use crate::fp::*;
use crate::fp2::*;
#[cfg(feature = "canon")]
use canonical_derive::Canon;
use core::fmt;
use core::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};
use parity_subtle as subtle;
use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
#[cfg(feature = "serde_req")]
use serde::{
self, de::Visitor, ser::SerializeStruct, Deserialize, Deserializer, Serialize, Serializer,
};
#[cfg_attr(feature = "canon", derive(Canon))]
pub struct Fp6 {
pub c0: Fp2,
pub c1: Fp2,
pub c2: Fp2,
}
impl From<Fp> for Fp6 {
fn from(f: Fp) -> Fp6 {
Fp6 {
c0: Fp2::from(f),
c1: Fp2::zero(),
c2: Fp2::zero(),
}
}
}
impl From<Fp2> for Fp6 {
fn from(f: Fp2) -> Fp6 {
Fp6 {
c0: f,
c1: Fp2::zero(),
c2: Fp2::zero(),
}
}
}
impl PartialEq for Fp6 {
fn eq(&self, other: &Fp6) -> bool {
self.ct_eq(other).into()
}
}
impl Copy for Fp6 {}
impl Clone for Fp6 {
#[inline]
fn clone(&self) -> Self {
*self
}
}
impl Default for Fp6 {
fn default() -> Self {
Fp6::zero()
}
}
impl fmt::Debug for Fp6 {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "{:?} + ({:?})*v + ({:?})*v^2", self.c0, self.c1, self.c2)
}
}
#[cfg(feature = "serde_req")]
impl Serialize for Fp6 {
fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
where
S: Serializer,
{
let mut fp2 = serializer.serialize_struct("struct Fp6", 3)?;
fp2.serialize_field("c0", &self.c0)?;
fp2.serialize_field("c1", &self.c1)?;
fp2.serialize_field("c2", &self.c2)?;
fp2.end()
}
}
#[cfg(feature = "serde_req")]
impl<'de> Deserialize<'de> for Fp6 {
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
where
D: Deserializer<'de>,
{
enum Field {
C0,
C1,
C2,
}
impl<'de> Deserialize<'de> for Field {
fn deserialize<D>(deserializer: D) -> Result<Field, D::Error>
where
D: Deserializer<'de>,
{
struct FieldVisitor;
impl<'de> Visitor<'de> for FieldVisitor {
type Value = Field;
fn expecting(
&self,
formatter: &mut ::core::fmt::Formatter,
) -> ::core::fmt::Result {
formatter.write_str("struct Fp6")
}
fn visit_str<E>(self, value: &str) -> Result<Field, E>
where
E: serde::de::Error,
{
match value {
"c0" => Ok(Field::C0),
"c1" => Ok(Field::C1),
"c2" => Ok(Field::C2),
_ => Err(serde::de::Error::unknown_field(value, FIELDS)),
}
}
}
deserializer.deserialize_identifier(FieldVisitor)
}
}
struct Fp6Visitor;
impl<'de> Visitor<'de> for Fp6Visitor {
type Value = Fp6;
fn expecting(&self, formatter: &mut ::core::fmt::Formatter) -> ::core::fmt::Result {
formatter.write_str("struct Fp6")
}
fn visit_seq<V>(self, mut seq: V) -> Result<Fp6, V::Error>
where
V: serde::de::SeqAccess<'de>,
{
let c0 = seq
.next_element()?
.ok_or_else(|| serde::de::Error::invalid_length(0, &self))?;
let c1 = seq
.next_element()?
.ok_or_else(|| serde::de::Error::invalid_length(0, &self))?;
let c2 = seq
.next_element()?
