Arithmetic in Fp
This commit is contained in:
Sean Bowe
parent
7f515bbe1c
commit
eaa0de2964
273
src/fp.rs
273
src/fp.rs
|
|
@ -1,12 +1,15 @@
|
|||
use rand::Rng;
|
||||
use num::{BigUint, Num};
|
||||
use std::ops::{Mul,Add,Sub,Neg};
|
||||
use std::cmp::{PartialEq, Eq};
|
||||
use std::convert::From;
|
||||
use std::fmt;
|
||||
use std::marker::PhantomData;
|
||||
|
||||
pub trait PrimeFieldParams {
|
||||
fn modulus() -> BigUint;
|
||||
fn bits() -> usize;
|
||||
fn name() -> &'static str;
|
||||
}
|
||||
|
||||
pub struct Fp<P: PrimeFieldParams> {
|
||||
|
|
@ -14,20 +17,112 @@ pub struct Fp<P: PrimeFieldParams> {
|
|||
_marker: PhantomData<P>
|
||||
}
|
||||
|
||||
impl<P: PrimeFieldParams> Fp<P> {
|
||||
pub fn zero() -> Self { unimplemented!() }
|
||||
pub fn one() -> Self { unimplemented!() }
|
||||
pub fn random<R: Rng>(rng: &mut R) -> Self { unimplemented!() }
|
||||
impl<P: PrimeFieldParams> fmt::Debug for Fp<P> {
|
||||
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
||||
write!(f, "{}({})", P::name(), self.value)
|
||||
}
|
||||
}
|
||||
|
||||
pub fn is_zero(&self) -> bool { unimplemented!() }
|
||||
pub fn inverse(&self) -> Self { unimplemented!() }
|
||||
pub fn squared(&self) -> Self { unimplemented!() }
|
||||
pub fn pow<P2: PrimeFieldParams>(&self, exp: &Fp<P2>) -> Self { unimplemented!() }
|
||||
pub fn test_bit(&self, bit: usize) -> bool { unimplemented!() }
|
||||
impl<P: PrimeFieldParams> Fp<P> {
|
||||
pub fn zero() -> Self {
|
||||
use num::Zero;
|
||||
|
||||
Fp {
|
||||
value: BigUint::zero(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
pub fn one() -> Self {
|
||||
use num::One;
|
||||
|
||||
Fp {
|
||||
value: BigUint::one(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
pub fn random<R: Rng>(rng: &mut R) -> Self {
|
||||
use num::num_bigint::RandBigInt;
|
||||
use num::Zero;
|
||||
|
||||
Fp {
|
||||
value: rng.gen_biguint_range(&BigUint::zero(), &P::modulus()),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
pub fn is_zero(&self) -> bool {
|
||||
use num::Zero;
|
||||
|
||||
self.value == BigUint::zero()
|
||||
}
|
||||
|
||||
pub fn inverse(&self) -> Self {
|
||||
if self.is_zero() {
|
||||
// TODO: this should likely bleed through the abstraction layers
|
||||
panic!("cannot get the multiplicative inverse of zero")
|
||||
} else {
|
||||
let mut res = Self::one();
|
||||
|
||||
let mut found_one = false;
|
||||
|
||||
let exp = Self::zero() - Self::one() - Self::one();
|
||||
|
||||
for i in (0..P::bits()).rev() {
|
||||
if found_one {
|
||||
res = res.squared();
|
||||
}
|
||||
|
||||
if exp.test_bit(i) {
|
||||
found_one = true;
|
||||
res = self * &res;
|
||||
}
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
pub fn squared(&self) -> Self {
|
||||
self * self
|
||||
}
|
||||
pub fn pow<P2: PrimeFieldParams>(&self, exp: &Fp<P2>) -> Self {
|
||||
let mut res = Self::one();
|
||||
|
||||
let mut found_one = false;
|
||||
|
||||
for i in (0..P2::bits()).rev() {
|
||||
if found_one {
|
||||
res = res.squared();
|
||||
}
|
||||
|
||||
if exp.test_bit(i) {
|
||||
found_one = true;
|
||||
res = res * self;
|
||||
}
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
pub fn test_bit(&self, bit: usize) -> bool {
|
||||
// TODO: This is a naive approach.
