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ff: Remove SqrtField trait

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The sqrt() function is now part of the Field trait. ff_derive returns an
error on fields for which it does not support generating a square root
function.

Note that Fq6 and Fq12 in pairing::bls12_381 leave the function
unimplemented. They will be dropped once the migration to the bls12_381
crate is complete. The equivalent structs in that crate are not exposed.
This commit is contained in:
Jack Grigg
2020-05-01 13:48:30 +12:00
parent b02cf3b467
commit 1761ebfb35
20 changed files with 124 additions and 137 deletions
Download Patch File Download Diff File Expand all files Collapse all files

140
ff/ff_derive/src/lib.rs
View File

@@ -163,8 +163,8 @@ pub fn prime_field(input: proc_macro::TokenStream) -> proc_macro::TokenStream {
&modulus,
&endianness,
limbs,
sqrt_impl,
));
gen.extend(sqrt_impl);
// Return the generated impl
gen.into()
@@ -486,89 +486,84 @@ fn prime_field_constants_and_sqrt(
biguint_to_u64_vec((exp(generator.clone(), &t, &modulus) * &r) % modulus, limbs);
let generator = biguint_to_u64_vec((generator.clone() * &r) % modulus, limbs);
let sqrt_impl = if (modulus % BigUint::from_str("4").unwrap())
== BigUint::from_str("3").unwrap()
{
// Addition chain for (r + 1) // 4
let mod_plus_1_over_4 = pow_fixed::generate(
&quote! {self},
(modulus + BigUint::from_str("1").unwrap()) >> 2,
);
let sqrt_impl =
if (modulus % BigUint::from_str("4").unwrap()) == BigUint::from_str("3").unwrap() {
// Addition chain for (r + 1) // 4
let mod_plus_1_over_4 = pow_fixed::generate(
&quote! {self},
(modulus + BigUint::from_str("1").unwrap()) >> 2,
);
quote! {
impl ::ff::SqrtField for #name {
fn sqrt(&self) -> ::subtle::CtOption<Self> {
use ::subtle::ConstantTimeEq;
quote! {
use ::subtle::ConstantTimeEq;
// Because r = 3 (mod 4)
// sqrt can be done with only one exponentiation,
// via the computation of self^((r + 1) // 4) (mod r)
let sqrt = {
#mod_plus_1_over_4
};
// Because r = 3 (mod 4)
// sqrt can be done with only one exponentiation,
// via the computation of self^((r + 1) // 4) (mod r)
let sqrt = {
#mod_plus_1_over_4
};
::subtle::CtOption::new(
sqrt,
(sqrt * &sqrt).ct_eq(self), // Only return Some if it's the square root.
)
}
::subtle::CtOption::new(
sqrt,
(sqrt * &sqrt).ct_eq(self), // Only return Some if it's the square root.
)
}
}
} else if (modulus % BigUint::from_str("16").unwrap()) == BigUint::from_str("1").unwrap() {
// Addition chain for (t - 1) // 2
let t_minus_1_over_2 = pow_fixed::generate(&quote! {self}, (&t - BigUint::one()) >> 1);
} else if (modulus % BigUint::from_str("16").unwrap()) == BigUint::from_str("1").unwrap() {
// Addition chain for (t - 1) // 2
let t_minus_1_over_2 = pow_fixed::generate(&quote! {self}, (&t - BigUint::one()) >> 1);
quote! {
impl ::ff::SqrtField for #name {
fn sqrt(&self) -> ::subtle::CtOption<Self> {
// Tonelli-Shank's algorithm for q mod 16 = 1
// https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
use ::subtle::{ConditionallySelectable, ConstantTimeEq};
quote! {
// Tonelli-Shank's algorithm for q mod 16 = 1
// https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
use ::subtle::{ConditionallySelectable, ConstantTimeEq};
// w = self^((t - 1) // 2)
let w = {
#t_minus_1_over_2
};
// w = self^((t - 1) // 2)
let w = {
#t_minus_1_over_2
};
let mut v = S;
let mut x = *self * &w;
let mut b = x * &w;
let mut v = S;
let mut x = *self * &w;
let mut b = x * &w;
// Initialize z as the 2^S root of unity.
let mut z = ROOT_OF_UNITY;
// Initialize z as the 2^S root of unity.
let mut z = ROOT_OF_UNITY;
for max_v in (1..=S).rev() {
let mut k = 1;
let mut tmp = b.square();
let mut j_less_than_v: ::subtle::Choice = 1.into();
for max_v in (1..=S).rev() {
let mut k = 1;
let mut tmp = b.square();
let mut j_less_than_v: ::subtle::Choice = 1.into();
for j in 2..max_v {
let tmp_is_one = tmp.ct_eq(&#name::one());
let squared = #name::conditional_select(&tmp, &z, tmp_is_one).square();
tmp = #name::conditional_select(&squared, &tmp, tmp_is_one);
let new_z = #name::conditional_select(&z, &squared, tmp_is_one);
j_less_than_v &= !j.ct_eq(&v);
k = u32::conditional_select(&j, &k, tmp_is_one);
z = #name::conditional_select(&z, &new_z, j_less_than_v);
}
let result = x * &z;
x = #name::conditional_select(&result, &x, b.ct_eq(&#name::one()));
z = z.square();
b *= &z;
v = k;
for j in 2..max_v {
let tmp_is_one = tmp.ct_eq(&#name::one());
let squared = #name::conditional_select(&tmp, &z, tmp_is_one).square();
tmp = #name::conditional_select(&squared, &tmp, tmp_is_one);
let new_z = #name::conditional_select(&z, &squared, tmp_is_one);
j_less_than_v &= !j.ct_eq(&v);
k = u32::conditional_select(&j, &k, tmp_is_one);
z = #name::conditional_select(&z, &new_z, j_less_than_v);
}
::subtle::CtOption::new(
x,
(x * &x).ct_eq(self), // Only return Some if it's the square root.
)
let result = x * &z;
x = #name::conditional_select(&result, &x, b.ct_eq(&#name::one()));
z = z.square();
b *= &z;
v = k;
}
::subtle::CtOption::new(
x,
(x * &x).ct_eq(self), // Only return Some if it's the square root.
)
}
}
} else {
quote! {}
};
} else {
syn::Error::new_spanned(
&name,
"ff_derive can't generate a square root function for this field.",
)
.to_compile_error()
};
// Compute R^2 mod m
let r2 = biguint_to_u64_vec((&r * &r) % modulus, limbs);
@@ -634,6 +629,7 @@ fn prime_field_impl(
modulus: &BigUint,
endianness: &ReprEndianness,
limbs: usize,
sqrt_impl: proc_macro2::TokenStream,
) -> proc_macro2::TokenStream {
// Returns r{n} as an ident.
fn get_temp(n: usize) -> syn::Ident {
@@ -1280,6 +1276,10 @@ fn prime_field_impl(
{
#squaring_impl
}
fn sqrt(&self) -> ::subtle::CtOption<Self> {
#sqrt_impl
}
}
impl #name {