.ok_or_else(|| serde::de::Error::invalid_length(0, &self))?;
Ok(Fp6 { c0, c1, c2 })
}
}
const FIELDS: &[&str] = &["c0", "c1", "c2"];
deserializer.deserialize_struct("Fp6", FIELDS, Fp6Visitor)
}
}
impl ConditionallySelectable for Fp6 {
#[inline(always)]
fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
Fp6 {
c0: Fp2::conditional_select(&a.c0, &b.c0, choice),
c1: Fp2::conditional_select(&a.c1, &b.c1, choice),
c2: Fp2::conditional_select(&a.c2, &b.c2, choice),
}
}
}
impl ConstantTimeEq for Fp6 {
#[inline(always)]
fn ct_eq(&self, other: &Self) -> Choice {
self.c0.ct_eq(&other.c0) & self.c1.ct_eq(&other.c1) & self.c2.ct_eq(&other.c2)
}
}
impl Fp6 {
#[inline]
pub fn zero() -> Self {
Fp6 {
c0: Fp2::zero(),
c1: Fp2::zero(),
c2: Fp2::zero(),
}
}
#[inline]
pub fn one() -> Self {
Fp6 {
c0: Fp2::one(),
c1: Fp2::zero(),
c2: Fp2::zero(),
}
}
pub fn mul_by_1(&self, c1: &Fp2) -> Fp6 {
let b_b = self.c1 * c1;
let t1 = (self.c1 + self.c2) * c1 - b_b;
let t1 = t1.mul_by_nonresidue();
let t2 = (self.c0 + self.c1) * c1 - b_b;
Fp6 {
c0: t1,
c1: t2,
c2: b_b,
}
}
pub fn mul_by_01(&self, c0: &Fp2, c1: &Fp2) -> Fp6 {
let a_a = self.c0 * c0;
let b_b = self.c1 * c1;
let t1 = (self.c1 + self.c2) * c1 - b_b;
let t1 = t1.mul_by_nonresidue() + a_a;
let t2 = (c0 + c1) * (self.c0 + self.c1) - a_a - b_b;
let t3 = (self.c0 + self.c2) * c0 - a_a + b_b;
Fp6 {
c0: t1,
c1: t2,
c2: t3,
}
}
pub fn mul_by_nonresidue(&self) -> Self {
Fp6 {
c0: self.c2.mul_by_nonresidue(),
c1: self.c0,
c2: self.c1,
}
}
#[inline(always)]
pub fn frobenius_map(&self) -> Self {
let c0 = self.c0.frobenius_map();
let c1 = self.c1.frobenius_map();
let c2 = self.c2.frobenius_map();
let c1 = c1
* Fp2 {
c0: Fp::zero(),
c1: Fp::from_raw_unchecked([
0xcd03c9e48671f071,
0x5dab22461fcda5d2,
0x587042afd3851b95,
0x8eb60ebe01bacb9e,
0x3f97d6e83d050d2,
0x18f0206554638741,
]),
};
let c2 = c2
* Fp2 {
c0: Fp::from_raw_unchecked([
0x890dc9e4867545c3,
0x2af322533285a5d5,
0x50880866309b7e2c,
0xa20d1b8c7e881024,
0x14e4f04fe2db9068,
0x14e56d3f1564853a,
]),
c1: Fp::zero(),
};
Fp6 { c0, c1, c2 }
}
#[inline(always)]
pub fn is_zero(&self) -> Choice {
self.c0.is_zero() & self.c1.is_zero() & self.c2.is_zero()
}
#[inline]
pub fn square(&self) -> Self {
let s0 = self.c0.square();
let ab = self.c0 * self.c1;
let s1 = ab + ab;
let s2 = (self.c0 - self.c1 + self.c2).square();
let bc = self.c1 * self.c2;
let s3 = bc + bc;
let s4 = self.c2.square();
Fp6 {
c0: s3.mul_by_nonresidue() + s0,
c1: s4.mul_by_nonresidue() + s1,
c2: s1 + s2 + s3 - s0 - s4,
}
}
#[inline]
pub fn invert(&self) -> CtOption<Self> {
let c0 = (self.c1 * self.c2).mul_by_nonresidue();
let c0 = self.c0.square() - c0;
