Merge remote-tracking branch 'hdevalence/feature/operator_scalar_mult_r2' into develop

This commit is contained in:
Isis Lovecruft 2017-05-14 09:34:45 +00:00
commit 61d07693ec
Failed to extract signature
6 changed files with 154 additions and 136 deletions

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@ -36,12 +36,10 @@ version = "^0.6"
version = "0.4"
[features]
nightly = ["basepoint_table_creation", "radix_51"]
nightly = ["radix_51"]
default = ["std"]
std = ["rand"]
yolocrypto = []
# Needs nightly for placement new
basepoint_table_creation = []
bench = []
# Radix-51 arithmetic using u128
radix_51 = []

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@ -24,6 +24,8 @@ use curve::ExtendedPoint;
use curve::AffineNielsPoint;
use curve::CompressedEdwardsY;
use curve::EdwardsBasepointTable;
#[cfg(feature = "yolocrypto")]
use decaf::{DecafPoint, DecafBasepointTable};
use scalar::Scalar;
#[cfg(feature="radix_51")]
@ -136,6 +138,10 @@ pub const BASE_CMPRSSD: CompressedEdwardsY =
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66]);
/// The Ed25519 basepoint, as a `DecafPoint`.
#[cfg(feature = "yolocrypto")]
pub const DECAF_ED25519_BASEPOINT: DecafPoint = DecafPoint(ED25519_BASEPOINT);
/// Basepoint has y = 4/5.
#[cfg(not(feature="radix_51"))]
pub const ED25519_BASEPOINT: ExtendedPoint = ExtendedPoint{
@ -384,6 +390,11 @@ pub const bi: [AffineNielsPoint; 8] = [
}
];
#[cfg(feature = "yolocrypto")]
/// The Ed25519 basepoint
pub const DECAF_ED25519_BASEPOINT_TABLE: DecafBasepointTable
= DecafBasepointTable(ED25519_BASEPOINT_TABLE);
/// Table containing precomputed multiples of the basepoint `B = (x,4/5)`.
///
/// The table is defined so `constants::base[i][j-1] = j*(16^2i)*B`,

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@ -79,7 +79,9 @@
use core::fmt::Debug;
use core::iter::Iterator;
use core::ops::{Add, Sub, Neg, Index};
use core::ops::{Add, Sub, Neg};
use core::ops::{Mul, MulAssign};
use core::ops::Index;
use constants;
use field::FieldElement;
@ -90,11 +92,6 @@ use subtle::CTAssignable;
use subtle::CTEq;
use subtle::CTNegatable;
#[cfg(all(not(feature = "std"), feature = "basepoint_table_creation"))]
use collections::boxed::Box;
#[cfg(all(feature = "std", feature = "basepoint_table_creation"))]
use std::boxed::Box;
// ------------------------------------------------------------------------
// Compressed points
// ------------------------------------------------------------------------
@ -789,18 +786,20 @@ impl<'a> Neg for &'a AffineNielsPoint {
// Scalar multiplication
// ------------------------------------------------------------------------
/// Trait for scalar multiplication of an arbitrary point.
pub trait ScalarMult<S> {
/// Compute `scalar * self`.
fn scalar_mult(&self, scalar: &S) -> Self;
impl<'b> MulAssign<&'b Scalar> for ExtendedPoint {
fn mul_assign(&mut self, scalar: &'b Scalar) {
let result = (self as &ExtendedPoint) * scalar;
*self = result;
}
}
impl ScalarMult<Scalar> for ExtendedPoint {
impl<'a, 'b> Mul<&'b Scalar> for &'a ExtendedPoint {
type Output = ExtendedPoint;
/// Scalar multiplication: compute `scalar * self`.
///
/// Uses a window of size 4. Note: for scalar multiplication of
/// the basepoint, `basepoint_mult` is approximately 4x faster.
fn scalar_mult(&self, scalar: &Scalar) -> ExtendedPoint {
fn mul(self, scalar: &'b Scalar) -> ExtendedPoint {
let A = self.to_projective_niels();
let mut As: [ProjectiveNielsPoint; 8] = [A; 8];
for i in 0..7 {
@ -822,27 +821,8 @@ impl ScalarMult<Scalar> for ExtendedPoint {
#[derive(Clone)]
pub struct EdwardsBasepointTable(pub [[AffineNielsPoint; 8]; 32]);
impl EdwardsBasepointTable {
/// Create a table of precomputed multiples of `basepoint`.
#[cfg(feature="basepoint_table_creation")]
pub fn create(basepoint: &ExtendedPoint) -> Box<EdwardsBasepointTable> {
// Create the table storage
// XXX can we be assured that this is not allocated on the stack?
// XXX can we skip the initialization without too much unsafety?
let mut table = box EdwardsBasepointTable([[AffineNielsPoint::identity(); 8]; 32]);
let mut P = basepoint.clone();
for i in 0..32 {
// P = (16^2)^i * B
let mut jP = P.to_affine_niels();
for j in 1..9 {
// table[i][j-1] is supposed to be j*(16^2)^i*B
table.0[i][j-1] = jP;
jP = (&P + &jP).to_extended().to_affine_niels();
}
P = P.mult_by_pow_2(8);
}
return table
}
impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTable {
type Output = ExtendedPoint;
/// Construct an `ExtendedPoint` from a `Scalar`, `scalar`, by
/// computing the multiple `aB` of the basepoint `B`.
@ -869,7 +849,7 @@ impl EdwardsBasepointTable {
/// We then use the `select_precomputed_point` function, which
/// takes `-8 ≤ x < 8` and `[16^2i * B, ..., 8 * 16^2i * B]`,
/// and returns `x * 16^2i * B` in constant time.
pub fn basepoint_mult(&self, scalar: &Scalar) -> ExtendedPoint {
fn mul(self, scalar: &'b Scalar) -> ExtendedPoint {
let e = scalar.to_radix_16();
let mut h = ExtendedPoint::identity();
let mut t: CompletedPoint;
@ -890,21 +870,32 @@ impl EdwardsBasepointTable {
}
}
/// Trait for scalar multiplication of a distinguished basepoint.
pub trait BasepointMult<S> {
/// Return the basepoint `B`.
fn basepoint() -> Self;
/// Compute `scalar * B`.
fn basepoint_mult(scalar: &S) -> Self;
}
impl BasepointMult<Scalar> for ExtendedPoint {
fn basepoint() -> ExtendedPoint {
constants::ED25519_BASEPOINT
impl EdwardsBasepointTable {
/// Create a table of precomputed multiples of `basepoint`.
pub fn create(basepoint: &ExtendedPoint) -> EdwardsBasepointTable {
// Create the table storage
// XXX can we skip the initialization without too much unsafety?
// stick 30K on the stack and call it a day.
let mut table = EdwardsBasepointTable([[AffineNielsPoint::identity(); 8]; 32]);
let mut P = basepoint.clone();
for i in 0..32 {
// P = (16^2)^i * B
let mut jP = P.to_affine_niels();
for j in 1..9 {
// table[i][j-1] is supposed to be j*(16^2)^i*B
table.0[i][j-1] = jP;
jP = (&P + &jP).to_extended().to_affine_niels();
}
P = P.mult_by_pow_2(8);
}
table
}
fn basepoint_mult(scalar: &Scalar) -> ExtendedPoint {
constants::ED25519_BASEPOINT_TABLE.basepoint_mult(scalar)
/// Get the basepoint for this table as an `ExtendedPoint`.
pub fn basepoint(&self) -> ExtendedPoint {
// self.0[0][0] has 1*(16^2)^0*B, but as an `AffineNielsPoint`
// Add identity to convert to extended.
(&ExtendedPoint::identity() + &self.0[0][0]).to_extended()
}
}
@ -1075,12 +1066,15 @@ pub mod vartime {
///
/// A vector of `Scalar`s and a vector of `ExtendedPoints`. It is an
/// error to call this function with two vectors of different lengths.
pub fn k_fold_scalar_mult(scalars: &Vec<Scalar>,
points: &Vec<ExtendedPoint>) -> ExtendedPoint {
assert_eq!(scalars.len(), points.len());
pub fn k_fold_scalar_mult<'a,'b,I,J>(scalars: I, points: J) -> ExtendedPoint
where I: IntoIterator<Item=&'a Scalar>, J: IntoIterator<Item=&'b ExtendedPoint>
{
//assert_eq!(scalars.len(), points.len());
let nafs: Vec<_> = scalars.iter().map(|c| c.non_adjacent_form()).collect();
let odd_multiples: Vec<_> = points.iter().map(|P| OddMultiples::create(&P)).collect();
let nafs: Vec<_> = scalars.into_iter()
.map(|c| c.non_adjacent_form()).collect();
let odd_multiples: Vec<_> = points.into_iter()
.map(|P| OddMultiples::create(P)).collect();
let mut r = ProjectivePoint::identity();
@ -1282,11 +1276,18 @@ mod test {
/// Test that computing 1*basepoint gives the correct basepoint.
#[test]
fn basepoint_mult_one_vs_basepoint() {
let bp = ExtendedPoint::basepoint_mult(&Scalar::one());
let bp = &constants::ED25519_BASEPOINT_TABLE * &Scalar::one();
let compressed = bp.compress_edwards();
assert_eq!(compressed, constants::BASE_CMPRSSD);
}
/// Test that `EdwardsBasepointTable::basepoint()` gives the correct basepoint.
#[test]
fn basepoint_table_basepoint_function_correct() {
let bp = constants::ED25519_BASEPOINT_TABLE.basepoint();
assert_eq!(bp.compress_edwards(), constants::BASE_CMPRSSD);
}
/// Test `impl Add<ExtendedPoint> for ExtendedPoint`
/// using basepoint + basepoint versus the 2*basepoint constant.
#[test]
@ -1334,7 +1335,7 @@ mod test {
#[test]
fn to_affine_niels_clears_denominators() {
// construct a point as aB so it has denominators (ie. Z != 1)
let aB = ExtendedPoint::basepoint_mult(&A_SCALAR);
let aB = &constants::ED25519_BASEPOINT_TABLE * &A_SCALAR;
let aB_affine_niels = aB.to_affine_niels();
let also_aB = (&ExtendedPoint::identity() + &aB_affine_niels).to_extended();
assert_eq!( aB.compress_edwards(),
@ -1344,14 +1345,15 @@ mod test {
/// Test basepoint_mult versus a known scalar multiple from ed25519.py
#[test]
fn basepoint_mult_vs_ed25519py() {
let aB = ExtendedPoint::basepoint_mult(&A_SCALAR);
let aB = &constants::ED25519_BASEPOINT_TABLE * &A_SCALAR;
assert_eq!(aB.compress_edwards(), A_TIMES_BASEPOINT);
}
/// Test that multiplication by the basepoint order kills the basepoint
#[test]
fn basepoint_mult_by_basepoint_order() {
let should_be_id = ExtendedPoint::basepoint_mult(&constants::l);
let B = &constants::ED25519_BASEPOINT_TABLE;
let should_be_id = B * &constants::l;
assert!(should_be_id.is_identity());
}
@ -1360,16 +1362,15 @@ mod test {
#[cfg(feature="basepoint_table_creation")]
fn test_precomputed_basepoint_mult() {
let table = EdwardsBasepointTable::create(&constants::ED25519_BASEPOINT);
let aB_1 = ExtendedPoint::basepoint_mult(&A_SCALAR);
let aB_2 = table.basepoint_mult(&A_SCALAR);
assert_eq!(aB_1.compress_edwards(),
aB_2.compress_edwards());
let aB_1 = &constants::ED25519_BASEPOINT_TABLE * &A_SCALAR;
let aB_2 = &table * &A_SCALAR;
assert_eq!(aB_1.compress_edwards(), aB_2.compress_edwards());
}
/// Test scalar_mult versus a known scalar multiple from ed25519.py
#[test]
fn scalar_mult_vs_ed25519py() {
let aB = constants::ED25519_BASEPOINT.scalar_mult(&A_SCALAR);
let aB = &constants::ED25519_BASEPOINT * &A_SCALAR;
assert_eq!(aB.compress_edwards(), A_TIMES_BASEPOINT);
}
@ -1384,7 +1385,7 @@ mod test {
#[test]
fn basepoint_mult_two_vs_basepoint2() {
let mut two_bytes = [0u8; 32]; two_bytes[0] = 2;
let bp2 = ExtendedPoint::basepoint_mult(&Scalar(two_bytes));
let bp2 = &constants::ED25519_BASEPOINT_TABLE * &Scalar(two_bytes);
assert_eq!(bp2.compress_edwards(), BASE2_CMPRSSD);
}
@ -1450,11 +1451,11 @@ mod test {
/// the type system and prove correctness).
#[test]
fn monte_carlo_overflow_underflow_debug_assert_test() {
let mut P = ExtendedPoint::basepoint();
let mut P = constants::ED25519_BASEPOINT;
// N.B. each scalar_mult does 1407 field mults, 1024 field squarings,
// so this does ~ 1M of each operation.
for _ in 0..1_000 {
P = P.scalar_mult(&A_SCALAR);
P *= &A_SCALAR;
}
}
@ -1473,9 +1474,10 @@ mod test {
#[test]
fn k_fold_scalar_mult_vs_ed25519py() {
let A = A_TIMES_BASEPOINT.decompress().unwrap();
let points = vec![A,constants::ED25519_BASEPOINT];
let scalars = vec![A_SCALAR, B_SCALAR];
let result = vartime::k_fold_scalar_mult(&scalars, &points);
let result = vartime::k_fold_scalar_mult(
&[A_SCALAR, B_SCALAR],
&[A, constants::ED25519_BASEPOINT]
);
assert_eq!(result.compress_edwards(), DOUBLE_SCALAR_MULT_RESULT);
}
}
@ -1495,13 +1497,14 @@ mod bench {
#[bench]
fn basepoint_mult(b: &mut Bencher) {
b.iter(|| ExtendedPoint::basepoint_mult(&A_SCALAR));
let B = &constants::ED25519_BASEPOINT_TABLE;
b.iter(|| B * &A_SCALAR);
}
#[bench]
fn scalar_mult(b: &mut Bencher) {
let bp = constants::ED25519_BASEPOINT;
b.iter(|| bp.scalar_mult(&A_SCALAR));
let B = &constants::ED25519_BASEPOINT;
b.iter(|| B * &A_SCALAR);
}
#[bench]
@ -1565,7 +1568,7 @@ mod bench {
#[cfg(feature="basepoint_table_creation")]
#[bench]
fn create_basepoint_table(b: &mut Bencher) {
let aB = ExtendedPoint::basepoint_mult(&A_SCALAR);
let aB = &constants::ED25519_BASEPOINT_TABLE * &A_SCALAR;
b.iter(|| EdwardsBasepointTable::create(&aB));
}
@ -1586,8 +1589,8 @@ mod bench {
// Create 10 random scalars
let scalars: Vec<_> = (0..10).map(|_| Scalar::random(&mut csprng)).collect();
// Create 10 points (by doing scalar mults)
let points: Vec<_> = scalars.iter()
.map(|s| ExtendedPoint::basepoint_mult(s)).collect();
let B = &constants::ED25519_BASEPOINT_TABLE;
let points: Vec<_> = scalars.iter().map(|s| B * &s).collect();
// XXX Currently Rust's benchmarking implementation doesn't
// allow you to specify a sequence of random inputs, but only

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@ -30,17 +30,11 @@ use subtle::CTAssignable;
use subtle::CTNegatable;
use core::ops::{Add, Sub, Neg};
#[cfg(all(not(feature = "std"), feature = "basepoint_table_creation"))]
use collections::boxed::Box;
#[cfg(all(feature = "std", feature = "basepoint_table_creation"))]
use std::boxed::Box;
use core::ops::{Mul, MulAssign};
use curve;
use curve::ExtendedPoint;
use curve::EdwardsBasepointTable;
use curve::BasepointMult;
use curve::ScalarMult;
use curve::Identity;
use scalar::Scalar;
@ -250,40 +244,42 @@ impl<'a> Neg for &'a DecafPoint {
}
}
impl ScalarMult<Scalar> for DecafPoint {
fn scalar_mult(&self, scalar: &Scalar) -> DecafPoint {
DecafPoint(self.0.scalar_mult(scalar))
impl<'b> MulAssign<&'b Scalar> for DecafPoint {
fn mul_assign(&mut self, scalar: &'b Scalar) {
let result = (self as &DecafPoint) * scalar;
*self = result;
}
}
impl BasepointMult<Scalar> for DecafPoint {
// XXX is this actually in the image of the isogeny,
// or do we need a different basepoint?
fn basepoint() -> DecafPoint {
DecafPoint(ExtendedPoint::basepoint())
}
fn basepoint_mult(scalar: &Scalar) -> DecafPoint {
DecafPoint(ExtendedPoint::basepoint_mult(scalar))
impl<'a, 'b> Mul<&'b Scalar> for &'a DecafPoint {
type Output = DecafPoint;
/// Scalar multiplication: compute `scalar * self`.
fn mul(self, scalar: &'b Scalar) -> DecafPoint {
DecafPoint(&self.0 * scalar)
}
}
/// Precomputation
#[derive(Clone)]
pub struct DecafBasepointTable(EdwardsBasepointTable);
pub struct DecafBasepointTable(pub EdwardsBasepointTable);
impl<'a, 'b> Mul<&'b Scalar> for &'a DecafBasepointTable {
type Output = DecafPoint;
fn mul(self, scalar: &'b Scalar) -> DecafPoint {
DecafPoint(&self.0 * scalar)
}
}
impl DecafBasepointTable {
/// Create a precomputed table of multiples of the given `basepoint`.
#[cfg(feature = "basepoint_table_creation")]
pub fn create(basepoint: &DecafPoint) -> Box<DecafBasepointTable> {
let edwards_table = EdwardsBasepointTable::create(&basepoint.0);
box DecafBasepointTable(*edwards_table)
pub fn create(basepoint: &DecafPoint) -> DecafBasepointTable {
DecafBasepointTable(EdwardsBasepointTable::create(&basepoint.0))
}
/// Use the precomputed table to quickly compute `scalar * basepoint`
pub fn basepoint_mult(&self, scalar: &Scalar) -> DecafPoint {
DecafPoint(self.0.basepoint_mult(scalar))
/// Get the basepoint for this table as a `DecafPoint`.
pub fn basepoint(&self) -> DecafPoint {
DecafPoint(self.0.basepoint())
}
}
@ -322,10 +318,11 @@ pub mod vartime {
///
/// A vector of `Scalar`s and a vector of `ExtendedPoints`. It is an
/// error to call this function with two vectors of different lengths.
pub fn k_fold_scalar_mult(scalars: &Vec<Scalar>,
points: &Vec<DecafPoint>) -> DecafPoint {
let extended_points: Vec<ExtendedPoint> = points.iter().map(|P| P.0).collect();
DecafPoint(curve::vartime::k_fold_scalar_mult(scalars, &extended_points))
pub fn k_fold_scalar_mult<'a,'b,I,J>(scalars: I, points: J) -> DecafPoint
where I: IntoIterator<Item=&'a Scalar>, J: IntoIterator<Item=&'b DecafPoint>
{
let extended_points = points.into_iter().map(|P| &P.0);
DecafPoint(curve::vartime::k_fold_scalar_mult(scalars, extended_points))
}
}
@ -341,7 +338,6 @@ mod test {
use constants;
use curve::CompressedEdwardsY;
use curve::ExtendedPoint;
use curve::BasepointMult;
use curve::Identity;
use super::*;
@ -367,17 +363,17 @@ mod test {
#[test]
fn decaf_basepoint_roundtrip() {
let bp_compressed_decaf = DecafPoint::basepoint().compress();
let bp_compressed_decaf = constants::DECAF_ED25519_BASEPOINT.compress();
let bp_recaf = bp_compressed_decaf.decompress().unwrap().0;
// Check that bp_recaf differs from bp by a point of order 4
let diff = &ExtendedPoint::basepoint() - &bp_recaf;
let diff4 = diff.mult_by_pow_2(4);
let diff = &constants::ED25519_BASEPOINT - &bp_recaf;
let diff4 = diff.mult_by_pow_2(4); // XXX this is wrong
assert_eq!(diff4.compress_edwards(), CompressedEdwardsY::identity());
}
#[test]
fn decaf_four_torsion_basepoint() {
let bp = DecafPoint::basepoint();
let bp = constants::DECAF_ED25519_BASEPOINT;
let bp_coset = bp.coset4();
for i in 0..4 {
assert_eq!(bp, DecafPoint(bp_coset[i]));
@ -387,8 +383,8 @@ mod test {
#[test]
fn decaf_four_torsion_random() {
let mut rng = OsRng::new().unwrap();
let s = Scalar::random(&mut rng);
let P = DecafPoint::basepoint_mult(&s);
let B = &constants::DECAF_ED25519_BASEPOINT_TABLE;
let P = B * &Scalar::random(&mut rng);
let P_coset = P.coset4();
for i in 0..4 {
assert_eq!(P, DecafPoint(P_coset[i]));
@ -398,27 +394,14 @@ mod test {
#[test]
fn decaf_random_roundtrip() {
let mut rng = OsRng::new().unwrap();
let B = &constants::DECAF_ED25519_BASEPOINT_TABLE;
for _ in 0..100 {
let s = Scalar::random(&mut rng);
let P = DecafPoint::basepoint_mult(&s);
let P = B * &Scalar::random(&mut rng);
let compressed_P = P.compress();
let Q = compressed_P.decompress().unwrap();
assert_eq!(P, Q);
}
}
/// Test basepoint_mult versus a newly-generated DecafBasepointTable
#[test]
#[cfg(feature = "basepoint_table_creation")]
fn basepoint_mult_vs_decafbasepointtable() {
let table = DecafBasepointTable::create(&DecafPoint::basepoint());
let mut rng = OsRng::new().unwrap();
let s = Scalar::random(&mut rng);
let basepoint_mult_s = DecafPoint::basepoint_mult(&s);
let table_basepoint_mult_s = table.basepoint_mult(&s);
assert_eq!(basepoint_mult_s, table_basepoint_mult_s);
}
}
#[cfg(all(test, feature = "bench"))]
@ -431,8 +414,8 @@ mod bench {
#[bench]
fn decompression(b: &mut Bencher) {
let mut rng = OsRng::new().unwrap();
let s = Scalar::random(&mut rng);
let P = DecafPoint::basepoint_mult(&s);
let B = &constants::DECAF_ED25519_BASEPOINT_TABLE;
let P = B * &Scalar::random(&mut rng);
let P_compressed = P.compress();
b.iter(|| P_compressed.decompress().unwrap());
}
@ -440,8 +423,8 @@ mod bench {
#[bench]
fn compression(b: &mut Bencher) {
let mut rng = OsRng::new().unwrap();
let s = Scalar::random(&mut rng);
let P = DecafPoint::basepoint_mult(&s);
let B = &constants::DECAF_ED25519_BASEPOINT_TABLE;
let P = B * &Scalar::random(&mut rng);
b.iter(|| P.compress());
}
}

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@ -11,10 +11,10 @@
#![cfg_attr(not(feature = "std"), no_std)]
#![cfg_attr(not(feature = "std"), feature(collections))]
#![cfg_attr(feature = "nightly", feature(box_syntax))]
#![cfg_attr(feature = "nightly", feature(i128_type))]
#![allow(unused_features)]
#![cfg_attr(feature = "bench", feature(test))]
#![allow(unused_features)]
#![deny(missing_docs)] // refuse to compile if documentation is missing
//! # curve25519-dalek

View file

@ -261,6 +261,15 @@ impl Scalar {
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ])
}
/// Construct a scalar from the given `u64`.
pub fn from_u64(x: u64) -> Scalar {
let mut s = Scalar::zero();
for i in 0..8 {
s[i] = (x >> (i*8)) as u8;
}
s
}
/// Compute the multiplicative inverse of this scalar.
pub fn invert(&self) -> Scalar {
self.unpack().invert().pack()
@ -727,6 +736,20 @@ mod test {
}
}
#[test]
fn from_unsigned() {
let val = 0xdeadbeefdeadbeef;
let s = Scalar::from_u64(val);
assert_eq!(s[7], 0xde);
assert_eq!(s[6], 0xad);
assert_eq!(s[5], 0xbe);
assert_eq!(s[4], 0xef);
assert_eq!(s[3], 0xde);
assert_eq!(s[2], 0xad);
assert_eq!(s[1], 0xbe);
assert_eq!(s[0], 0xef);
}
#[test]
fn scalar_multiply_by_one() {
let one = Scalar::one();