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#![allow(dead_code)]
use core::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};
use rand::Rng;
use crate::{
fields::{FieldElement, Fq, Fq2},
u256::U256,
One, Zero,
};
#[derive(Copy, Clone, Debug, PartialEq, Eq)]
#[repr(C)]
pub struct Fq4 {
pub(crate) c0: Fq2,
pub(crate) c1: Fq2,
}
impl Fq4 {
pub fn new(c0: Fq2, c1: Fq2) -> Self {
Fq4 { c0, c1 }
}
//Algorithm 7
pub fn scale(&self, by: &Fq2) -> Self {
Fq4 {
c0: self.c0 * by,
c1: self.c1 * by,
}
}
pub fn scale_fq(&self, by: &Fq) -> Self {
Fq4 {
c0: self.c0.scale(by),
c1: self.c1.scale(by),
}
}
#[inline]
pub fn mul_by_nonresidue(&self) -> Self {
//c0 = c1 * u
//c1 = c0
Fq4 {
c0: self.c1.mul_by_nonresidue(),
c1: self.c0,
}
}
#[inline]
pub fn frobenius_map(&self, power: usize) -> Self {
match power {
10 => Fq4 {
c0: self.c0.unitary_inverse(),
c1: self
.c1
.unitary_inverse()
.scale(&Fq::new(*SM9_ALPHA3).unwrap()),
},
11 => Fq4 {
c0: self
.c0
.unitary_inverse()
.scale(&Fq::new(*SM9_ALPHA1).unwrap()),
c1: self
.c1
.unitary_inverse()
.scale(&Fq::new(*SM9_ALPHA4).unwrap()),
},
12 => Fq4 {
c0: self
.c0
.unitary_inverse()
.scale(&Fq::new(*SM9_ALPHA2).unwrap()),
c1: self
.c1
.unitary_inverse()
.scale(&Fq::new(*SM9_ALPHA5).unwrap()),
},
21 => self
.unitary_inverse()
.scale_fq(&Fq::new(*SM9_ALPHA2).unwrap()),
22 => self
.unitary_inverse()
.scale_fq(&Fq::new(*SM9_ALPHA4).unwrap()),
30 => Fq4 {
c0: self.c0.unitary_inverse(),
c1: self
.c1
.unitary_inverse()
.mul(Fq2::new(Fq::new(*SM9_BETA).unwrap(), Fq::zero()))
.neg(),
},
31 => Fq4 {
c0: self
.c0
.unitary_inverse()
.mul(Fq2::new(Fq::new(*SM9_BETA).unwrap(), Fq::zero())),
c1: self.c1.unitary_inverse(),
},
32 => Fq4 {
c0: self.c0.unitary_inverse().neg(),
c1: self
.c1
.unitary_inverse()
.mul(Fq2::new(Fq::new(*SM9_BETA).unwrap(), Fq::zero())),
},
_ => unimplemented!(),
}
}
#[inline]
pub fn unitary_inverse(&self) -> Fq4 {
Fq4 {
c0: self.c0,
c1: -self.c1,
}
}
/// Converts an element into a byte representation in
/// big-endian byte order.
pub fn to_slice(self) -> [u8; 128] {
let mut res = [0u8; 128];
let b1 = self.c1.to_slice();
let b0 = self.c0.to_slice();
res[..64].copy_from_slice(&b1);
res[64..].copy_from_slice(&b0);
res
}
/// Returns `c = self * b` ,only use for b.c0 == 0
pub fn mul_1(&self, b: &Fq4) -> Fq4 {
let bb = self.c1.mul_inplace(&b.c1);
let ab = self.c0.mul_inplace(&b.c1);
Fq4 {
c0: bb.mul_by_nonresidue(),
c1: ab,
}
}
/// Returns `c = self * b`.
///
/// Implements the full-tower interleaving strategy from
/// [ePrint 2022-376](https://eprint.iacr.org/2022/367).
#[inline]
pub fn mul_inplace(&self, b: &Fq4) -> Fq4 {
//c0,0 =a0,0b0,0 - 2a0,1b0,1 - 2a1,0b1,1 - 2a1,1b1,0
//c0,1 =a0,0b0,1 + a0,1b0,0 + a1,0b1,0 - 2a1,1b1,1
//c1,0 =a0,0b1,0 − 2a0,1b1,1 + a1,0b0,0 − 2a1,1b0,1
//c1,1 =a0,0b1,1 + a0,1b1,0 + a1,0b0,1 + a1,1b0,0
//Each of these is a "sum of products", which we can compute efficiently.