let c1 = self.c2.square().mul_by_nonresidue();
let c1 = c1 - (self.c0 * self.c1);
let c2 = self.c1.square();
let c2 = c2 - (self.c0 * self.c2);
let tmp = ((self.c1 * c2) + (self.c2 * c1)).mul_by_nonresidue();
let tmp = tmp + (self.c0 * c0);
tmp.invert().map(|t| Fp6 {
c0: t * c0,
c1: t * c1,
c2: t * c2,
})
}
}
impl<'a, 'b> Mul<&'b Fp6> for &'a Fp6 {
type Output = Fp6;
#[inline]
fn mul(self, other: &'b Fp6) -> Self::Output {
let aa = self.c0 * other.c0;
let bb = self.c1 * other.c1;
let cc = self.c2 * other.c2;
let t1 = other.c1 + other.c2;
let tmp = self.c1 + self.c2;
let t1 = t1 * tmp;
let t1 = t1 - bb;
let t1 = t1 - cc;
let t1 = t1.mul_by_nonresidue();
let t1 = t1 + aa;
let t3 = other.c0 + other.c2;
let tmp = self.c0 + self.c2;
let t3 = t3 * tmp;
let t3 = t3 - aa;
let t3 = t3 + bb;
let t3 = t3 - cc;
let t2 = other.c0 + other.c1;
let tmp = self.c0 + self.c1;
let t2 = t2 * tmp;
let t2 = t2 - aa;
let t2 = t2 - bb;
let cc = cc.mul_by_nonresidue();
let t2 = t2 + cc;
Fp6 {
c0: t1,
c1: t2,
c2: t3,
}
}
}
impl<'a, 'b> Add<&'b Fp6> for &'a Fp6 {
type Output = Fp6;
#[inline]
fn add(self, rhs: &'b Fp6) -> Self::Output {
Fp6 {
c0: self.c0 + rhs.c0,
c1: self.c1 + rhs.c1,
c2: self.c2 + rhs.c2,
}
}
}
impl<'a> Neg for &'a Fp6 {
type Output = Fp6;
#[inline]
fn neg(self) -> Self::Output {
Fp6 {
c0: -self.c0,
c1: -self.c1,
c2: -self.c2,
}
}
}
impl Neg for Fp6 {
type Output = Fp6;
#[inline]
fn neg(self) -> Self::Output {
-&self
}
}
impl<'a, 'b> Sub<&'b Fp6> for &'a Fp6 {
type Output = Fp6;
#[inline]
fn sub(self, rhs: &'b Fp6) -> Self::Output {
Fp6 {
c0: self.c0 - rhs.c0,
c1: self.c1 - rhs.c1,
c2: self.c2 - rhs.c2,
}
}
}
impl_binops_additive!(Fp6, Fp6);
impl_binops_multiplicative!(Fp6, Fp6);
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_arithmetic() {
use crate::fp::*;
let a = Fp6 {
c0: Fp2 {
c0: Fp::from_raw_unchecked([
0x47f9cb98b1b82d58,
0x5fe911eba3aa1d9d,
0x96bf1b5f4dd81db3,
0x8100d27cc9259f5b,
0xafa20b9674640eab,
0x9bbcea7d8d9497d,
]),
c1: Fp::from_raw_unchecked([
0x303cb98b1662daa,
0xd93110aa0a621d5a,
0xbfa9820c5be4a468,
0xba3643ecb05a348,
0xdc3534bb1f1c25a6,
0x6c305bb19c0e1c1,
]),
},
c1: Fp2 {
c0: Fp::from_raw_unchecked([
0x46f9cb98b162d858,
0xbe9109cf7aa1d57,
0xc791bc55fece41d2,
0xf84c57704e385ec2,
0xcb49c1d9c010e60f,
0xacdb8e158bfe3c8,
]),
c1: Fp::from_raw_unchecked([
0x8aefcb98b15f8306,
0x3ea1108fe4f21d54,
0xcf79f69fa1b7df3b,
0xe4f54aa1d16b1a3c,
0xba5e4ef86105a679,
0xed86c0797bee5cf,
]),
},
c2: Fp2 {
c0: Fp::from_raw_unchecked([
0xcee5cb98b15c2db4,
0x71591082d23a1d51,
0xd76230e944a17ca4,
0xd19e3dd3549dd5b6,
0xa972dc1701fa66e3,
0x12e31f2dd6bde7d6,
]),
c1: Fp::from_raw_unchecked([
0xad2acb98b1732d9d,