|
||||
use num::{One, Zero};
|
||||
|
||||
let mut b = BigUint::one();
|
||||
let two = &b + &b;
|
||||
for _ in 0..bit {
|
||||
b = &b + &b;
|
||||
}
|
||||
|
||||
(&self.value / b) % two != BigUint::zero()
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, P: PrimeFieldParams> From<&'a str> for Fp<P> {
|
||||
fn from(s: &'a str) -> Self { unimplemented!() }
|
||||
fn from(s: &'a str) -> Self {
|
||||
Fp {
|
||||
value: BigUint::from_str_radix(s, 10).unwrap() % P::modulus(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: PrimeFieldParams> Clone for Fp<P> {
|
||||
|
|
@ -37,25 +132,66 @@ impl<P: PrimeFieldParams> Clone for Fp<P> {
|
|||
impl<'a, 'b, P: PrimeFieldParams> Add<&'b Fp<P>> for &'a Fp<P> {
|
||||
type Output = Fp<P>;
|
||||
|
||||
fn add(self, other: &Fp<P>) -> Fp<P> { unimplemented!() }
|
||||
fn add(self, other: &Fp<P>) -> Fp<P> {
|
||||
let tmp = &self.value + &other.value;
|
||||
if tmp >= P::modulus() {
|
||||
Fp {
|
||||
value: tmp - P::modulus(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
} else {
|
||||
Fp {
|
||||
value: tmp,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, 'b, P: PrimeFieldParams> Sub<&'b Fp<P>> for &'a Fp<P> {
|
||||
type Output = Fp<P>;
|
||||
|
||||
fn sub(self, other: &Fp<P>) -> Fp<P> { unimplemented!() }
|
||||
fn sub(self, other: &Fp<P>) -> Fp<P> {
|
||||
if other.value > self.value {
|
||||
Fp {
|
||||
value: (&self.value + P::modulus()) - &other.value,
|
||||
_marker: PhantomData
|
||||
}
|
||||
} else {
|
||||
Fp {
|
||||
value: &self.value - &other.value,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, 'b, P: PrimeFieldParams> Mul<&'b Fp<P>> for &'a Fp<P> {
|
||||
type Output = Fp<P>;
|
||||
|
||||
fn mul(self, other: &Fp<P>) -> Fp<P> { unimplemented!() }
|
||||
fn mul(self, other: &Fp<P>) -> Fp<P> {
|
||||
Fp {
|
||||
value: (&self.value * &other.value) % &P::modulus(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, P: PrimeFieldParams> Neg for &'a Fp<P> {
|
||||
type Output = Fp<P>;
|
||||
|
||||
fn neg(self) -> Fp<P> { unimplemented!() }
|
||||
fn neg(self) -> Fp<P> {
|
||||
use num::Zero;
|
||||
|
||||
Fp {
|
||||
value: if self.value.is_zero() {
|
||||
self.value.clone()
|
||||
} else {
|
||||
P::modulus() - &self.value
|
||||
},
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: PrimeFieldParams> Neg for Fp<P> {
|
||||
|
|
@ -66,4 +202,113 @@ impl<P: PrimeFieldParams> Neg for Fp<P> {
|
|||
}
|
||||
}
|
||||
|
||||
impl<P: PrimeFieldParams> PartialEq for Fp<P> {
|
||||
fn eq(&self, other: &Self) -> bool {
|
||||
self.value == other.value
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: PrimeFieldParams> Eq for Fp<P> {}
|
||||
|
||||
forward_all_binop_to_ref_ref!(impl(P: PrimeFieldParams) Mul for Fp<P>, mul);
|
||||
|
||||
#[cfg(test)]
|
||||
mod large_field_tests {
|
||||
use super::*;
|
||||
use num::{BigUint, Num};
|
||||
|
||||
struct Small;
|
||||
|
||||
impl PrimeFieldParams for Small {
|
||||
fn modulus() -> BigUint {
|
||||
BigUint::from_str_radix("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10).unwrap()
|
||||
}
|
||||
|
||||
fn bits() -> usize { 254 }
|
||||
fn name() -> &'static str { "Small" }
|
||||
}
|
||||
|
||||
type Ft = Fp<Small>;
|
||||
|
||||
#[test]
|
||||