let a = self;
let a01d = -a.c0.c1.double();
let a11d = -a.c1.c1.double();
Fq4 {
c0: Fq2 {
c0: Fq::sum_of_products(
&[a.c0.c0, a01d, -a.c1.c0.double(), a11d],
&[b.c0.c0, b.c0.c1, b.c1.c1, b.c1.c0],
),
c1: Fq::sum_of_products(
&[a.c0.c0, a.c0.c1, a.c1.c0, a11d],
&[b.c0.c1, b.c0.c0, b.c1.c0, b.c1.c1],
),
},
c1: Fq2 {
c0: Fq::sum_of_products(
&[a.c0.c0, a01d, a.c1.c0, a11d],
&[b.c1.c0, b.c1.c1, b.c0.c0, b.c0.c1],
),
c1: Fq::sum_of_products(
&[a.c0.c0, a.c0.c1, a.c1.c0, a.c1.c1],
&[b.c1.c1, b.c1.c0, b.c0.c1, b.c0.c0],
),
},
}
}
#[inline]
pub fn sub_inplace(&self, rhs: &Fq4) -> Fq4 {
Fq4 {
c0: self.c0.sub_inplace(&rhs.c0),
c1: self.c1.sub_inplace(&rhs.c1),
}
}
#[inline]
pub fn add_inplace(&self, rhs: &Fq4) -> Fq4 {
Fq4 {
c0: self.c0.add_inplace(&rhs.c0),
c1: self.c1.add_inplace(&rhs.c1),
}
}
#[inline]
pub fn neg_inplace(&self) -> Fq4 {
Fq4 {
c0: self.c0.neg_inplace(),
c1: self.c1.neg_inplace(),
}
}
}
impl_binops_additive!(Fq4, Fq4);
impl_binops_multiplicative!(Fq4, Fq4);
impl_binops_negative!(Fq4);
impl Zero for Fq4 {
fn zero() -> Self {
Fq4 {
c0: Fq2::zero(),
c1: Fq2::zero(),
}
}
fn is_zero(&self) -> bool {
self.c0.is_zero() && self.c1.is_zero()
}
}
impl One for Fq4 {
#[inline]
fn one() -> Self {
Fq4 {
c0: Fq2::one(),
c1: Fq2::zero(),
}
}
}
impl FieldElement for Fq4 {
fn random<R: Rng>(rng: &mut R) -> Self {
Fq4 {
c0: Fq2::random(rng),
c1: Fq2::random(rng),
}
}
/// double this element
#[inline(always)]
fn double(&self) -> Self {
Fq4 {
c0: self.c0.double(),
c1: self.c1.double(),
}
}
/// triple this element
#[inline(always)]
fn triple(&self) -> Self {
Fq4 {
c0: self.c0.triple(),
c1: self.c1.triple(),
}
}
/// Squares this element
fn squared(&self) -> Self {
// Devegili OhEig Scott Dahab
// Multiplication and Squaring on Pairing-Friendly Fields.pdf
// Section 3 (Complex squaring), which takes 2M + 3A + 2B
let a0 = self.c0;
let a1 = self.c1;
let v0 = a0 * a1;
Fq4 {
c0: (a0 + a1) * (a0 + a1.mul_by_nonresidue()) - v0 - v0.mul_by_nonresidue(),
c1: v0.double(),
}
}
/// Computes the multiplicative inverse of this field element
/// return None in the case that this element is zero
//"High-Speed Software Implementation of the Optimal Ate AbstractPairing over Barreto-Naehrig Curves"
// Algorithm 23
fn inverse(&self) -> Option<Self> {
(self.c0.squared() - self.c1.squared().mul_by_nonresidue())
.inverse()
.map(|t| Self::new(self.c0 * t, -(self.c1 * t)))
}
}
lazy_static::lazy_static! {
// beta = 0x6c648de5dc0a3f2c f55acc93ee0baf15 9f9d411806dc5177 f5b21fd3da24d011
// alpha1 = 0x3f23ea58e5720bdb 843c6cfa9c086749 47c5c86e0ddd04ed a91d8354377b698b
// alpha2 = 0xf300000002a3a6f2 780272354f8b78f4 d5fc11967be65334
// alpha3 = 0x6c648de5dc0a3f2c f55acc93ee0baf15 9f9d411806dc5177 f5b21fd3da24d011
// alpha4 = 0xf300000002a3a6f2 780272354f8b78f4 d5fc11967be65333
// alpha5 = 0x2d40a38cf6983351 711e5f99520347cc 57d778a9f8ff4c8a 4c949c7fa2a96686
static ref SM9_BETA: U256 = U256::from([
0xf5b21fd3da24d011,
0x9f9d411806dc5177,
0xf55acc93ee0baf15,
0x6c648de5dc0a3f2c
]);
static ref SM9_ALPHA1: U256 = U256::from([
0xa91d8354377b698b,
0x47c5c86e0ddd04ed,
0x843c6cfa9c086749,
0x3f23ea58e5720bdb
]);
static ref SM9_ALPHA2: U256 = U256::from([
0xd5fc11967be65334,
0x780272354f8b78f4,
0xf300000002a3a6f2,
0x0
]);
static ref SM9_ALPHA3: U256 = U256::from([
0xf5b21fd3da24d011,
0x9f9d411806dc5177,
0xf55acc93ee0baf15,
0x6c648de5dc0a3f2c
]);
static ref SM9_ALPHA4: U256 = U256::from([
0xd5fc11967be65333,
0x780272354f8b78f4,
0xf300000002a3a6f2,
0x0
]);
static ref SM9_ALPHA5: U256 = U256::from([
0x4c949c7fa2a96686,
0x57d778a9f8ff4c8a,
0x711e5f99520347cc,
0x2d40a38cf6983351
]);
}