0x2cfd10dd06961d64,
0x7396b86c6ef24e8,
0xbd76e2fdb1bfc820,
0x6afea7f6de94d0d5,
0x10994b0c5744c040,
]),
},
};
let b = Fp6 {
c0: Fp2 {
c0: Fp::from_raw_unchecked([
0xf120cb98b16fd84b,
0x5fb510cff3de1d61,
0xf21a5d069d8c251,
0xaa1fd62f34f2839a,
0x5a1335157f89913f,
0x14a3fe329643c247,
]),
c1: Fp::from_raw_unchecked([
0x3516cb98b16c82f9,
0x926d10c2e1261d5f,
0x1709e01a0cc25fba,
0x96c8c960b8253f14,
0x4927c234207e51a9,
0x18aeb158d542c44e,
]),
},
c1: Fp2 {
c0: Fp::from_raw_unchecked([
0xbf0dcb98b16982fc,
0xa67910b71d1a1d5c,
0xb7c147c2b8fb06ff,
0x1efa710d47d2e7ce,
0xed20a79c7e27653c,
0x2b85294dac1dfba,
]),
c1: Fp::from_raw_unchecked([
0x9d52cb98b18082e5,
0x621d111151761d6f,
0xe79882603b48af43,
0xad31637a4f4da37,
0xaeac737c5ac1cf2e,
0x6e7e735b48b824,
]),
},
c2: Fp2 {
c0: Fp::from_raw_unchecked([
0xe148cb98b17d2d93,
0x94d511043ebe1d6c,
0xef80bca9de324cac,
0xf77c0969282795b1,
0x9dc1009afbb68f97,
0x47931999a47ba2b,
]),
c1: Fp::from_raw_unchecked([
0x253ecb98b179d841,
0xc78d10f72c061d6a,
0xf768f6f3811bea15,
0xe424fc9aab5a512b,
0x8cd58db99cab5001,
0x883e4bfd946bc32,
]),
},
};
let c = Fp6 {
c0: Fp2 {
c0: Fp::from_raw_unchecked([
0x6934cb98b17682ef,
0xfa4510ea194e1d67,
0xff51313d2405877e,
0xd0cdefcc2e8d0ca5,
0x7bea1ad83da0106b,
0xc8e97e61845be39,
]),
c1: Fp::from_raw_unchecked([
0x4779cb98b18d82d8,
0xb5e911444daa1d7a,
0x2f286bdaa6532fc2,
0xbca694f68baeff0f,
0x3d75e6b81a3a7a5d,
0xa44c3c498cc96a3,
]),
},
c1: Fp2 {
c0: Fp::from_raw_unchecked([
0x8b6fcb98b18a2d86,
0xe8a111373af21d77,
0x3710a624493ccd2b,
0xa94f88280ee1ba89,
0x2c8a73d6bb2f3ac7,
0xe4f76ead7cb98aa,
]),
c1: Fp::from_raw_unchecked([
0xcf65cb98b186d834,
0x1b59112a283a1d74,
0x3ef8e06dec266a95,
0x95f87b5992147603,
0x1b9f00f55c23fb31,
0x125a2a1116ca9ab1,
]),
},
c2: Fp2 {
c0: Fp::from_raw_unchecked([
0x135bcb98b18382e2,
0x4e11111d15821d72,
0x46e11ab78f1007fe,
0x82a16e8b1547317d,
0xab38e13fd18bb9b,
0x1664dd3755c99cb8,
]),
c1: Fp::from_raw_unchecked([
0xce65cb98b1318334,
0xc7590fdb7c3a1d2e,
0x6fcb81649d1c8eb3,
0xd44004d1727356a,
0x3746b738a7d0d296,
0x136c144a96b134fc,
]),
},
};
assert_eq!(a.square(), &a * &a);
assert_eq!(b.square(), &b * &b);
assert_eq!(c.square(), &c * &c);
assert_eq!(
(a + b) * c.square(),
&(&(&c * &c) * &a) + &(&(&c * &c) * &b)
);
assert_eq!(
&a.invert().unwrap() * &b.invert().unwrap(),
(&a * &b).invert().unwrap()
);
assert_eq!(&a.invert().unwrap() * &a, Fp6::one());
}
#[test]
#[cfg(feature = "serde_req")]
fn fp6_serde_roundtrip() {
use bincode;
let fp6 = Fp6 {
c0: Fp2::one(),
c1: Fp2::one(),
c2: Fp2::one(),
};
let ser = bincode::serialize(&fp6).unwrap();
let deser: Fp6 = bincode::deserialize(&ser).unwrap();
assert_eq!(fp6, deser);
}
}