13
ff/src/lib.rs
View File

@@ -75,6 +75,10 @@ pub trait Field:
/// Exponentiates this element by a power of the base prime modulus via
/// the Frobenius automorphism.
fn frobenius_map(&mut self, power: usize);
/// Returns the square root of the field element, if it is
/// quadratic residue.
fn sqrt(&self) -> CtOption<Self>;
}
pub trait PowVartime<L>: Field
@@ -124,13 +128,6 @@ impl<T: Field> PowVartime<u64> for T {
const LIMB_SIZE: u64 = 64;
}
/// This trait represents an element of a field that has a square root operation described for it.
pub trait SqrtField: Field {
/// Returns the square root of the field element, if it is
/// quadratic residue.
fn sqrt(&self) -> CtOption<Self>;
}
/// This represents an element of a prime field.
pub trait PrimeField:
Field + Ord + From<u64> + BitAnd<u64, Output = u64> + Shr<u32, Output = Self>
@@ -230,7 +227,7 @@ pub trait PrimeField:
/// pairing-friendly curve) can be defined in a subtrait.
pub trait ScalarEngine: Sized + 'static + Clone {
/// This is the scalar field of the engine's groups.
type Fr: PrimeField + SqrtField;
type Fr: PrimeField;
}
#[derive(Debug)]