push(0);
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn double_negation(x: UCN) -> bool {
|
||
let mut x2 = x.clone().not();
|
||
expand_to_match(&mut x2, &x);
|
||
let mut x3 = x2.not();
|
||
expand_to_match(&mut x3, &x);
|
||
x3 == x
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn or_associative(a: UCN, b: UCN, c: UCN) -> bool {
|
||
((&a | &b) | &c) == (&a | (&b | &c))
|
||
}
|
||
fn xor_associative(a: UCN, b: UCN, c: UCN) -> bool {
|
||
((&a ^ &b) ^ &c) == (&a ^ (&b ^ &c))
|
||
}
|
||
fn and_associative(a: UCN, b: UCN, c: UCN) -> bool {
|
||
((&a & &b) & &c) == (&a & (&b & &c))
|
||
}
|
||
fn add_associative(a: UCN, b: UCN, c: UCN) -> bool {
|
||
((&a + &b) + &c) == (&a + (&b + &c))
|
||
}
|
||
fn mul_associative(a: UCN, b: UCN, c: UCN) -> bool {
|
||
((&a * &b) * &c) == (&a * (&b * &c))
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn or_commutative(a: UCN, b: UCN) -> bool {
|
||
(&a | &b) == (&b | &a)
|
||
}
|
||
fn xor_commutative(a: UCN, b: UCN) -> bool {
|
||
(&a ^ &b) == (&b ^ &a)
|
||
}
|
||
fn and_commutative(a: UCN, b: UCN) -> bool {
|
||
(&a & &b) == (&b & &a)
|
||
}
|
||
fn add_commutative(a: UCN, b: UCN) -> bool {
|
||
let ab = &a + &b;
|
||
let ba = &b + &a;
|
||
(ab == ba)
|
||
}
|
||
fn mul_commutative(a: UCN, b: UCN) -> bool {
|
||
let ab = &a * &b;
|
||
let ba = &b * &a;
|
||
(ab == ba)
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn or_identity(a: UCN) -> bool {
|
||
(&a | &UCN{ contents: vec![] }) == a
|
||
}
|
||
fn xor_identity(a: UCN) -> bool {
|
||
(&a ^ &UCN{ contents: vec![] }) == a
|
||
}
|
||
fn and_identity(a: UCN) -> bool {
|
||
let mut contents = Vec::new();
|
||
contents.resize(a.contents.len(), 0xFFFFFFFFFFFFFFFF);
|
||
let effs = UCN{ contents: contents };
|
||
(&a & &effs) == a
|
||
}
|
||
fn shl_identity(a: UCN) -> bool {
|
||
(&a << 0) == a
|
||
}
|
||
fn shr_identity(a: UCN) -> bool {
|
||
(&a >> 0) == a
|
||
}
|
||
fn add_identity(a: UCN) -> bool {
|
||
(&a + &UCN{ contents: vec![] }) == a
|
||
}
|
||
fn sub_identity(a: UCN) -> bool {
|
||
(&a - &UCN{ contents: vec![] }) == a
|
||
}
|
||
fn mul_identity(a: UCN) -> bool {
|
||
let one = UCN{ contents: vec![1] };
|
||
(&a * &one) == a
|
||
}
|
||
fn div_identity(a: UCN) -> bool {
|
||
let one = UCN{ contents: vec![1] };
|
||
(&a / &one) == a
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn or_annihilator(a: UCN) -> bool {
|
||
let mut contents = Vec::new();
|
||
contents.resize(a.contents.len(), 0xFFFFFFFFFFFFFFFF);
|
||
let effs = UCN{ contents: contents };
|
||
(&a | &effs) == effs
|
||
}
|
||
fn and_annihilator(a: UCN) -> bool {
|
||
let zero = UCN{ contents: vec![] };
|
||
(&a & &zero) == zero
|
||
}
|
||
fn shl_shr_annihilate(a: UCN, b: u8) -> bool {
|
||
let left = &a << b;
|
||
let right = &left >> b;
|
||
right == a
|
||
}
|
||
fn sub_annihilation(a: UCN) -> bool {
|
||
(&a - &a) == UCN{ contents: vec![] }
|
||
}
|
||
fn mul_annihilation(a: UCN) -> bool {
|
||
let zero = UCN{ contents: vec![] };
|
||
(&a * &zero) == zero
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn xor_inverse(a: UCN, b: UCN) -> bool {
|
||
((&a ^ &b) ^ &b) == a
|
||
}
|
||
fn or_idempotent(a: UCN, b: UCN) -> bool {
|
||
(&a | &b) == ((&a | &b) | &b)
|
||
}
|
||
fn and_idempotent(a: UCN, b: UCN) -> bool {
|
||
(&a & &b) == ((&a & &b) & &b)
|
||
}
|
||
fn andor_absorbtion(a: UCN, b: UCN) -> bool {
|
||
(&a & (&a | &b)) == a
|
||
}
|
||
fn orand_absorbtion(a: UCN, b: UCN) -> bool {
|
||
(&a | (&a & &b)) == a
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn mod_plus1_identity(a: UCN) -> bool {
|
||
let one = UCN{ contents: vec![1] };
|
||
let ap1 = &a + &one;
|
||
(&a % ap1) == a
|
||
}
|
||
fn mod_min1_is_one(a: UCN) -> bool {
|
||
let one = UCN{ contents: vec![1] };
|
||
let am1 = &a - &one;
|
||
(&a % am1) == one
|
||
}
|
||
#[should_panic]
|
||
fn div0_fails(a: UCN) -> bool {
|
||
(&a / &UCN{ contents: vec![] }) == a
|
||
}
|
||
fn euclid_is_alive(a: UCN, b: UCN) -> bool {
|
||
let zero = UCN{ contents: vec![] };
|
||
if &b == &zero {
|
||
return true;
|
||
}
|
||
let q = &a / &b;
|
||
let r = &a % &b;
|
||
let res = (b * q) + r;
|
||
a == res
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn and_over_or_distribution(a: UCN, b: UCN, c: UCN) -> bool {
|
||
(&a & (&b | &c)) == ((&a & &b) | (&a & &c))
|
||
}
|
||
fn and_over_xor_distribution(a: UCN, b: UCN, c: UCN) -> bool {
|
||
(&a & (&b ^ &c)) == ((&a & &b) ^ (&a & &c))
|
||
}
|
||
fn or_over_and_distribution(a: UCN, b: UCN, c: UCN) -> bool {
|
||
(&a | (&b & &c)) == ((&a | &b) & (&a | &c))
|
||
}
|
||
fn demorgans(a: UCN, b: UCN) -> bool {
|
||
let mut a2 = if a.contents.len() < b.contents.len() {a.clone()}
|
||
else {b.clone()};
|
||
let b2 = if a.contents.len() < b.contents.len() {b.clone()}
|
||
else {a.clone()};
|
||
expand_to_match(&mut a2, &b2);
|
||
(!(&a2 | &b2)) == (!a2 & !b2)
|
||
}
|
||
fn shift_multiply_equiv(a: UCN, b: u8) -> bool {
|
||
let one = UCN{ contents: vec![1] };
|
||
let pow2 = one << b;
|
||
(&a << b) == (&a * pow2)
|
||
}
|
||
fn shl_mul_equiv(a: UCN) -> bool {
|
||
(&a << 1) == (&a * UCN::from(2 as u64)) &&
|
||
(&a << 3) == (&a * UCN::from(8 as u64)) &&
|
||
(&a << 4) == (&a * UCN::from(16 as u64)) &&
|
||
(&a << 43) == (&a * UCN::from(8796093022208 as u64))
|
||
}
|
||
fn shr_div_equiv(a: UCN) -> bool {
|
||
(&a >> 1) == (&a / UCN::from(2 as u64)) &&
|
||
(&a >> 3) == (&a / UCN::from(8 as u64)) &&
|
||
(&a >> 4) == (&a / UCN::from(16 as u64)) &&
|
||
(&a >> 43) == (&a / UCN::from(8796093022208 as u64))
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn barrett_check(a: UCN, b: UCN) -> bool {
|
||
let barrett = b.barrett_u();
|
||
(&a % &b) == a.reduce(&barrett)
|
||
}
|
||
fn fastmodexp(ina: UCN, b: UCN, c: UCN) -> bool {
|
||
let mut a = ina.clone();
|
||
|
||
if c.contents.len() == 0 {
|
||
return true;
|
||
}
|
||
|
||
if a.contents.len() > c.contents.len() {
|
||
a.contents.resize(c.contents.len(), 0);
|
||
}
|
||
|
||
let cu = c.barrett_u();
|
||
let slow = a.modexp(&b, &c);
|
||
let fast = a.fastmodexp(&b, &cu);
|
||
slow == fast
|
||
}
|
||
fn modinv(a: UCN, b: UCN) -> bool {
|
||
let i = a.modinv(&b);
|
||
i.is_zero() || ( ((a * i) % b) == UCN::from(1 as u64) )
|
||
}
|
||
}
|
||
|
||
quickcheck! {
|
||
fn serialization_works1(a: UCN) -> bool {
|
||
let bytelen = a.contents.len() * 8;
|
||
UCN::from_bytes(&a.to_bytes(bytelen)) == a
|
||
}
|
||
fn serialization_works2(inb: Vec<u8>) -> bool {
|
||
let b = inb.clone();
|
||
UCN::from_bytes(&b).to_bytes(b.len()) == b
|
||
}
|
||
}
|
||
}
|