fn bit_testing() {
|
||||
let a = Ft::from("13");
|
||||
assert!(a.test_bit(0) == true);
|
||||
assert!(a.test_bit(1) == false);
|
||||
assert!(a.test_bit(2) == true);
|
||||
assert!(a.test_bit(3) == true);
|
||||
|
||||
let expected: Vec<bool> = [1,1,0,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0,1,1]
|
||||
.iter().map(|a| *a == 1).rev().collect();
|
||||
|
||||
let a = Ft::from("453624211");
|
||||
|
||||
for (i, b) in expected.into_iter().enumerate() {
|
||||
assert!(a.test_bit(i) == b);
|
||||
}
|
||||
|
||||
let expected: Vec<bool> = [1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,1,1,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,1,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,1,0,1,1,0,0]
|
||||
.iter().map(|a| *a == 1).rev().collect();
|
||||
let a = Ft::from("13888242871869275222244405745257275088696211157297823662689037894645226208556");
|
||||
|
||||
for (i, b) in expected.into_iter().enumerate() {
|
||||
assert!(a.test_bit(i) == b);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod small_field_tests {
|
||||
use super::*;
|
||||
use num::{BigUint, Num};
|
||||
|
||||
struct Small;
|
||||
|
||||
impl PrimeFieldParams for Small {
|
||||
fn modulus() -> BigUint {
|
||||
BigUint::from_str_radix("13", 10).unwrap()
|
||||
}
|
||||
|
||||
fn bits() -> usize { 6 }
|
||||
fn name() -> &'static str { "Small" }
|
||||
}
|
||||
|
||||
type Ft = Fp<Small>;
|
||||
|
||||
#[test]
|
||||
fn field_ops() {
|
||||
fn test_field_operation<C: Fn(&Ft, &Ft) -> Ft>(a: u64, b: u64, f: C, expected: u64) {
|
||||
let af = Ft::from(format!("{}", a).as_ref());
|
||||
let bf = Ft::from(format!("{}", b).as_ref());
|
||||
let expectedf = Ft::from(format!("{}", expected).as_ref());
|
||||
|
||||
let res = f(&af, &bf);
|
||||
|
||||
if res != expectedf {
|
||||
panic!("res={:?} != expectedf={:?} (a={}, b={}, expected={})", res, expectedf, a, b, expected);
|
||||
}
|
||||
}
|
||||
|
||||
const MODULO: u64 = 13;
|
||||
|
||||
for a in 0..13u64 {
|
||||
for b in 0..13u64 {
|
||||
test_field_operation(a, b, |a,b| {a * b}, (a*b)%MODULO);
|
||||
test_field_operation(a, b, |a,b| {a + b}, (a+b)%MODULO);
|
||||
test_field_operation(a, b, |a,b| {a - b}, {
|
||||
let mut tmp = (a as i64) - (b as i64);
|
||||
if tmp < 0 {
|
||||
tmp += MODULO as i64;
|
||||
}
|
||||
|
||||
tmp as u64
|
||||
});
|
||||
test_field_operation(a, b, |a,b| {a.pow(b)}, (a.pow(b as u32))%MODULO);
|
||||
}
|
||||
test_field_operation(a, 0, |a,_| {-a}, if a == 0 { 0 } else { MODULO - a });
|
||||
if a > 0 {
|
||||
test_field_operation(a, 0, |a,_| {&a.inverse() * a}, 1);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
|
|||
|
|
@ -8,6 +8,7 @@ impl PrimeFieldParams for FrParams {
|
|||
BigUint::from_str_radix("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10).unwrap()
|
||||
}
|
||||
fn bits() -> usize { 254 }
|
||||
fn name() -> &'static str { "Fr" }
|
||||
}
|
||||
|
||||
pub struct FqParams;
|
||||
|
|
@ -17,4 +18,5 @@ impl PrimeFieldParams for FqParams {
|
|||
BigUint::from_str_radix("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10).unwrap()
|
||||
}
|
||||
fn bits() -> usize { 254 }
|
||||
fn name() -> &'static str { "Fq" }
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue